Floyd's triangle
You are encouraged to solve this task according to the task description, using any language you may know.
Floyd's triangle lists the natural numbers in a right triangle aligned to the left where
- the first row is 1 (unity)
- successive rows start towards the left with the next number followed by successive naturals listing one more number than the line above.
The first few lines of a Floyd triangle looks like this:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- Task
-
- Write a program to generate and display here the first n lines of a Floyd triangle.
(Use n=5 and n=14 rows). - Ensure that when displayed in a mono-space font, the numbers line up in vertical columns as shown and that only one space separates numbers of the last row.
- Write a program to generate and display here the first n lines of a Floyd triangle.
11l
<lang 11l>F floyd(rowcount)
V rows = 1 L rows.len < rowcount V n = rows.last.last + 1 rows.append(Array(n .. n + rows.last.len)) R rows
F pfloyd(rows)
V colspace = rows.last.map(n -> String(n).len)
L(row) rows
print(zip(colspace, row).map2((space, n) -> String(n).rjust(space)).join(‘ ’))
pfloyd(floyd(5)) pfloyd(floyd(14))</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
360 Assembly
A very concise coding, an illustration of CISC power of the S/360 operation codes. Also an example of the use of EDMK and EX instructions. For macro usage see Structured Macros . <lang 360asm>* Floyd's triangle 21/06/2018 FLOYDTRI PROLOG
L R5,NN nn
BCTR R5,0 -1
M R4,NN nn*(nn-1)
SRA R5,1 /2
A R5,NN m=(nn*(nn-1))/2+nn; max_value
CVD R5,XDEC binary to packed decimal (PL8)
EDMK ZN,XDEC+4 packed dec (PL4) to char (CL8)
S R1,=A(ZN) r1=number of spaces
L R9,=A(L'ZN+1) length(zn08)+1
SR R9,R1 s=length(m)+1
SR R8,R8 k=0
LA R6,1 i=1
DO WHILE=(C,R6,LE,NN) do i=1 to nn
LA R10,PG pgi=0
LA R7,1 j=1
DO WHILE=(CR,R7,LE,R6) do j=1 to i
LA R8,1(R8) k=k+1
XDECO R8,XDEC k
LA R11,XDEC+12 +12
SR R11,R9 -s
LR R2,R9 s
BCTR R2,0 -1
EX R2,MVCX mvc @PG+pgi,@XDEC+12-s,LEN=s
AR R10,R9 pgi+=s
LA R7,1(R7) j++
ENDDO , enddo j
XPRNT PG,L'PG print buffer
LA R6,1(R6) i++
ENDDO , enddo i
EPILOG
MVCX MVC 0(0,R10),0(R11) mvc PG,XDEC NN DC F'14' number of rows PG DC CL80' ' buffer XDEC DS CL12 temp ZN DC X'4020202020202020' mask CL8 7num
YREGS
END FLOYDTRI</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Action!
<lang Action!>PROC Triangle(BYTE level)
INT v,i BYTE x,y BYTE ARRAY widths(20) CHAR ARRAY tmp(5)
v=1 FOR y=1 TO level-1 DO v==+y OD FOR x=0 TO level-1 DO StrI(v+x,tmp) widths(x)=tmp(0) OD
v=1
FOR y=1 TO level
DO
FOR x=0 TO y-1
DO
StrI(v,tmp)
FOR i=tmp(0) TO widths(x)-1
DO
Put(32)
OD
Print(tmp)
IF x<y-1 THEN
Put(32)
ELSE
PutE()
FI
v==+1
OD
OD
RETURN
PROC Main()
BYTE LMARGIN=$52,oldLMARGIN
oldLMARGIN=LMARGIN LMARGIN=0 ;remove left margin on the screen
Put(125) PutE() ;clear the screen Triangle(5) PutE() Triangle(13)
LMARGIN=oldLMARGIN ;restore left margin on the screen
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
Ada
<lang Ada> with Ada.Text_IO, Ada.Integer_Text_IO, Ada.Command_Line;
procedure Floyd_Triangle is
rows : constant Natural := Natural'Value(Ada.Command_Line.Argument(1));
begin
for r in 1..rows loop
for i in 1..r loop
Ada.Integer_Text_IO.put (r*(r-1)/2+i, Width=> Natural'Image(rows*(rows-1)/2+i)'Length);
end loop;
Ada.Text_IO.New_Line;
end loop;
end Floyd_Triangle; </lang>
- Output:
> ./floyd_triangle_triangle 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 > ./floyd_triangle 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
ALGOL 68
<lang algol68># procedure to print a Floyd's Triangle with n lines # PROC floyds triangle = ( INT n )VOID: BEGIN
# calculate the number of the highest number that will be printed # # ( the sum of the integers 1, 2, ... n ) # INT max number = ( n * ( n + 1 ) ) OVER 2;
# determine the widths required to print the numbers of the final row #
[ n ]INT widths;
INT number := max number + 1;
FOR col FROM n BY -1 TO 1 DO
widths[ col ] := - ( UPB whole( number -:= 1, 0 ) + 1 )
OD;
# print the triangle #
INT element := 0;
FOR row TO n DO
FOR col TO row DO
print( ( whole( element +:= 1, widths[ col ] ) ) )
OD;
print( ( newline ) )
OD
END; # floyds triangle #
main: (
floyds triangle( 5 ); print( ( newline ) ); floyds triangle( 14 )
)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
ALGOL W
<lang algolw>begin
% prints a Floyd's Triangle with n lines %
procedure floydsTriangle ( integer value n ) ;
begin
% the triangle should be left aligned with the individual numbers %
% right-aligned with only one space before the number in the final %
% row %
% calculate the highest number that will be printed %
% ( the sum of the integeregers 1, 2, ... n ) %
integer array widths( 1 :: n );
integer maxNumber, number;
maxNumber := ( n * ( n + 1 ) ) div 2;
% determine the widths required to print the numbers of the final row %
number := maxNumber;
for col := n step -1 until 1 do begin
integer v, w;
w := 0;
v := number;
number := number - 1;
while v > 0 do begin
w := w + 1;
v := v div 10
end while_v_gt_0 ;
widths( col ) := w
end for_col;
% print the triangle %
number := 0;
for row := 1 until n do begin
for col := 1 until row do begin
number := number + 1;
writeon( i_w := widths( col ), s_w := 0, " ", number )
end for_col ;
write()
end for_row
end; % floyds triangle %
floydsTriangle( 5 ); write(); floydsTriangle( 14 )
end.</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
AppleScript
Functional
(mapAccumL versions)
<lang AppleScript>-- FLOYDs TRIANGLE -----------------------------------------------------------
-- floyd :: Int -> Int on floyd(n)
script floydRow
on |λ|(start, row)
{start + row + 1, enumFromTo(start, start + row)}
end |λ|
end script
snd(mapAccumL(floydRow, 1, enumFromTo(0, n - 1)))
end floyd
-- showFloyd :: Int -> String on showFloyd(xss)
set ws to map(compose({my succ, my |length|, my show}), |last|(xss))
script aligned
on |λ|(xs)
script pad
on |λ|(w, x)
justifyRight(w, space, show(x))
end |λ|
end script
concat(zipWith(pad, ws, xs))
end |λ|
end script
unlines(map(aligned, xss))
end showFloyd
-- TEST ----------------------------------------------------------------------
on run
script test
on |λ|(n)
showFloyd(floyd(n)) & linefeed
end |λ|
end script
unlines(map(test, {5, 14}))
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- compose :: [(a -> a)] -> (a -> a) on compose(fs)
script
on |λ|(x)
script
on |λ|(f, a)
mReturn(f)'s |λ|(a)
end |λ|
end script
foldr(result, x, fs)
end |λ|
end script
end compose
-- concat :: a -> [a] | [String] -> String on concat(xs)
if length of xs > 0 and class of (item 1 of xs) is string then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to length of xs
set acc to acc & item i of xs
end repeat
acc
end concat
-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- foldr :: (b -> a -> a) -> a -> [b] -> a on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(item i of xs, v, i, xs)
end repeat
return v
end tell
end foldr
-- intercalate :: Text -> [Text] -> Text on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate
-- justifyRight :: Int -> Char -> Text -> Text on justifyRight(n, cFiller, strText)
if n > length of strText then
text -n thru -1 of ((replicate(n, cFiller) as text) & strText)
else
strText
end if
end justifyRight
-- last :: [a] -> a on |last|(xs)
if length of xs > 0 then
item -1 of xs
else
missing value
end if
end |last|
-- length :: [a] -> Int on |length|(xs)
length of xs
end |length|
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- 'The mapAccumL function behaves like a combination of map and foldl; -- it applies a function to each element of a list, passing an -- accumulating parameter from left to right, and returning a final -- value of this accumulator together with the new list.' (see Hoogle)
-- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) on mapAccumL(f, acc, xs)
script
on |λ|(a, x)
tell mReturn(f) to set pair to |λ|(item 1 of a, x)
[item 1 of pair, (item 2 of a) & {item 2 of pair}]
end |λ|
end script
foldl(result, [acc, []], xs)
end mapAccumL
-- min :: Ord a => a -> a -> a on min(x, y)
if y < x then
y
else
x
end if
end min
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- Egyptian multiplication - progressively doubling a list, appending -- stages of doubling to an accumulator where needed for binary -- assembly of a target length
-- replicate :: Int -> a -> [a] on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}
repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- snd :: (a, b) -> b on snd(xs)
if class of xs is list and length of xs > 1 then
item 2 of xs
else
missing value
end if
end snd
-- show :: a -> String on show(e)
set c to class of e
if c = list then
script serialized
on |λ|(v)
show(v)
end |λ|
end script
"{" & intercalate(", ", map(serialized, e)) & "}"
else if c = record then
script showField
on |λ|(kv)
set {k, v} to kv
k & ":" & show(v)
end |λ|
end script
"{" & intercalate(", ", ¬
map(showField, zip(allKeys(e), allValues(e)))) & "}"
else if c = date then
("date \"" & e as text) & "\""
else if c = text then
"\"" & e & "\""
else
try
e as text
on error
("«" & c as text) & "»"
end try
end if
end show
-- succ :: Int -> Int on succ(x)
x + 1
end succ
-- unlines :: [String] -> String on unlines(xs)
intercalate(linefeed, xs)
end unlines
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
set lst to {}
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, item i of ys)
end repeat
return lst
end tell
end zipWith</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Or, defining only the relationship between successive terms:
<lang applescript>-- floyd :: [Int] -> [Int] on floyd(xs)
set n to succ(length of xs)
if n < 2 then
{1}
else
enumFromTo(succ(n * (pred(n)) div 2), n * (succ(n)) div 2)
end if
end floyd
-- floydN :: Int -> Int
on floydN(n)
take(n, iterate(floyd, {1}))
end floydN
-- showFloyd :: Int -> String
on showFloyd(xs)
script
on |λ|(ns)
script
on |λ|(n)
justifyRight(4, space, n as string)
end |λ|
end script
concat(map(result, ns))
end |λ|
end script
unlines(map(result, xs))
end showFloyd
-- TEST -------------------------------------------------------------
on run
showFloyd(floydN(5))
end run
-- GENERIC ABSTRACTIONS ---------------------------------------
-- concat :: a -> [a] -- concat :: [String] -> String on concat(xs)
set lng to length of xs
if 0 < lng and string is class of (item 1 of xs) then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to lng
set acc to acc & item i of xs
end repeat
acc
end concat
-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
return lst
else
return {}
end if
end enumFromTo
-- iterate :: (a -> a) -> a -> Gen [a] on iterate(f, x)
script
property v : missing value
property g : mReturn(f)'s |λ|
on |λ|()
if missing value is v then
set v to x
else
set v to g(v)
end if
return v
end |λ|
end script
end iterate
-- justifyRight :: Int -> Char -> String -> String
on justifyRight(n, cFiller, strText)
if n > length of strText then
text -n thru -1 of ((replicate(n, cFiller) as text) & strText)
else
strText
end if
end justifyRight
-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- min :: Ord a => a -> a -> a on min(x, y)
if y < x then
y
else
x
end if
end min
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: First-class m => (a -> b) -> m (a -> b) on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- pred :: Int -> Int on pred(x)
(-1) + x
end pred
-- Egyptian multiplication - progressively doubling a list, appending -- stages of doubling to an accumulator where needed for binary -- assembly of a target length -- replicate :: Int -> a -> [a] on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}
repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- succ :: Int -> Int on succ(x)
1 + x
end succ
-- take :: Int -> [a] -> [a] -- take :: Int -> String -> String on take(n, xs)
set c to class of xs
if list is c then
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
else if string is c then
if 0 < n then
text 1 thru min(n, length of xs) of xs
else
""
end if
else if script is c then
set ys to {}
repeat with i from 1 to n
set v to xs's |λ|()
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
else
missing value
end if
end take
-- unlines :: [String] -> String on unlines(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Or as a partially populated matrix:
<lang applescript>--------------------- FLOYD'S TRIANGLE -------------------
-- floyd :: Int -> Maybe Int on floyd(n)
script go
on |λ|(y, x)
if x ≤ y then
x + (y * (y - 1)) div 2
else
missing value
end if
end |λ|
end script
matrix(n, n, go)
end floyd
TEST -------------------------
on run
-- Floyd triangles of dimensions 5 and 14
unlines(map(compose(showMatrix, floyd), {5, 14}))
end run
GENERIC ------------------------
-- compose (<<<) :: (b -> c) -> (a -> b) -> a -> c on compose(f, g)
script
property mf : mReturn(f)
property mg : mReturn(g)
on |λ|(x)
mf's |λ|(mg's |λ|(x))
end |λ|
end script
end compose
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set xs to {}
repeat with i from m to n
set end of xs to i
end repeat
xs
else
{}
end if
end enumFromTo
-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- justifyRight :: Int -> Char -> String -> String
on justifyRight(n, cFiller)
script
on |λ|(s)
if n > length of s then
text -n thru -1 of ((replicate(n, cFiller) as text) & s)
else
s
end if
end |λ|
end script
end justifyRight
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f
-- to each element of xs.
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- matrix :: Int -> Int -> ((Int, Int) -> a) -> a
on matrix(nRows, nCols, f)
-- A matrix of a given number of columns and rows,
-- in which each value is a given function of its
-- (zero-based) column and row indices.
script go
property g : mReturn(f)'s |λ|
on |λ|(iRow)
set xs to {}
repeat with iCol from 1 to nCols
set end of xs to g(iRow, iCol)
end repeat
xs
end |λ|
end script
map(go, enumFromTo(1, nRows))
end matrix
-- max :: Ord a => a -> a -> a
on max(x, y)
if x > y then
x
else
y
end if
end max
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> String -> String
on replicate(n, s)
-- Egyptian multiplication - progressively doubling a list,
-- appending stages of doubling to an accumulator where needed
-- for binary assembly of a target length
script p
on |λ|({n})
n ≤ 1
end |λ|
end script
script f
on |λ|({n, dbl, out})
if (n mod 2) > 0 then
set d to out & dbl
else
set d to out
end if
{n div 2, dbl & dbl, d}
end |λ|
end script
set xs to |until|(p, f, {n, s, ""})
item 2 of xs & item 3 of xs
end replicate
-- showMatrix :: Maybe a -> String
on showMatrix(rows)
-- String representation of rows
-- as a matrix.
script showRow
on |λ|(a, row)
set {maxWidth, prevRows} to a
script showCell
on |λ|(acc, cell)
set {w, xs} to acc
if missing value is cell then
{w, xs & ""}
else
set s to cell as string
{max(w, length of s), xs & s}
end if
end |λ|
end script
set {rowMax, cells} to foldl(showCell, {0, {}}, row)
{max(maxWidth, rowMax), prevRows & {cells}}
end |λ|
end script
set {w, stringRows} to foldl(showRow, {0, {}}, rows)
script go
on |λ|(row)
unwords(map(justifyRight(w, space), row))
end |λ|
end script
unlines(map(go, stringRows)) & linefeed
end showMatrix
-- str :: a -> String
on str(x)
x as string
end str
-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set s to xs as text
set my text item delimiters to dlm
s
end unlines
-- until :: (a -> Bool) -> (a -> a) -> a -> a
on |until|(p, f, x)
set v to x
set mp to mReturn(p)
set mf to mReturn(f)
repeat until mp's |λ|(v)
set v to mf's |λ|(v)
end repeat
v
end |until|
-- unwords :: [String] -> String
on unwords(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, space}
set s to xs as text
set my text item delimiters to dlm
return s
end unwords</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Straightforward
<lang applescript>on FloydsTriangle(n)
set triangle to {}
set i to 0
repeat with w from 1 to n
set row to {}
repeat with i from (i + 1) to (i + w)
set end of row to i
end repeat
set end of triangle to row
end repeat
return triangle
end FloydsTriangle
-- Task code: on matrixToText(matrix, w)
script o
property matrix : missing value
property row : missing value
end script
set o's matrix to matrix
set padding to " "
repeat with r from 1 to (count o's matrix)
set o's row to o's matrix's item r
repeat with i from 1 to (count o's row)
set o's row's item i to text -w thru end of (padding & o's row's item i)
end repeat
set o's matrix's item r to join(o's row, "")
end repeat
return join(o's matrix, linefeed)
end matrixToText
on join(lst, delim)
set astid to AppleScript's text item delimiters set AppleScript's text item delimiters to delim set txt to lst as text set AppleScript's text item delimiters to astid return txt
end join
local triangle5, text5, triangle14, text14 set triangle5 to FloydsTriangle(5) set text5 to matrixToText(triangle5, (count (end of end of triangle5 as text)) + 1) set triangle14 to FloydsTriangle(14) set text14 to matrixToText(triangle14, (count (end of end of triangle14 as text)) + 1) return linefeed & text5 & (linefeed & linefeed & text14 & linefeed)</lang>
- Output:
<lang applescript>"
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
"</lang>
Arturo
<lang rebol>floyd: function [rowcount][
result: new 1 while [rowcount > size result][ n: inc last last result row: new [] loop n..n+size last result 'k -> 'row ++ @[k] 'result ++ @[row] ] return result
]
loop [5 14] 'j [
f: floyd j loop f 'row -> print map row 'r [pad to :string r 3] print ""
]</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
AutoHotkey
<lang AutoHotkey>Floyds_triangle(row){ i = 0 loop %row% { n := A_Index loop, %n% { m := n, j := i, i++ while (m<row) j += m , m++ res .= spaces(StrLen(j+1)-StrLen(i) +(A_Index=1?0:1)) i } if (A_Index < row) res .= "`r`n" } return res } Spaces(no){ loop, % no res.=" " return % res }</lang> Examples:<lang AutoHotkey>MsgBox % Floyds_triangle(14)</lang>
Outputs:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
AWK
<lang AWK>#!/bin/awk -f
BEGIN { if (rows !~ /^[0-9]+$/ || rows < 0) { print "invalid rows or missing from command line" print "syntax: awk -v rows=14 -f floyds_triangle.awk" exit 1 }
for (row=cols=1; row<=rows; row++ cols++) { width[row] = length(row + (rows * (rows-1))/2) for (col=1; col<=cols; col++) printf("%*d%c", width[col], ++n, row == col ? "\n" : " ") } } </lang>
output from: awk -f floyds_triangle.awk -v rows=5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
output from: awk -f floyds_triangle.awk -v rows=14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
BASIC
Applesoft BASIC
Line 150,160 creates a vector of the length of all entries is the last row. These values are used in line 210,220 to put the cursor at the correct horizontal position.
<lang basic>
100 : 110 REM FLOYD'S TRIANGLE 120 : 130 DEF FN Q(A) = INT ( LOG (A) / LOG (10)) + 1 140 N = 14 150 DIM P(N): P(0) = - 1: FOR J = 1 TO N: I = (N * N - N) / 2 + J 160 P(J) = P(J - 1) + FN Q(I) + 1: NEXT J 200 FOR R = 1 TO N: FOR C = 1 TO R 210 NR = NR + 1:COL = P(C) - ( FN Q(NR) - 1) 220 HTAB COL: PRINT NR;: NEXT C 230 PRINT : NEXT R
</lang>
- Output:
]RUN 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
]RUN 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
BASIC256
<lang BASIC256> function trianglevalue(col, row)
return (row-1)*row\2 + col
end function
subroutine printtriangle(numrows)
for row = 1 to numrows
for col = 1 to row-1
colwidth = length(""+trianglevalue(col, numrows))
print right(" "*colwidth+trianglevalue(col, row), colwidth);" ";
next col
colwidth = length(""+trianglevalue(col, numrows))
print right(" "*colwidth+trianglevalue(col, row), colwidth)
next row
end subroutine
call printtriangle(5) print call printtriangle(14) </lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
BBC BASIC
<lang bbcbasic> n = 14
num = 1
last = (n^2 - n + 2) DIV 2
FOR row = 1 TO n
col = last
FOR num = num TO num + row - 1
@% = LEN(STR$(col)) + 1 : REM set column width
PRINT num ;
col += 1
NEXT
PRINT
NEXT row</lang>
Output for n = 5:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Output for n = 14:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Commodore BASIC
<lang basic>100 print chr$(14);chr$(147);"Floyd's triangle" 110 print "How many rows? "; 120 open 1,0:input#1,ro$:close 1:print 130 ro=val(ro$):if ro<1 then 110 140 li=ro*(ro+1)/2 150 dim w(ro-1) 160 n=li-ro+1 170 for i=0 to ro-1:w(i)=len(str$(n)):n=n+1:next i 180 n=1 190 for i=1 to ro 200 : for j=0 to i-1 210 : n$=mid$(str$(n),2) 220 : if len(n$)<w(j) then for k=1 to w(j)-len(n$):print" ";:next k 230 : print n$; 240 : n=n+1 250 : next j 260 : print 270 next i 280 end</lang>
- Output:
Floyd's triangle How many rows? 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 How many rows? 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
IS-BASIC
<lang IS-BASIC>100 PROGRAM "FloydT.bas" 110 LET N=14:LET J=1 120 TEXT 80 130 FOR I=1 TO N 140 FOR J=J TO J+I-1 150 PRINT USING " ###":J; 160 NEXT 170 PRINT 180 NEXT</lang>
MasmBasic
Builds with Masm, UAsm or AsmC plus the MasmBasic library <lang MasmBasic>include \masm32\MasmBasic\MasmBasic.inc
SetGlobals rows, columns, ct, maxrows=4 Init .Repeat
For_ rows=0 To maxrows For_ columns=0 To rows inc ct Print Str$("%__i", ct) .if columns>6 Print " " .endif Next Print Next Print Clr ct add maxrows, 9 ; 4+9=13
.Until maxrows>13 Inkey
EndOfCode</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
QBasic
<lang QBasic>SUB FloydTriangle (fila)
DIM numColum(fila)
FOR colum = 1 TO fila
numColum(colum) = LEN(STR$(colum + fila * (fila - 1) / 2))
NEXT colum
PRINT "output for "; STR$(fila): PRINT
thisNum = 1
FOR r = 1 TO fila
FOR colum = 1 TO r
PRINT RIGHT$(" " + STR$(thisNum), numColum(colum)); " ";
thisNum = thisNum + 1
NEXT colum
PRINT
NEXT
END SUB
FloydTriangle (5) PRINT FloydTriangle (14)</lang>
Yabasic
<lang freebasic>sub FloydTriangle (fila)
dim numColum(fila)
for colum = 1 to fila
numColum(colum) = len(str$(colum + fila * (fila - 1) / 2))
next colum
print "output for ", str$(fila), "\n"
thisNum = 1
for r = 1 to fila
for colum = 1 to r
print right$(" " + str$(thisNum), numColum(colum)), " ";
thisNum = thisNum + 1
next colum
print
next
end sub
FloydTriangle (5) print FloydTriangle (14)</lang>
Batch File
<lang dos>:: Floyd's triangle Task from Rosetta Code
- Batch File Implementation
@echo off rem main thing setlocal enabledelayedexpansion call :floydtriangle 5 echo( call :floydtriangle 14 exit /b 0
- floydtriangle
set "fila=%1" for /l %%c in (1,1,%fila%) do (
set /a "lastRowNum=%%c+fila*(fila-1)/2" rem count number of digits of whole number trick rem source: https://stackoverflow.com/a/45472269 set /a "Log=1!lastRowNum:~1!-!lastRowNum:~1!-0" set /a "numColum[%%c]=!Log:0=+1!"
) echo(Output for %fila% set "thisNum=1" for /l %%r in (1,1,%fila%) do (
set "printLine="
for /l %%c in (1,1,%%r) do (
rem count number of digits of whole number trick
set /a "Log=1!thisNum:~1!-!thisNum:~1!-0"
set /a "thisNumColum=!Log:0=+1!"
rem handle spacing
set "space= "
set /a "extra=!numColum[%%c]!-!thisNumColum!"
for /l %%s in (1,1,!extra!) do set "space=!space! "
rem append current number to printLine
set "printLine=!printLine!!space!!thisNum!"
set /a "thisNum=!thisNum!+1"
)
echo(!printLine!
) goto :EOF</lang>
- Output:
Output for 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Output for 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
BCPL
<lang bcpl>get "libhdr"
let width(n) = n<10 -> 1, 1 + width(n/10)
let floyd(rows) be $( let maxno = rows * (rows+1)/2
let num = 1
for r = 1 to rows
$( for c = 1 to r
$( writed(num, 1 + width(maxno-rows+c))
num := num + 1
$)
wrch('*N')
$)
$)
let start() be $( floyd(5)
wrch('*N')
floyd(14)
$)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Befunge
<lang Befunge>0" :seniL">:#,_&>:!#@_55+,:00p::1+*2/1v vv+1:\-1p01g5-\g00<v`*9"o"\+`"c"\`9:::_ $>>\:::9`\"c"`+\9v:>>+00g1-:00p5p1-00g^ <v\*84-\g01+`*"o"<^<<p00:+1\+1/2*+1:::\ ^>:#\1#,-#:\_$$.\:#^_$$>>1+\1-55+,:!#@_</lang>
- Output:
Lines: 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Lines: 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Bracmat
<lang bracmat> ( ( floyd
= lowerLeftCorner lastInColumn lastInRow row i W w
. put$(str$("Floyd " !arg ":\n"))
& !arg*(!arg+-1)*1/2+1
: ?lowerLeftCorner
: ?lastInColumn
& 1:?lastInRow:?row:?i
& whl
' ( !row:~>!arg
& @(!lastInColumn:? [?W)
& @(!i:? [?w)
& whl'(!w+1:~>!W:?w&put$" ")
& put$!i
& ( !i:<!lastInRow
& put$" "
& 1+!lastInColumn:?lastInColumn
| put$\n
& (1+!row:?row)+!lastInRow:?lastInRow
& !lowerLeftCorner:?lastInColumn
)
& 1+!i:?i
)
)
& floyd$5
& floyd$14
);</lang>
Output:
Floyd 5: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Floyd 14: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
C
<lang c>#include <stdio.h>
void t(int n) { int i, j, c, len;
i = n * (n - 1) / 2; for (len = c = 1; c < i; c *= 10, len++); c -= i; // c is the col where width changes
- define SPEED_MATTERS 0
- if SPEED_MATTERS // in case we really, really wanted to print huge triangles often
char tmp[32], s[4096], *p;
sprintf(tmp, "%*d", len, 0);
inline void inc_numstr(void) { int k = len;
redo: if (!k--) return;
if (tmp[k] == '9') { tmp[k] = '0'; goto redo; }
if (++tmp[k] == '!') tmp[k] = '1'; }
for (p = s, i = 1; i <= n; i++) { for (j = 1; j <= i; j++) { inc_numstr(); __builtin_memcpy(p, tmp + 1 - (j >= c), len - (j < c)); p += len - (j < c);
*(p++) = (i - j)? ' ' : '\n';
if (p - s + len >= 4096) { fwrite(s, 1, p - s, stdout); p = s; } } }
fwrite(s, 1, p - s, stdout);
- else // NO_IT_DOESN'T
int num; for (num = i = 1; i <= n; i++) for (j = 1; j <= i; j++) printf("%*d%c", len - (j < c), num++, i - j ? ' ':'\n');
- endif
}
int main(void) { t(5), t(14);
// maybe not // t(10000); return 0; }</lang> Output identical to D's.
C#
<lang csharp>using System; using System.Text;
public class FloydsTriangle {
internal static void Main(string[] args)
{
int count;
if (args.Length >= 1 && int.TryParse(args[0], out count) && count > 0)
{
Console.WriteLine(MakeTriangle(count));
}
else
{
Console.WriteLine(MakeTriangle(5));
Console.WriteLine();
Console.WriteLine(MakeTriangle(14));
}
}
public static string MakeTriangle(int rows)
{
int maxValue = (rows * (rows + 1)) / 2;
int digit = 0;
StringBuilder output = new StringBuilder();
for (int row = 1; row <= rows; row++)
{
for (int column = 0; column < row; column++)
{
int colMaxDigit = (maxValue - rows) + column + 1;
if (column > 0)
{
output.Append(' ');
}
digit++;
output.Append(digit.ToString().PadLeft(colMaxDigit.ToString().Length));
}
output.AppendLine();
}
return output.ToString(); }
}</lang>
C++
<lang cpp>
- include <windows.h>
- include <sstream>
- include <iostream>
//-------------------------------------------------------------------------------------------------- using namespace std;
//-------------------------------------------------------------------------------------------------- class floyds_tri { public:
floyds_tri() { lastLineLen = 0; }
~floyds_tri() { killArray(); }
void create( int rows )
{
_rows = rows; calculateLastLineLen(); display();
}
private:
void killArray()
{
if( lastLineLen ) delete [] lastLineLen;
}
void calculateLastLineLen()
{
killArray(); lastLineLen = new BYTE[_rows];
int s = 1 + ( _rows * ( _rows - 1 ) ) / 2;
for( int x = s, ix = 0; x < s + _rows; x++, ix++ ) { ostringstream cvr; cvr << x; lastLineLen[ix] = static_cast<BYTE>( cvr.str().size() ); }
}
void display()
{
cout << endl << "Floyd\'s Triangle - " << _rows << " rows" << endl << "===============================================" << endl; int number = 1; for( int r = 0; r < _rows; r++ ) { for( int c = 0; c <= r; c++ ) { ostringstream cvr; cvr << number++; string str = cvr.str(); while( str.length() < lastLineLen[c] ) str = " " + str; cout << str << " "; } cout << endl; }
}
int _rows; BYTE* lastLineLen;
}; //-------------------------------------------------------------------------------------------------- int main( int argc, char* argv[] ) {
floyds_tri t;
int s;
while( true )
{
cout << "Enter the size of the triangle ( 0 to QUIT ): "; cin >> s; if( !s ) return 0; if( s > 0 ) t.create( s );
cout << endl << endl; system( "pause" );
}
return 0;
} //--------------------------------------------------------------------------------------------------</lang>
- Output:
Floyd's Triangle - 5 rows =============================================== 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Floyd's Triangle - 14 rows =============================================== 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Clojure
I didn't translete this, it's from my own creation. <lang clojure> (defn TriangleList [n]
(let [l (map inc (range))]
(loop [l l x 1 nl []]
(if (= n (count nl))
nl
(recur (drop x l) (inc x) (conj nl (take x l)))))))
(defn TrianglePrint [n]
(let [t (TriangleList n)
m (count (str (last (last t))))
f (map #(map str %) t)
l (map #(map (fn [x] (if (> m (count x))
(str (apply str (take (- m (count x))
(repeat " "))) x)
x)) %) f)
e (map #(map (fn [x] (str " " x)) %) l)]
(map #(println (apply str %)) e)))
</lang> By Average-user.
- Output:
(TrianglePrint 5) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (TrianglePrint 14) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
CLU
<lang clu>floyd = cluster is triangle
rep = null
width = proc (n: int) returns (int)
w: int := 1
while n >= 10 do
w := w + 1
n := n / 10
end
return (w)
end width
triangle = proc (rows: int) returns (string)
ss: stream := stream$create_output()
maxno: int := rows * (rows+1)/2
num: int := 1
for row: int in int$from_to(1, rows) do
for col: int in int$from_to(1, row) do
stream$putright(ss, int$unparse(num), 1 + width(maxno-rows+col))
num := num + 1
end
stream$putl(ss, "")
end
return (stream$get_contents(ss))
end triangle
end floyd
start_up = proc ()
po: stream := stream$primary_output() stream$putl(po, floyd$triangle(5)) stream$putl(po, floyd$triangle(14))
end start_up</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
COBOL
<lang cobol> IDENTIFICATION DIVISION.
PROGRAM-ID. FLOYD-TRIANGLE.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 VARIABLES COMP.
02 NUM-LINES PIC 99.
02 CUR-LINE PIC 99.
02 CUR-COL PIC 99.
02 CUR-NUM PIC 999.
02 ZERO-SKIP PIC 9.
02 LINE-PTR PIC 99.
02 MAX-NUM PIC 999.
01 OUTPUT-FORMAT.
02 OUT-LINE PIC X(72).
02 ONE-DIGIT PIC B9.
02 TWO-DIGITS PIC BZ9.
02 THREE-DIGITS PIC BZZ9.
02 MAX-COL-NUM PIC 999.
PROCEDURE DIVISION.
BEGIN.
MOVE 5 TO NUM-LINES. PERFORM FLOYD.
DISPLAY ' '.
MOVE 14 TO NUM-LINES. PERFORM FLOYD.
STOP RUN.
FLOYD.
MOVE 1 TO CUR-NUM.
COMPUTE MAX-NUM = NUM-LINES * (NUM-LINES + 1) / 2.
PERFORM FLOYD-LINE
VARYING CUR-LINE FROM 1 BY 1
UNTIL CUR-LINE IS GREATER THAN NUM-LINES.
FLOYD-LINE.
MOVE ' ' TO OUT-LINE.
MOVE 1 TO LINE-PTR.
PERFORM FLOYD-NUM
VARYING CUR-COL FROM 1 BY 1
UNTIL CUR-COL IS GREATER THAN CUR-LINE.
DISPLAY OUT-LINE.
FLOYD-NUM.
COMPUTE MAX-COL-NUM = MAX-NUM - NUM-LINES + CUR-COL.
MOVE 0 TO ZERO-SKIP.
INSPECT MAX-COL-NUM TALLYING ZERO-SKIP FOR LEADING '0'.
IF ZERO-SKIP IS EQUAL TO ZERO
PERFORM FLOYD-THREE-DIGITS
ELSE IF ZERO-SKIP IS EQUAL TO 1
PERFORM FLOYD-TWO-DIGITS
ELSE IF ZERO-SKIP IS EQUAL TO 2
PERFORM FLOYD-ONE-DIGIT.
ADD 1 TO CUR-NUM.
FLOYD-ONE-DIGIT.
MOVE CUR-NUM TO ONE-DIGIT.
STRING ONE-DIGIT DELIMITED BY SIZE INTO OUT-LINE
WITH POINTER LINE-PTR.
FLOYD-TWO-DIGITS.
MOVE CUR-NUM TO TWO-DIGITS.
STRING TWO-DIGITS DELIMITED BY SIZE INTO OUT-LINE
WITH POINTER LINE-PTR.
FLOYD-THREE-DIGITS.
MOVE CUR-NUM TO THREE-DIGITS.
STRING THREE-DIGITS DELIMITED BY SIZE INTO OUT-LINE
WITH POINTER LINE-PTR.</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
CoffeeScript
<lang coffeescript>triangle = (array) -> for n in array
console.log "#{n} rows:"
printMe = 1
printed = 0
row = 1
to_print = ""
while row <= n
cols = Math.ceil(Math.log10(n * (n - 1) / 2 + printed + 2.0))
p = ("" + printMe).length
while p++ <= cols
to_print += ' '
to_print += printMe + ' '
if ++printed == row
console.log to_print
to_print = ""
row++
printed = 0
printMe++
triangle [5, 14]</lang> Output as Kotlin.
Common Lisp
Version 1
<lang lisp>;;;using flet to define local functions and storing precalculated column widths in array
- verbose, but more readable and efficient than version 2
(defun floydtriangle (rows)
(let (column-widths)
(setf column-widths (make-array rows :initial-element nil))
(flet (
(lazycat (n)
(/ (+ (expt n 2) n 2) 2))
(width (v)
(+ 1 (floor (log v 10)))))
(dotimes (i rows)
(setf (aref column-widths i)(width (+ i (lazycat (- rows 1))))))
(dotimes (row rows)
(dotimes (col (+ 1 row))
(format t "~vd " (aref column-widths col)(+ col (lazycat row))))
(format t "~%")))))</lang>
Version 2 - any base
<lang lisp>;;; more concise than version 1 but less efficient for a large triangle
- optional "base" parameter will allow use of any base from 2 to 36
(defun floydtriangle (rows &optional (base 10))
(dotimes (row rows)
(dotimes (column (+ 1 row))
(format t "~v,vr " base (length (format nil "~vr" base (+ column (/ (+ (expt (- rows 1) 2) (- rows 1) 2) 2)))) (+ column (/ (+ (expt row 2) row 2) 2))))
(format t "~%")))</lang>
- Output:
(floydtriangle 5) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (floydtriangle 14) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 (floydtriangle 5 2) 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 (floydtriangle 14 36) 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 1G 1H 1I 1J 1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T 1U 1V 1W 1X 1Y 1Z 20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F 2G 2H 2I 2J 2K 2L 2M 2N 2O 2P 2Q 2R 2S 2T 2U 2V 2W 2X
Cowgol
<lang cowgol>include "cowgol.coh";
sub width(n: uint16): (w: uint8) is
w := 1;
while n >= 10 loop
n := n / 10;
w := w + 1;
end loop;
end sub;
sub print_fixed(n: uint16, w: uint8) is
w := w - width(n);
while w > 0 loop
print_char(' ');
w := w - 1;
end loop;
print_i16(n);
end sub;
sub floyd(rows: uint16) is
var maxno := rows * (rows+1)/2;
var num: uint16 := 1;
var row: uint16 := 1;
while row <= rows loop
var col: uint16 := 1;
while col <= row loop
print_fixed(num, 1 + width(maxno - rows + col));
num := num + 1;
col := col + 1;
end loop;
print_nl();
row := row + 1;
end loop;
end sub;
floyd(5); print_nl(); floyd(14);</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
D
<lang d>import std.stdio, std.conv;
void floydTriangle(in uint n) {
immutable lowerLeftCorner = n * (n - 1) / 2 + 1;
foreach (r; 0 .. n)
foreach (c; 0 .. r + 1)
writef("%*d%c",
text(lowerLeftCorner + c).length,
r * (r + 1) / 2 + c + 1,
c == r ? '\n' : ' ');
}
void main() {
floydTriangle(5); floydTriangle(14);
}</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Elixir
<lang elixir>defmodule Floyd do
def triangle(n) do
max = trunc(n * (n + 1) / 2)
widths = for m <- (max - n + 1)..max, do: (m |> Integer.to_string |> String.length) + 1
format = Enum.map(widths, fn wide -> "~#{wide}w" end) |> List.to_tuple
line(n, 0, 1, format)
end
def line(n, n, _, _), do: :ok
def line(n, i, count, format) do
Enum.each(0..i, fn j -> :io.fwrite(elem(format,j), [count+j]) end)
IO.puts ""
line(n, i+1, count+i+1, format)
end
end
Floyd.triangle(5) Floyd.triangle(14)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Erlang
<lang erlang> -module( floyds_triangle ).
-export( [integers/1, print/1, strings/1, task/0] ).
integers( N ) ->
lists:reverse( integers_reversed(N) ).
print( N ) ->
[io:fwrite("~s~n", [lists:flatten(X)]) || X <- strings(N)].
strings( N ) ->
Strings_reversed = [strings_from_integers(X) || X <- integers_reversed(N)],
Paddings = paddings( [lengths(X) || X <- Strings_reversed] ),
[formats(X, Y) || {X, Y} <- lists:zip(Paddings, lists:reverse(Strings_reversed))].
task() ->
print( 5 ),
print( 14 ).
formats( Paddings, Strings ) -> [lists:flatten(io_lib:format(" ~*s", [X, Y])) || {X, Y} <- lists:zip(Paddings, Strings)].
integers_reversed( N ) ->
{_End, Integers_reversed} = lists:foldl( fun integers_reversed/2, {1, []}, lists:seq(0, N - 1) ),
Integers_reversed.
integers_reversed( N, {Start, Acc} ) ->
End = Start + N,
{End + 1, [lists:seq(Start, End) | Acc]}.
lengths( Strings ) -> [string:len(X) || X <- Strings].
paddings( [Last_line | T] ) ->
{[], Paddings} = lists:foldl( fun paddings/2, {paddings_lose_last(Last_line), [Last_line]}, lists:seq(1, erlang:length(T)) ),
Paddings.
paddings( _N, {Current, Acc} ) -> {paddings_lose_last(Current), [Current | Acc]}.
paddings_lose_last( List ) -> [_H | T] = lists:reverse( List ), lists:reverse( T ).
strings_from_integers( Integers ) -> [erlang:integer_to_list(X) || X <- Integers]. </lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
ERRE
<lang ERRE> PROGRAM FLOYD
! ! for rosettacode.org !
BEGIN
N=14
NUM=1
LAST=(N^2-N+2) DIV 2
FOR ROW=1 TO N DO
FOR J=1 TO ROW DO
US$=STRING$(LEN(STR$(LAST-1+J))-1,"#")
WRITE(US$;NUM;)
PRINT(" ";)
NUM+=1
END FOR
PRINT
END FOR
END PROGRAM </lang> Example for n=14
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Excel
LAMBDA
We can define this declaratively in Excel by binding the name floydTriangle to the following lambda expression in the Name Manager of the Excel WorkBook:
(See LAMBDA: The ultimate Excel worksheet function)
<lang lisp>floydTriangle =LAMBDA(n,
IF(0 < n,
LET(
ixs, SEQUENCE(
n, n,
0, 1
),
x, MOD(ixs, n),
y, QUOTIENT(ixs, n),
IF(x > y,
"",
x + 1 + QUOTIENT(
y * (1 + y),
2
)
)
),
""
)
)</lang>
- Output:
The formula in cell B2, for example, defines an array which populates the whole range B2:F6
| fx | =floydTriangle(A2) | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | ||
| 1 | Row count | |||||||||||||||
| 2 | 5 | 1 | ||||||||||||||
| 3 | 2 | 3 | ||||||||||||||
| 4 | 4 | 5 | 6 | |||||||||||||
| 5 | 7 | 8 | 9 | 10 | ||||||||||||
| 6 | 11 | 12 | 13 | 14 | 15 | |||||||||||
| 7 | 14 | 1 | ||||||||||||||
| 8 | 2 | 3 | ||||||||||||||
| 9 | 4 | 5 | 6 | |||||||||||||
| 10 | 7 | 8 | 9 | 10 | ||||||||||||
| 11 | 11 | 12 | 13 | 14 | 15 | |||||||||||
| 12 | 16 | 17 | 18 | 19 | 20 | 21 | ||||||||||
| 13 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | |||||||||
| 14 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | ||||||||
| 15 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | |||||||
| 16 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | ||||||
| 17 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | |||||
| 18 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | ||||
| 19 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | |||
| 20 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 | 105 | ||
F#
<lang fsharp>open System
[<EntryPoint>] let main argv =
// columns and rows are 0-based, so the input has to be decremented:
let maxRow =
match UInt32.TryParse(argv.[0]) with
| (true, v) when v > 0u -> int (v - 1u)
| (_, _) -> failwith "not a positive integer"
let len (n: int) = int (Math.Floor(Math.Log10(float n)))
let col0 row = row * (row + 1) / 2 + 1
let col0maxRow = col0 maxRow
for row in [0 .. maxRow] do
for col in [0 .. row] do
let value = (col0 row) + col
let pad = String(' ', (len (col0maxRow + col) - len (value) + 1))
printf "%s%d" pad value
printfn ""
0</lang>
Output for 5 and 14 (via command line argument)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Factor
<lang factor>USING: io kernel math math.functions math.ranges prettyprint sequences ; IN: rosetta-code.floyds-triangle
- floyd. ( n -- )
[ dup 1 - * 2 / 1 + dup 1 ] [ [1,b] ] bi
[
[
2dup [ log10 1 + >integer ] bi@ -
[ " " write ] times dup pprint bl [ 1 + ] bi@
] times nl [ drop dup ] dip
] each nl 3drop ;
5 14 [ floyd. ] bi@</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Forth
<lang forth>: lastn ( rows -- n ) dup 1- * 2/ ;
- width ( n -- n ) s>f flog ftrunc f>s 2 + ;
- triangle ( rows -- )
dup lastn 0 rot ( last 0 rows )
0 do
over cr
i 1+ 0 do
1+ swap 1+ swap
2dup width u.r
loop
drop
loop
2drop ;
</lang>
Fortran
Please find compilation instructions on GNU/linux system at the beginning of the source. There, also, are the example output triangles produced by running the program. The environment variable setting and command line argument are vestigial. Ignore them. The code demonstrates writing to an in memory buffer, an old feature of FORTRAN. <lang FORTRAN> !-*- mode: compilation; default-directory: "/tmp/" -*- !Compilation started at Tue May 21 22:55:08 ! !a=./f && make $a && OMP_NUM_THREADS=2 $a 1223334444 !gfortran -std=f2008 -Wall -ffree-form -fall-intrinsics f.f08 -o f ! 1 ! 2 3 ! 4 5 6 ! 7 8 9 10 ! 11 12 13 14 15 ! ! ! 1 ! 2 3 ! 4 5 6 ! 7 8 9 10 ! 11 12 13 14 15 ! 16 17 18 19 20 21 ! 22 23 24 25 26 27 28 ! 29 30 31 32 33 34 35 36 ! 37 38 39 40 41 42 43 44 45 ! 46 47 48 49 50 51 52 53 54 55 ! 56 57 58 59 60 61 62 63 64 65 66 ! 67 68 69 70 71 72 73 74 75 76 77 78 ! 79 80 81 82 83 84 85 86 87 88 89 90 91 ! 92 93 94 95 96 97 98 99 100 101 102 103 104 105 ! ! ! !Compilation finished at Tue May 21 22:55:08
program p
integer, dimension(2) :: examples = [5, 14] integer :: i do i=1, size(examples) call floyd(examples(i)) write(6, '(/)') end do
contains
subroutine floyd(rows)
integer, intent(in) :: rows
integer :: n, i, j, k
integer, dimension(60) :: L
character(len=504) :: fmt
n = (rows*(rows+1))/2 ! Gauss's formula
do i=1,rows ! compute format of final row
L(i) = 2+int(log10(real(n-rows+i)))
end do
k = 0
do i=1,rows
do j=1,i
k = k+1
write(fmt,'(a2,i1,a1)')'(i',L(j),')'
write(6,fmt,advance='no') k
enddo
write(6,*)
end do
end subroutine floyd
end program p </lang>
FreeBASIC
<lang freebasic>' version 19-09-2015 ' compile with: fbc -s console
Sub pascal_triangle(n As UInteger)
Dim As UInteger a = 1, b, i, j, switch = n + 1 Dim As String frmt, frmt_1, frmt_2
' last number of the last line i = (n * (n + 1)) \ 2 frmt_2 = String(Len(Str(i)) + 1, "#") ' first number of the last line i = ((n - 1) * n) \ 2 + 1 frmt_1 = String(Len(Str(i)) + 1, "#")
' we have 2 different formats strings
' find the point where we have to make the switch
If frmt_1 <> frmt_2 Then
j = i + 1
While Len(Str(i)) = Len(Str(J))
j = j + 1
Wend
switch = j - i
End If
Print "output for "; Str(n) : Print
For i = 1 To n
frmt = frmt_1
b = (i * (i + 1)) \ 2
For j = a To b
' if we have the switching point change format string
If j - a = switch Then frmt = frmt_2
Print Using frmt; j;
Next j
Print
a = b + 1
Next i
Print
End Sub
' ------=< MAIN >=------
pascal_triangle(5)
pascal_triangle(14)
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</lang>
- Output:
output for 5 output for 14
1 1
2 3 2 3
4 5 6 4 5 6
7 8 9 10 7 8 9 10
11 12 13 14 15 11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Gambas
Click this link to run this code <lang gambas>Public Sub Main() Dim siCount, siNo, siCounter As Short Dim siLine As Short = 1 Dim siInput As Short[] = [5, 14]
For siCount = 0 To siInput.Max
Print "Floyd's triangle to " & siInput[siCount] & " lines"
Do
Inc siNo
Inc siCounter
Print Format(siNo, "####");
If siLine = siCounter Then
Print
Inc siLine
siCounter = 0
End If
If siLine - 1 = siInput[siCount] Then Break
Loop
siLine = 1
siCounter = 0
siNo = 0
Print
Next
End</lang> Output:
Floyd's triangle to 5 lines 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Floyd's triangle to 14 lines 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Go
<lang go>package main
import "fmt"
func main() {
floyd(5) floyd(14)
}
func floyd(n int) {
fmt.Printf("Floyd %d:\n", n)
lowerLeftCorner := n*(n-1)/2 + 1
lastInColumn := lowerLeftCorner
lastInRow := 1
for i, row := 1, 1; row <= n; i++ {
w := len(fmt.Sprint(lastInColumn))
if i < lastInRow {
fmt.Printf("%*d ", w, i)
lastInColumn++
} else {
fmt.Printf("%*d\n", w, i)
row++
lastInRow += row
lastInColumn = lowerLeftCorner
}
}
}</lang>
- Output:
Floyd 5: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Floyd 14: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Groovy
<lang groovy>class Floyd {
static void main(String[] args) {
printTriangle(5)
printTriangle(14)
}
private static void printTriangle(int n) {
println(n + " rows:")
int printMe = 1
int numsPrinted = 0
for (int rowNum = 1; rowNum <= n; printMe++) {
int cols = (int) Math.ceil(Math.log10(n * (n - 1) / 2 + numsPrinted + 2))
printf("%" + cols + "d ", printMe)
if (++numsPrinted == rowNum) {
println()
rowNum++
numsPrinted = 0
}
}
}
}</lang>
- Output:
5 rows: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 14 rows: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Haskell
<lang haskell>--------------------- FLOYDS TRIANGLE --------------------
floydTriangle :: Int floydTriangle =
( zipWith
(fmap (.) enumFromTo <*> (\a b -> pred (a + b)))
<$> scanl (+) 1
<*> id
)
[1 ..]
TEST -------------------------
main :: IO () main = mapM_ (putStrLn . formatFT) [5, 14]
DISPLAY ------------------------
formatFT :: Int -> String formatFT n = unlines $ unwords . zipWith alignR ws <$> t
where t = take n floydTriangle ws = length . show <$> last t
alignR :: Int -> Int -> String alignR n =
( (<>)
=<< flip replicate ' '
. (-) n
. length
)
. show</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Or, simplifying a little by delegating the recursion scheme to mapAccumL
<lang haskell>import Control.Monad ((>=>)) import Data.List (mapAccumL)
FLOYD'S TRIANGLE -------------------
floyd :: Int -> Int floyd n =
snd $
mapAccumL
(\a x -> ((,) . succ <*> enumFromTo a) (a + x))
1
[0 .. pred n]
TEST -------------------------
main :: IO () main = mapM_ putStrLn $ showFloyd . floyd <$> [5, 14]
showFloyd :: Int -> String showFloyd x =
let padRight n = (drop . length) <*> (replicate n ' ' <>)
in unlines
( fmap
( zipWith
(\n v -> padRight n (show v))
(fmap (succ . length . show) (last x))
>=> id
)
x
)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Or, defining just the relationship between successive terms:
<lang haskell>----------------- LINES OF FLOYDS TRIANGLE ---------------
floyds :: Int floyds = iterate floyd [1]
floyd :: [Int] -> [Int] floyd xs
| n < 2 = [1]
| otherwise =
[ succ (div (n * pred n) 2)
.. div (n * succ n) 2
]
where
n = succ (length xs)
TEST -------------------------
main :: IO () main = do
mapM_ print $ take 5 floyds putStrLn "" mapM_ print $ take 14 floyds</lang>
- Output:
[1] [2,3] [4,5,6] [7,8,9,10] [11,12,13,14,15] [1] [2,3] [4,5,6] [7,8,9,10] [11,12,13,14,15] [16,17,18,19,20,21] [22,23,24,25,26,27,28] [29,30,31,32,33,34,35,36] [37,38,39,40,41,42,43,44,45] [46,47,48,49,50,51,52,53,54,55] [56,57,58,59,60,61,62,63,64,65,66] [67,68,69,70,71,72,73,74,75,76,77,78] [79,80,81,82,83,84,85,86,87,88,89,90,91] [92,93,94,95,96,97,98,99,100,101,102,103,104,105]
Or as a partially populated matrix:
<lang haskell>import Control.Monad (join) import Data.Matrix (Matrix, getElem, matrix, nrows, toLists)
FLOYDS TRIANGLE --------------------
floyd :: Int -> Matrix (Maybe Int) floyd n = matrix n n go
where
go (y, x)
| x > y = Nothing
| otherwise = Just (x + quot (pred y * y) 2)
TEST -------------------------
main :: IO () main = mapM_ putStrLn $ showFloyd . floyd <$> [5, 14]
DISPLAY ------------------------
showFloyd :: Matrix (Maybe Int) -> String showFloyd m =
(unlines . fmap unwords . toLists) $ go <$> m where go Nothing = "" go (Just n) = padRight w (show n) Just v = join getElem (nrows m) m w = length (show v)
padRight :: Int -> String -> String padRight n = (drop . length) <*> (replicate n ' ' <>)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Icon and Unicon
The following solution works in both languages: <lang unicon>procedure main(a)
n := integer(a[1]) | 5
w := ((n*(n-1))/2)-n
c := create seq()
every row := 1 to n do {
every col := 1 to row do {
width := *(w+col)+1
every writes(right(@c,width))
}
write()
}
end</lang>
Sample outputs:
->ft 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ->
->ft 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 ->
J
Note: require 'strings' does nothing in J7, but is harmless (strings is already incorporated in J7).
<lang J>require 'strings' floyd=: [: rplc&(' 0';' ')"1@":@(* ($ $ +/\@,)) >:/~@:i.</lang>
Note, the parenthesis around ($ $ +/\@,) is optional, and only included for emphasis.
Example use:
<lang J> floyd 5
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15
floyd 14 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105</lang>
How it works:
First, we create a square lower triangular matrix with our argument as the length of one side. We have 1s along the diagonal and the lower triangle, and 0s for the upper triangle.
Second, we create a running sum of these values (treating rows as being adjacent horizontally for this purpose). Then, we multiply this result by our lower triangular matrix (forcing the upper triangle to be 0s).
Then, we format the matrix as text (which gives us the required vertical alignment), and in each row we replace each space followed by a zero with two spaces.
Efficiency note: In a measurement of time used: in floyd 100, 80% the time here goes into the string manipulations -- sequential additions and multiplications are cheap. In floyd 1000 this jumps to 98% of the time. Here's a faster version (about 3x on floyd 1000) courtesy of Aai of the J forums:
<lang J>floyd=: [: ({.~ i.&1@E.~&' 0')"1@":@(* ($ $ +/\@,)) >:/~@:i.</lang>
Java
<lang java> public class Floyd { public static void main(String[] args){ printTriangle(5); printTriangle(14); }
private static void printTriangle(int n){ System.out.println(n + " rows:"); for(int rowNum = 1, printMe = 1, numsPrinted = 0; rowNum <= n; printMe++){ int cols = (int)Math.ceil(Math.log10(n*(n-1)/2 + numsPrinted + 2)); System.out.printf("%"+cols+"d ", printMe); if(++numsPrinted == rowNum){ System.out.println(); rowNum++; numsPrinted = 0; } } } }</lang> Output:
5 rows: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 14 rows: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
JavaScript
ES5
(In a functional idiom of JavaScript)
Two main functions:
- An expression of the Floyd triangle as a list of lists (a function of the number of rows),
- and a mapping of that expression to a formatted string.
<lang JavaScript>(function () {
'use strict';
// FLOYD's TRIANGLE -------------------------------------------------------
// floyd :: Int -> Int function floyd(n) { return snd(mapAccumL(function (start, row) { return [start + row + 1, enumFromTo(start, start + row)]; }, 1, enumFromTo(0, n - 1))); };
// showFloyd :: Int -> String function showFloyd(xss) { var ws = map(compose([succ, length, show]), last(xss)); return unlines(map(function (xs) { return concat(zipWith(function (w, x) { return justifyRight(w, ' ', show(x)); }, ws, xs)); }, xss)); };
// GENERIC FUNCTIONS ------------------------------------------------------
// compose :: [(a -> a)] -> (a -> a)
function compose(fs) {
return function (x) {
return fs.reduceRight(function (a, f) {
return f(a);
}, x);
};
};
// concat :: a -> [a] | [String] -> String function concat(xs) { if (xs.length > 0) { var unit = typeof xs[0] === 'string' ? : []; return unit.concat.apply(unit, xs); } else return []; };
// enumFromTo :: Int -> Int -> [Int]
function enumFromTo(m, n) {
return Array.from({
length: Math.floor(n - m) + 1
}, function (_, i) {
return m + i;
});
};
// justifyRight :: Int -> Char -> Text -> Text
function justifyRight(n, cFiller, strText) {
return n > strText.length ? (cFiller.repeat(n) + strText)
.slice(-n) : strText;
};
// last :: [a] -> a
function last(xs) {
return xs.length ? xs.slice(-1)[0] : undefined;
};
// length :: [a] -> Int
function length(xs) {
return xs.length;
};
// map :: (a -> b) -> [a] -> [b]
function map(f, xs) {
return xs.map(f);
};
// 'The mapAccumL function behaves like a combination of map and foldl; // it applies a function to each element of a list, passing an accumulating // parameter from left to right, and returning a final value of this // accumulator together with the new list.' (See hoogle )
// mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
function mapAccumL(f, acc, xs) {
return xs.reduce(function (a, x) {
var pair = f(a[0], x);
return [pair[0], a[1].concat([pair[1]])];
}, [acc, []]);
};
// show :: // (a -> String) f, Num n => // a -> maybe f -> maybe n -> String var show = JSON.stringify;
// snd :: (a, b) -> b
function snd(tpl) {
return Array.isArray(tpl) ? tpl[1] : undefined;
};
// succ :: Int -> Int
function succ(x) {
return x + 1;
};
// unlines :: [String] -> String
function unlines(xs) {
return xs.join('\n');
};
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
function zipWith(f, xs, ys) {
var ny = ys.length;
return (xs.length <= ny ? xs : xs.slice(0, ny))
.map(function (x, i) {
return f(x, ys[i]);
});
};
// TEST ( n=5 and n=14 rows ) ---------------------------------------------
return unlines(map(function (n) {
return showFloyd(floyd(n)) + '\n';
}, [5, 14]));
})();</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
ES6
(mapAccumL version)
<lang JavaScript>(() => {
'use strict';
// FLOYD's TRIANGLE -------------------------------------------------------
// floyd :: Int -> Int const floyd = n => snd(mapAccumL( (start, row) => [start + row + 1, enumFromTo(start, start + row)], 1, enumFromTo(0, n - 1) ));
// showFloyd :: Int -> String const showFloyd = xss => { const ws = map(compose([succ, length, show]), last(xss)); return unlines( map(xs => concat(zipWith( (w, x) => justifyRight(w, ' ', show(x)), ws, xs )), xss ) ); };
// GENERIC FUNCTIONS ------------------------------------------------------
// compose :: [(a -> a)] -> (a -> a) const compose = fs => x => fs.reduceRight((a, f) => f(a), x);
// concat :: a -> [a] | [String] -> String const concat = xs => { if (xs.length > 0) { const unit = typeof xs[0] === 'string' ? : []; return unit.concat.apply(unit, xs); } else return []; };
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);
// justifyRight :: Int -> Char -> Text -> Text
const justifyRight = (n, cFiller, strText) =>
n > strText.length ? (
(cFiller.repeat(n) + strText)
.slice(-n)
) : strText;
// last :: [a] -> a const last = xs => xs.length ? xs.slice(-1)[0] : undefined;
// length :: [a] -> Int const length = xs => xs.length;
// map :: (a -> b) -> [a] -> [b] const map = (f, xs) => xs.map(f)
// 'The mapAccumL function behaves like a combination of map and foldl; // it applies a function to each element of a list, passing an accumulating // parameter from left to right, and returning a final value of this // accumulator together with the new list.' (See hoogle )
// mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
const mapAccumL = (f, acc, xs) =>
xs.reduce((a, x) => {
const pair = f(a[0], x);
return [pair[0], a[1].concat([pair[1]])];
}, [acc, []]);
// show :: // (a -> String) f, Num n => // a -> maybe f -> maybe n -> String const show = JSON.stringify;
// snd :: (a, b) -> b const snd = tpl => Array.isArray(tpl) ? tpl[1] : undefined;
// succ :: Int -> Int const succ = x => x + 1
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = (f, xs, ys) => {
const ny = ys.length;
return (xs.length <= ny ? xs : xs.slice(0, ny))
.map((x, i) => f(x, ys[i]));
};
// TEST ( n=5 and n=14 rows ) ---------------------------------------------
return unlines(map(n => showFloyd(floyd(n)) + '\n', [5, 14]))
})();</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Spidermonkey
(Used TCL example as a starting point.)
<lang javascript>#!/usr/bin/env js
function main() {
print('Floyd 5:');
floyd(5);
print('\nFloyd 14:');
floyd(14);
}
function padLeft(s, w) {
for (s = String(s); s.length < w; s = ' ' + s); return s;
}
function floyd(nRows) {
var lowerLeft = nRows * (nRows - 1) / 2 + 1;
var lowerRight = nRows * (nRows + 1) / 2;
var colWidths = [];
for (var col = lowerLeft; col <= lowerRight; col++) {
colWidths.push(String(col).length);
}
var num = 1;
for (var row = 0; row < nRows; row++) {
var line = [];
for (var col = 0; col <= row; col++, num++) {
line.push(padLeft(num, colWidths[col]));
}
print(line.join(' '));
}
}
main();</lang>
- Output:
Floyd 5: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Floyd 14: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
jq
<lang jq># floyd(n) creates an n-row floyd's triangle def floyd(n):
def lpad(len): tostring | (((len - length) * " ") + .);
# Construct an array of widths. # Assuming N is the last integer on the last row (i.e. (n+1)*n/2), # the last row has n entries from (1+N-n) through N: def widths: ((n+1)*n/2) as $N | [range(1 + $N - n; $N + 1) | tostring | length];
# emit line k assuming it starts with the integer "start"
def line(start; k; widths):
reduce range(start; start+k) as $i
(""; . + ($i|lpad(widths[$i - start])) + " ");
widths as $widths
| (reduce range(0;n) as $row
( [0, ""]; # state: i, string
(.[0] + 1) as $i | .[1] as $string
| [ ($i + $row),
($string + "\n" + line($i; $row + 1; $widths )) ] )
| .[1] ) ;</lang>
Task: <lang jq>(5,14) | "floyd(\(.)): \(floyd(.))\n"</lang>
- Output:
<lang sh>$ jq -M -r -n -f floyds_triangle.jq > floyds_triangle.out floyd(5):
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15
floyd(14):
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 </lang>
Julia
<lang julia>function floydtriangle(rows)
r = collect(1:div(rows *(rows + 1), 2))
for i in 1:rows
for j in 1:i
print(rpad(lpad(popfirst!(r), j > 8 ? 3 : 2), j > 8 ? 4 : 3))
end
println()
end
end
floydtriangle(5); println(); floydtriangle(14)
</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Kotlin
<lang scala>fun main(args: Array<String>) = args.forEach { Triangle(it.toInt()) }
internal class Triangle(n: Int) {
init {
println("$n rows:")
var printMe = 1
var printed = 0
var row = 1
while (row <= n) {
val cols = Math.ceil(Math.log10(n * (n - 1) / 2 + printed + 2.0)).toInt()
print("%${cols}d ".format(printMe))
if (++printed == row) { println(); row++; printed = 0 }
printMe++
}
}
}</lang> Output as Java.
Lasso
<lang Lasso>define floyds_triangle(n::integer) => {
local(out = array(array(1)),comp = array, num = 1)
while(#out->size < #n) => {
local(new = array)
loop(#out->last->size + 1) => {
#num++
#new->insert(#num)
}
#out->insert(#new)
}
local(pad = #out->last->last->asString->size)
with line in #out do => {
local(lineout = string)
with i in #line do => {
#i != #line->first ? #lineout->append(' ')
#lineout->append((' '*(#pad - #i->asString->size))+#i)
}
#comp->insert(#lineout)
}
return #comp->join('\r')
}
floyds_triangle(5)
'\r\r'
floyds_triangle(14)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Liberty BASIC
<lang lb>input "Number of rows needed:- "; rowsNeeded
dim colWidth(rowsNeeded) ' 5 rows implies 5 columns
for col=1 to rowsNeeded
colWidth(col) = len(str$(col + rowsNeeded*(rowsNeeded-1)/2))
next
currentNumber =1
for row=1 to rowsNeeded
for col=1 to row
print right$( " "+str$( currentNumber), colWidth(col)); " ";
currentNumber = currentNumber + 1
next
print
next</lang>
- Output:
Number of rows needed:- 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Number of rows needed:- 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Lua
<lang lua>function print_floyd(rows) local c = 1 local h = rows*(rows-1)/2 for i=1,rows do local s = "" for j=1,i do for k=1, #tostring(h+j)-#tostring(c) do s = s .. " " end if j ~= 1 then s = s .. " " end s = s .. tostring(c) c = c + 1 end print(s) end end
print_floyd(5) print_floyd(14)</lang>
Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Maple
<lang maple>floyd := proc(rows) local num, numRows, numInRow, i, digits; digits := Array([]); for i to 2 do num := 1; numRows := 1; numInRow := 1; while numRows <= rows do if i = 2 then printf(cat("%", digits[numInRow], "a "), num); end if; num := num + 1; if i = 1 and numRows = rows then digits(numInRow) := StringTools[Length](convert(num-1, string)); end if; if numInRow >= numRows then if i = 2 then printf("\n"); end if; numInRow := 1; numRows := numRows + 1; else numInRow := numInRow +1; end if; end do; end do; return NULL; end proc:
floyd(5); floyd(14);</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Mathematica / Wolfram Language
<lang Mathematica> f=Function[n, Most/@(Range@@@Partition[FindSequenceFunction[{1,2,4,7,11}]/@Range[n+1],2,1])] TableForm[f@5,TableAlignments->Right,TableSpacing->{1,1}] TableForm[f@14,TableAlignments->Right,TableSpacing->{1,1}] </lang> Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
MATLAB / Octave
<lang Matlab>function floyds_triangle(n)
s = 1; for k = 1 : n disp(s : s + k - 1) s = s + k; end</lang>
- Output:
octave:22> floyds_triangle(5) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Modula-2
<lang modula2>MODULE FloydTriangle; FROM FormatString IMPORT FormatString; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE WriteInt(n : INTEGER); VAR buf : ARRAY[0..9] OF CHAR; BEGIN
FormatString("%4i", buf, n);
WriteString(buf)
END WriteInt;
PROCEDURE Print(r : INTEGER); VAR n,i,limit : INTEGER; BEGIN
IF r<0 THEN RETURN END;
n := 1;
limit := 1;
WHILE r#0 DO
FOR i:=1 TO limit DO
WriteInt(n);
INC(n)
END;
WriteLn;
DEC(r);
INC(limit)
END
END Print;
BEGIN
Print(5); WriteLn; Print(14);
ReadChar
END FloydTriangle.</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
NetRexx
Both REXX versions lend themselves very well to conversion into NetRexx programs with few changes.
Version 1
<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols binary /* REXX ***************************************************************
- 12.07.2012 Walter Pachl - translated from Python
- /
Parse Arg rowcount . if rowcount.length() == 0 then rowcount = 1 say 'Rows:' rowcount say col = 0 len = Rexx ll = -- last line of triangle Loop j = rowcount * (rowcount - 1) / 2 + 1 to rowcount * (rowcount + 1) / 2
col = col + 1 -- column number ll = ll j -- build last line len[col] = j.length() -- remember length of column End j
Loop i = 1 To rowcount - 1 -- now do and output the rest
ol = col = 0 Loop j = i * (i - 1) / 2 + 1 to i * (i + 1) / 2 -- elements of line i col = col + 1 ol=ol j.right(len[col]) -- element in proper length end Say ol -- output ith line end i
Say ll -- output last line </lang> Output:
Rows: 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Rows: 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Version 2
<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols binary /*REXX program constructs & displays Floyd's triangle for any number of rows.*/ parse arg numRows . if numRows == then numRows = 1 -- assume 1 row if not given maxVal = numRows * (numRows + 1) % 2 -- calculate the max value. say 'displaying a' numRows "row Floyd's triangle:" say digit = 1 loop row = 1 for numRows
col = 0 output = loop digit = digit for row col = col + 1 colMaxDigit = maxVal - numRows + col output = output Rexx(digit).right(colMaxDigit.length()) end digit say output end row
</lang>
Output:
displaying a 5 row Floyd's triangle: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 displaying a 14 row Floyd's triangle: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Nim
<lang nim>import strutils
proc floyd(rowcount = 5): seq[seq[int]] =
result = @[@[1]]
while result.len < rowcount:
let n = result[result.high][result.high] + 1
var row = newSeq[int]()
for i in n .. n + result[result.high].len:
row.add i
result.add row
proc pfloyd(rows: seq[seq[int]]) =
var colspace = newSeq[int]()
for n in rows[rows.high]: colspace.add(($n).len)
for row in rows:
for i, x in row:
stdout.write align($x, colspace[i])," "
echo ""
for i in [5, 14]:
pfloyd(floyd(i)) echo ""</lang>
Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
OCaml
<lang ocaml>let ( |> ) f g x = g (f x) let rec last = function x::[] -> x | _::tl -> last tl | [] -> raise Not_found let rec list_map2 f l1 l2 =
match (l1, l2) with | ([], _) | (_, []) -> [] | (x::xs, y::ys) -> (f x y) :: list_map2 f xs ys
let floyd n =
let rec aux acc cur len i j =
if (List.length acc) = n then (List.rev acc) else
if j = len
then aux ((List.rev cur)::acc) [] (succ len) i 0
else aux acc (i::cur) len (succ i) (succ j)
in
aux [] [] 1 1 0
let print_floyd f =
let lens = List.map (string_of_int |> String.length) (last f) in
List.iter (fun row ->
print_endline (
String.concat " " (
list_map2 (Printf.sprintf "%*d") lens row))
) f
let () =
print_floyd (floyd (int_of_string Sys.argv.(1)))</lang>
OxygenBasic
<lang oxygenbasic>
function Floyd(sys n) as string
sys i,t
for i=1 to n
t+=i
next string s=str t sys le=1+len s string cr=chr(13,10) sys lc=len cr string buf=space(le*t+n*lc) sys j,o,p=1 t=0 for i=1 to n
for j=1 to i t++ s=str t o=le-len(s)-1 'right justify mid buf,p+o,str t p+=le next mid buf,p,cr p+=lc
next return left buf,p-1 end function
putfile "s.txt",Floyd(5)+floyd(14) </lang>
PARI/GP
<lang parigp>{floyd(m)=my(lastrow_a,lastrow_e,lastrow_len=m,fl,idx);
\\ +++ fl is a vector of fieldlengths in the last row
lastrow_e=m*(m+1)/2;lastrow_a=lastrow_e+1-m;
fl=vector(lastrow_len);
for(k=1,m,fl[k] = 1 + #Str(k-1+lastrow_a) );
\\
idx=0;
for(i=1,m,
for(j=1,i,
idx++;
printf(Str("%" fl[j] "d"),idx)
);
print()
);
return();}
floyd(5) floyd(14) </lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Pascal
<lang pascal>Program FloydDemo (input, output);
function digits(number: integer): integer;
begin digits := trunc(ln(number) / ln(10)) + 1; end;
procedure floyd1 (numberOfLines: integer); { variant with repeat .. until loop }
var
i, j, numbersInLine, startOfLastlLine: integer;
begin
startOfLastlLine := (numberOfLines - 1) * numberOfLines div 2 + 1;
i := 1;
j := 1;
numbersInLine := 1;
repeat
repeat
write(i: digits(startOfLastlLine - 1 + j), ' ');
inc(i);
inc(j);
until (j > numbersInLine);
writeln;
j := 1;
inc(numbersInLine);
until (numbersInLine > numberOfLines);
end;
procedure floyd2 (numberOfLines: integer); { Variant with for .. do loop }
var
i, j, numbersInLine, startOfLastlLine: integer;
begin
startOfLastlLine := (numberOfLines - 1) * numberOfLines div 2 + 1;
i := 1;
for numbersInLine := 1 to numberOfLines do
begin
for j := 1 to numbersInLine do
begin
write(i: digits(startOfLastlLine - 1 + j), ' ');
inc(i);
end;
writeln;
end;
end;
begin
writeln ('*** Floyd 5 ***');
floyd1(5);
writeln;
writeln ('*** Floyd 14 ***');
floyd2(14);
end.</lang> Output:
% ./Floyd *** Floyd 5 *** 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 *** Floyd 14 *** 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Perl
<lang perl>#!/usr/bin/env perl use strict; use warnings;
sub displayFloydTriangle {
my $numRows = shift;
print "\ndisplaying a $numRows row Floyd's triangle:\n\n";
my $maxVal = int($numRows * ($numRows + 1) / 2); # calculate the max value.
my $digit = 0;
foreach my $row (1 .. $numRows) {
my $col = 0;
my $output = ;
foreach (1 .. $row) {
++$digit;
++$col;
my $colMaxDigit = $maxVal - $numRows + $col;
$output .= sprintf " %*d", length($colMaxDigit), $digit;
}
print "$output\n";
}
return;
}
- ==== Main ================================================
my @counts; @counts = @ARGV; @counts = (5, 14) unless @ARGV;
foreach my $count (@counts) {
displayFloydTriangle($count);
}
0; __END__ </lang> Output:
displaying a 5 row Floyd's triangle: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 displaying a 14 row Floyd's triangle: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Phix
with javascript_semantics procedure Floyds_triangle(integer n) sequence widths = repeat(0,n) integer k = (n * (n-1))/2 for i=1 to n do widths[i] = sprintf("%%%dd",length(sprintf("%d",i+k))+1) end for k = 1 for i=1 to n do for j=1 to i do printf(1,widths[j],k) k += 1 end for printf(1,"\n") end for end procedure Floyds_triangle(5) Floyds_triangle(14)
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
PHP
<lang php> <?php floyds_triangle(5); floyds_triangle(14);
function floyds_triangle($n) {
echo "n = " . $n . "\r\n";
for($r = 1, $i = 1, $c = 0; $r <= $n; $i++) {
$cols = ceil(log10($n*($n-1)/2 + $c + 2));
printf("%".$cols."d ", $i);
if(++$c == $r) {
echo "\r\n";
$r++;
$c = 0;
}
}
?> </lang>
- Output:
n = 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 n = 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
PicoLisp
Calculate widths relative to lower left corner
<lang PicoLisp>(de floyd (N)
(let LLC (/ (* N (dec N)) 2)
(for R N
(for C R
(prin
(align
(length (+ LLC C))
(+ C (/ (* R (dec R)) 2)) ) )
(if (= C R) (prinl) (space)) ) ) ) )</lang>
Pre-calculate all rows, and take format from last one
<lang PicoLisp>(de floyd (N)
(let
(Rows
(make
(for ((I . L) (range 1 (/ (* N (inc N)) 2)) L)
(link (cut I 'L)) ) )
Fmt (mapcar length (last Rows)) )
(map inc (cdr Fmt))
(for R Rows
(apply tab R Fmt) ) ) )</lang>
Output in both cases:
: (floyd 5) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 : (floyd 14) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
PL/I
<lang pli>(fofl, size): floyd: procedure options (main); /* Floyd's Triangle. Wiki 12 July 2012 */
declare (i, m, n) fixed (10), (j, k, w, nr) fixed binary;
put list ('How many rows do you want?');
get list (nr); /* the number of rows */
n = nr*(nr+1)/2; /* the total number of values */
j,k = 1; m = n - nr + 1;
do i = 1 to n;
put edit (i) ( x(1), f(length(trim(m))) );
if k > 1 then do; k = k - 1; m = m + 1; end;
else do; k,j = j + 1; m = n - nr + 1; put skip; end;
end;
end floyd;</lang>
- Output:
How many rows do you want? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 How many rows do you want? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 Final row for n=45: 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035
Prolog
Works with SWI-Prolog version 6.5.3 <lang Prolog>floyd(N) :- forall(between(1, N, I), ( forall(between(1,I, J), ( Last is N * (N-1)/2+J, V is I * (I-1) /2 + J, get_column(Last, C), sformat(AR, '~~t~~w~~~w| ', [C]), sformat(AF, AR, [V]), writef(AF))), nl)).
get_column(Last, C) :- name(Last, N1), length(N1,C). </lang> Output :
?- floyd(5). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 true. ?- floyd(14). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 true.
PureBasic
<lang PureBasic>Procedure.i sumTo(n)
Protected r,i For i=1 To n r+i Next ProcedureReturn r.i
EndProcedure
- [1]
- array rsA(n)... string-lengths of the numbers
- in the bottom row
- [2]
- sumTo(i-1)+1 to sumTo(i)
; 11 12 13 14 15 ; here k is the column-index for array rsA(k)
Procedure.s FloydsTriangle(n)
Protected r.s,s.s,t.s,i,j,k
; [1]
Dim rsA(n)
i=0
For j=sumTo(n-1)+1 To sumTo(n)
i+1
rsA(i)=Len(Str(j))
Next
; [2]
For i=1 To n
t.s="":k=0
For j=sumTo(i-1)+1 To sumTo(i)
k+1:t.s+RSet(Str(j),rsA(k)," ")+" "
Next
r.s+RTrim(t.s)+Chr(13)+Chr(10)
Next
r.s=Left(r.s,Len(r.s)-2)
ProcedureReturn r.s
EndProcedure
If OpenConsole()
n=5 r.s=FloydsTriangle(n) PrintN(r.s) n=14 r.s=FloydsTriangle(n) PrintN(r.s) Print(#crlf$ + #crlf$ + "Press ENTER to exit"): Input() CloseConsole()
EndIf</lang>
Sample Output
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Python
Procedural
<lang python>>>> def floyd(rowcount=5): rows = 1 while len(rows) < rowcount: n = rows[-1][-1] + 1 rows.append(list(range(n, n + len(rows[-1]) + 1))) return rows
>>> floyd() [[1], [2, 3], [4, 5, 6], [7, 8, 9, 10], [11, 12, 13, 14, 15]] >>> def pfloyd(rows=[[1], [2, 3], [4, 5, 6], [7, 8, 9, 10]]): colspace = [len(str(n)) for n in rows[-1]] for row in rows: print( ' '.join('%*i' % space_n for space_n in zip(colspace, row)))
>>> pfloyd()
1
2 3
4 5 6
7 8 9 10
>>> pfloyd(floyd(5))
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 >>> pfloyd(floyd(14))
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 >>> </lang>
Functional
Using the mathematical formula for each row directly, either in a list comprehension: <lang python>def floyd(rowcount=5):
return [list(range(i * (i - 1) // 2 + 1, i * (i + 1) // 2 + 1))
for i in range(1, rowcount + 1)]</lang>
or in terms of concatMap:
<lang python>Floyd triangle in terms of concatMap
from itertools import chain
- floyd :: Int -> Int
def floyd(n):
n rows of a Floyd triangle.
def f(i):
return [
enumFromTo(i * pred(i) // 2 + 1)(
i * succ(i) // 2
)
]
return concatMap(f)(enumFromTo(1)(n))
- main :: IO ()
def main():
Test
print(unlines(
map(str, floyd(5))
))
- GENERIC FUNCTIONS ---------------------------------------
- enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
Integer enumeration from m to n. return lambda n: list(range(m, 1 + n))
- concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
Concatenated list over which a function has been mapped.
The list monad can be derived by using a function f which
wraps its output in a list,
(using an empty list to represent computational failure).
return lambda xs: list(
chain.from_iterable(
map(f, xs)
)
)
- pred :: Enum a => a -> a
def pred(x):
The predecessor of a value. For numeric types, (- 1).
return x - 1 if isinstance(x, int) else (
chr(ord(x) - 1)
)
- succ :: Enum a => a -> a
def succ(x):
The successor of a value. For numeric types, (1 +).
return 1 + x if isinstance(x, int) else (
chr(1 + ord(x))
)
- unlines :: [String] -> String
def unlines(xs):
A single string derived by the intercalation
of a list of strings with the newline character.
return '\n'.join(xs)
if __name__ == '__main__':
main()</lang>
Or alternatively, defining just the relationship between successive terms:
<lang python>Floyd triangle in terms of iterate(f)(x)
from itertools import islice
- floyd :: Int -> Int
def floyd(n):
n rows of a Floyd triangle. return take(n)(iterate(nextFloyd)([1]))
- nextFloyd :: [Int] -> [Int]
def nextFloyd(xs):
A Floyd triangle row derived from
the preceding row.
n = succ(len(xs))
return [1] if n < 2 else (
enumFromTo(succ(n * pred(n) // 2))(
n * succ(n) // 2
)
)
- showFloyd :: Int -> String
def showFloyd(xs):
A stringification of Floyd triangle rows. return unlines(str(x) for x in xs)
- main :: IO ()
def main():
Test
print(showFloyd(
floyd(5)
))
- GENERIC ABSTRACTIONS ------------------------------------
- enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
Integer enumeration from m to n. return lambda n: list(range(m, 1 + n))
- iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
An infinite list of repeated applications of f to x.
def go(x):
v = x
while True:
yield v
v = f(v)
return lambda x: go(x)
- pred :: Enum a => a -> a
def pred(x):
The predecessor of a value. For numeric types, (- 1).
return x - 1 if isinstance(x, int) else (
chr(ord(x) - 1)
)
- succ :: Enum a => a -> a
def succ(x):
The successor of a value. For numeric types, (1 +).
return 1 + x if isinstance(x, int) else (
chr(1 + ord(x))
)
- take :: Int -> [a] -> [a]
- take :: Int -> String -> String
def take(n):
The prefix of xs of length n,
or xs itself if n > length xs.
return lambda xs: (
xs[0:n]
if isinstance(xs, list)
else list(islice(xs, n))
)
- unlines :: [String] -> String
def unlines(xs):
A single string derived by the intercalation
of a list of strings with the newline character.
return '\n'.join(xs)
- MAIN ----------------------------------------------------
if __name__ == '__main__':
main()</lang>
- Output:
[1] [2, 3] [4, 5, 6] [7, 8, 9, 10] [11, 12, 13, 14, 15]
q
<lang q> floyd:{n:1+ til sum 1+til x;
t:d:0;
while[1+x-:1;0N!(t+:1)#(d+:t)_n]}
floyd2:{n:1+ til sum 1+til x;
t:d:0;
while[1+x-:1;1 (" " sv string each (t+:1)#(d+:t)_n),"\n"]}
//The latter function 'floyd2' includes logic to remove the leading "," before "1" in the first row.
floyd[5] floyd2[14]</lang>
- Output:
,1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Quackery
<lang Quackery> [ dup 1+ * 2 / ] is triangulared ( n --> n )
[ number$ tuck size - times sp echo$ ] is rightecho ( n n --> )
[ dup triangulared
number$ size 1+
0 rot times
[ i^ 1+ times
[ 1+ 2dup
rightecho ]
cr ]
2drop ] is floyd ( n --> )
5 floyd cr 14 floyd</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
R
If it weren't for the printing requirements, we could do this in one line. <lang rsplus>Floyd <- function(n) {
#The first argument of the seq call is a well-known formula for triangle numbers.
out <- t(sapply(seq_len(n), function(i) c(seq(to = 0.5 * (i * (i + 1)), by = 1, length.out = i), rep(NA, times = n - i))))
dimnames(out) <- list(rep("", times = nrow(out)), rep("", times = ncol(out)))
print(out, na.print = "")
} Floyd(5) Floyd(14)</lang>
- Output:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Racket
<lang racket>
- lang racket
(require math)
(define (tri n)
(if (zero? n) 0 (triangle-number n)))
(define (floyd n)
(define (width x) (string-length (~a x)))
(define (~n x c) (~a x
#:width (width (+ (tri (- n 1)) 1 c))
#:align 'right #:left-pad-string " "))
(for ([r n])
(for ([c (+ r 1)])
(display (~a (~n (+ (tri r) 1 c) c) " ")))
(newline)))
(floyd 5) (floyd 14) </lang> Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Raku
(formerly Perl 6) Here's two ways of doing it. <lang perl6>constant @floyd1 = (1..*).rotor(1..*); constant @floyd2 = gather for 1..* -> $s { take [++$ xx $s] }
sub format-rows(@f) {
my @table;
my @formats = @f[@f-1].map: {"%{.chars}s"}
for @f -> @row {
@table.push: (@row Z @formats).map: -> ($i, $f) { $i.fmt($f) }
}
join "\n", @table;
}
say format-rows(@floyd1[^5]); say ; say format-rows(@floyd2[^14]);</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
REXX
version 1
<lang rexx> /* REXX ***************************************************************
- Parse Arg rowcount
- 12.07.2012 Walter Pachl - translated from Python
- /
Parse Arg rowcount col=0 ll= /* last line of triangle */ Do j=rowcount*(rowcount-1)/2+1 to rowcount*(rowcount+1)/2
col=col+1 /* column number */ ll=ll j /* build last line */ len.col=length(j) /* remember length of column */ End
Do i=1 To rowcount-1 /* now do and output the rest */
ol= col=0 Do j=i*(i-1)/2+1 to i*(i+1)/2 /* elements of line i */ col=col+1 ol=ol right(j,len.col) /* element in proper length */ end Say ol /* output ith line */ end
Say ll /* output last line */ </lang> Output:
n=5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 n=14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
version 2, simple formula
This REXX version uses a simple formula to calculate the maximum value (triangle element) displayed. <lang rexx>/*REXX program constructs & displays Floyd's triangle for any number of specified rows.*/ parse arg N .; if N== | N=="," then N= 5 /*Not specified? Then use the default.*/ mx= N * (N+1) % 2 - N /*calculate the maximum of any value. */ say 'displaying a ' N " row Floyd's triangle:" /*show the header for Floyd's triangle.*/ say /*display a blank line below the title.*/
- =1; do r=1 for N; i= 0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i= i + 1 /*start to construct a row of triangle.*/
_= _ right(#, length( mx+i ) ) /*build a row of the Floyd's triangle. */
end /*#*/ /*calculate the max length on the fly. */
say substr(_, 2) /*remove 1st leading blank in the line.*/
end /*r*/ /*stick a fork in it, we're all done. */</lang>
- output when using the default input:
displaying a 5 row Floyd's triangle: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- output when using the default input of: 14
displaying a 14 row Floyd's triangle: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
- output (only showing the last row) when using the input of: 45
··· 44 rows not shown ··· 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035
version 3, hexadecimal
<lang rexx>/*REXX program constructs & displays Floyd's triangle for any number of rows in base 16.*/ parse arg N .; if N== | N=="," then N=6 /*Not specified? Then use the default.*/ mx=N * (N+1) % 2 - N /*calculate maximum value of any value.*/ say 'displaying a ' N " row Floyd's triangle in base 16:" /*show triangle header.*/ say
- =1; do r=1 for N; i=0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i=i+1 /*start to construct a row of triangle.*/
_=_ right( d2x(#), length( d2x(mx+i))) /*build a row of the Floyd's triangle. */
end /*#*/
say substr(_, 2) /*remove 1st leading blank in the line.*/
end /*r*/ /*stick a fork in it, we're all done. */</lang>
- output when using the default input:
displaying a 6 row Floyd's triangle in base 16: 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 15
- output when using the input of: 23
displaying a 23 row Floyd's triangle in base 16: 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F 30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F 40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F 50 51 52 53 54 55 56 57 58 59 5A 5B 5C 5D 5E 5F 60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F 70 71 72 73 74 75 76 77 78 79 7A 7B 7C 7D 7E 7F 80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F 90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 AA AB AC AD AE AF B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 BA BB BC BD BE BF C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 CA CB CC CD CE CF D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 DA DB DC DD DE DF E0 E1 E2 E3 E4 E5 E6 E7 E8 E9 EA EB EC ED EE EF F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 FA FB FC FD FE FF 100 101 102 103 104 105 106 107 108 109 10A 10B 10C 10D 10E 10F 110 111 112 113 114
version 4, up to base 90
This REXX version could be extended to even higher bases, all that is needed is to append more viewable characters to express "higher" numerals ("digits" in base X).
This version of the base function has some boilerplate for signed numbers and various error checking. <lang rexx>/*REXX program constructs/shows Floyd's triangle for any number of rows in any base ≤90.*/ parse arg N radx . /*obtain optional arguments from the CL*/ if N== | N=="," then N= 5 /*Not specified? Then use the default.*/ if radx== | radx=="," then radx=10 /* " " " " " " */ mx=N * (N+1) % 2 - N /*calculate maximum value of any value.*/ say 'displaying a ' N " row Floyd's triangle in base" radx':' /*display the header.*/ say
- =1; do r=1 for N; i=0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i=i+1 /*start to construct a row of triangle.*/
_=_ right(base(#, radx), length( base(mx+i, radx) ) ) /*build triangle row.*/
end /*#*/
say substr(_, 2) /*remove 1st leading blank in the line,*/
end /*r*/ /* [↑] introduced by first abutment. */
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ base: procedure; parse arg x 1 ox,toB,inB /*obtain number, toBase, inBase. */
@abc= 'abcdefghijklmnopqrstuvwxyz' /*lowercase Latin alphabet. */
@abcU=@abc; upper @abcU /*go whole hog and extend 'em. */
@@@= '0123456789'@abc || @abcU /*prefix 'em with numeric digits.*/
@@@=@@@'<>[]{}()?~!@#$%^&*_=|\/;:¢¬≈' /*add some special chars as well.*/
/* [↑] handles up to base 90, all chars must be viewable.*/
numeric digits 3000 /*what the hey, support gihugeics*/
mxB=length(@@@) /*max base (radix) supported here*/
if toB== | toB=="," then toB=10 /*if skipped, assume default (10)*/
if inB== | inB=="," then inB=10 /* " " " " " */
if inB<2 | inb>mxB then call erb 'inBase',inB /*invalid/illegal arg: inBase. */
if toB<2 | tob>mxB then call erb 'toBase',toB /* " " " toBase. */
if x== then call erm /* " " " number. */
sigX=left(x, 1) /*obtain a possible leading sign.*/
if pos(sigX, '-+')\==0 then x=substr(x, 2) /*X number has a leading sign? */
else sigX= /* ··· no leading sign.*/
#=0
do j=1 for length(x); _=substr(x, j, 1) /*convert X, base inB ──► base 10*/
v=pos(_, @@@) /*get the value of this "digit". */
if v==0 | v>inB then call erd x,j,inB /*is this an illegal "numeral" ? */
#=# * inB + v - 1 /*construct new num, dig by dig. */
end /*j*/
y=
do while # >= toB /*convert #, base 10 ──► base toB*/
y=substr(@@@, (# // toB) + 1, 1)y /*construct the number for output*/
#=# % toB /* ··· and whittle # down also.*/
end /*while*/
y=sigX || substr(@@@, #+1, 1)y /*prepend the sign if it existed.*/
return y /*return the number in base toB.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ erb: call ser 'illegal' arg(2) "base: " arg(1) "must be in range: 2──► " mxB erd: call ser 'illegal "digit" in' x":" _ erm: call ser 'no argument specified.' ser: say; say '***error***'; say arg(1); say; exit 13</lang>
- output when using the input of: 6 2
displaying a 6 row Floyd's triangle in base 2:
1
10 11
100 101 110
111 1000 1001 1010
1011 1100 1101 1110 1111
10000 10001 10010 10011 10100 10101
- output when using the input of: 23 2
displaying a 12 row Floyd's triangle in base 2:
1
10 11
100 101 110
111 1000 1001 1010
1011 1100 1101 1110 1111
10000 10001 10010 10011 10100 10101
10110 10111 11000 11001 11010 11011 11100
11101 11110 11111 100000 100001 100010 100011 100100
100101 100110 100111 101000 101001 101010 101011 101100 101101
101110 101111 110000 110001 110010 110011 110100 110101 110110 110111
111000 111001 111010 111011 111100 111101 111110 111111 1000000 1000001 1000010
1000011 1000100 1000101 1000110 1000111 1001000 1001001 1001010 1001011 1001100 1001101 1001110
- output when using the input of: 40 81
displaying a 40 row Floyd's triangle in base 81:
1
2 3
4 5 6
7 8 9 a
b c d e f
g h i j k l
m n o p q r s
t u v w x y z A
B C D E F G H I J
K L M N O P Q R S T
U V W X Y Z < > [ ] {
} ( ) ? ~ ! @ # $ % ^ &
* _ 10 11 12 13 14 15 16 17 18 19 1a
1b 1c 1d 1e 1f 1g 1h 1i 1j 1k 1l 1m 1n 1o
1p 1q 1r 1s 1t 1u 1v 1w 1x 1y 1z 1A 1B 1C 1D
1E 1F 1G 1H 1I 1J 1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T
1U 1V 1W 1X 1Y 1Z 1< 1> 1[ 1] 1{ 1} 1( 1) 1? 1~ 1!
1@ 1# 1$ 1% 1^ 1& 1* 1_ 20 21 22 23 24 25 26 27 28 29
2a 2b 2c 2d 2e 2f 2g 2h 2i 2j 2k 2l 2m 2n 2o 2p 2q 2r 2s
2t 2u 2v 2w 2x 2y 2z 2A 2B 2C 2D 2E 2F 2G 2H 2I 2J 2K 2L 2M
2N 2O 2P 2Q 2R 2S 2T 2U 2V 2W 2X 2Y 2Z 2< 2> 2[ 2] 2{ 2} 2( 2)
2? 2~ 2! 2@ 2# 2$ 2% 2^ 2& 2* 2_ 30 31 32 33 34 35 36 37 38 39 3a
3b 3c 3d 3e 3f 3g 3h 3i 3j 3k 3l 3m 3n 3o 3p 3q 3r 3s 3t 3u 3v 3w 3x
3y 3z 3A 3B 3C 3D 3E 3F 3G 3H 3I 3J 3K 3L 3M 3N 3O 3P 3Q 3R 3S 3T 3U 3V
3W 3X 3Y 3Z 3< 3> 3[ 3] 3{ 3} 3( 3) 3? 3~ 3! 3@ 3# 3$ 3% 3^ 3& 3* 3_ 40 41
42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e 4f 4g 4h 4i 4j 4k 4l 4m 4n 4o 4p 4q 4r
4s 4t 4u 4v 4w 4x 4y 4z 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L 4M 4N 4O 4P 4Q 4R 4S
4T 4U 4V 4W 4X 4Y 4Z 4< 4> 4[ 4] 4{ 4} 4( 4) 4? 4~ 4! 4@ 4# 4$ 4% 4^ 4& 4* 4_ 50 51
52 53 54 55 56 57 58 59 5a 5b 5c 5d 5e 5f 5g 5h 5i 5j 5k 5l 5m 5n 5o 5p 5q 5r 5s 5t 5u
5v 5w 5x 5y 5z 5A 5B 5C 5D 5E 5F 5G 5H 5I 5J 5K 5L 5M 5N 5O 5P 5Q 5R 5S 5T 5U 5V 5W 5X 5Y
5Z 5< 5> 5[ 5] 5{ 5} 5( 5) 5? 5~ 5! 5@ 5# 5$ 5% 5^ 5& 5* 5_ 60 61 62 63 64 65 66 67 68 69 6a
6b 6c 6d 6e 6f 6g 6h 6i 6j 6k 6l 6m 6n 6o 6p 6q 6r 6s 6t 6u 6v 6w 6x 6y 6z 6A 6B 6C 6D 6E 6F 6G
6H 6I 6J 6K 6L 6M 6N 6O 6P 6Q 6R 6S 6T 6U 6V 6W 6X 6Y 6Z 6< 6> 6[ 6] 6{ 6} 6( 6) 6? 6~ 6! 6@ 6# 6$
6% 6^ 6& 6* 6_ 70 71 72 73 74 75 76 77 78 79 7a 7b 7c 7d 7e 7f 7g 7h 7i 7j 7k 7l 7m 7n 7o 7p 7q 7r 7s
7t 7u 7v 7w 7x 7y 7z 7A 7B 7C 7D 7E 7F 7G 7H 7I 7J 7K 7L 7M 7N 7O 7P 7Q 7R 7S 7T 7U 7V 7W 7X 7Y 7Z 7< 7>
7[ 7] 7{ 7} 7( 7) 7? 7~ 7! 7@ 7# 7$ 7% 7^ 7& 7* 7_ 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f 8g 8h 8i
8j 8k 8l 8m 8n 8o 8p 8q 8r 8s 8t 8u 8v 8w 8x 8y 8z 8A 8B 8C 8D 8E 8F 8G 8H 8I 8J 8K 8L 8M 8N 8O 8P 8Q 8R 8S 8T
8U 8V 8W 8X 8Y 8Z 8< 8> 8[ 8] 8{ 8} 8( 8) 8? 8~ 8! 8@ 8# 8$ 8% 8^ 8& 8* 8_ 90 91 92 93 94 95 96 97 98 99 9a 9b 9c
9d 9e 9f 9g 9h 9i 9j 9k 9l 9m 9n 9o 9p 9q 9r 9s 9t 9u 9v 9w 9x 9y 9z 9A 9B 9C 9D 9E 9F 9G 9H 9I 9J 9K 9L 9M 9N 9O 9P
9Q 9R 9S 9T 9U 9V 9W 9X 9Y 9Z 9< 9> 9[ 9] 9{ 9} 9( 9) 9? 9~ 9! 9@ 9# 9$ 9% 9^ 9& 9* 9_ a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 aa
Ring
<lang ring> rows = 10 n = 0 for r = 1 to rows
for c = 1 to r
n = n + 1
see string(n) + " "
next
see nl
next
</lang> Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Ruby
<lang ruby>def floyd(rows)
max = (rows * (rows + 1)) / 2
widths = ((max - rows + 1)..max).map {|n| n.to_s.length + 1}
n = 0
rows.times do |r|
puts (0..r).map {|i| n += 1; "%#{widths[i]}d" % n}.join
end
end
floyd(5) floyd(14)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Run BASIC
<lang runbasic>input "Number of rows: "; rows dim colSize(rows) for col=1 to rows
colSize(col) = len(str$(col + rows * (rows-1)/2))
next
thisNum = 1 for r = 1 to rows
for col = 1 to r
print right$( " "+str$(thisNum), colSize(col)); " ";
thisNum = thisNum + 1
next
print
next</lang>
Number of rows: ?14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Rust
<lang rust>fn main() {
floyds_triangle(5); floyds_triangle(14);
}
fn floyds_triangle(n: u32) {
let mut triangle: Vec<Vec<String>> = Vec::new();
let mut current = 0;
for i in 1..=n {
let mut v = Vec::new();
for _ in 0..i {
current += 1;
v.push(current);
}
let row = v.iter().map(|x| x.to_string()).collect::<Vec<_>>();
triangle.push(row);
}
for row in &triangle {
let arranged_row: Vec<_> = row
.iter()
.enumerate()
.map(|(i, number)| {
let space_len = triangle.last().unwrap()[i].len() - number.len() + 1;
let spaces = " ".repeat(space_len);
let mut padded_number = spaces;
padded_number.push_str(&number);
padded_number
})
.collect();
println!("{}", arranged_row.join(""))
}
}
</lang>
Scala
<lang scala>def floydstriangle( n:Int ) = {
val s = (1 to n)
val t = s map {i => (s.take(i-1).sum) + 1}
(s zip t) foreach { n =>
var m = n._2;
for( i <- 0 until n._1 ) {
val w = (t.last + i).toString.length + 1 // Column width from last row
print(" " + m takeRight w )
m+=1
}
print("\n")
}
}
// Test floydstriangle(5) floydstriangle(14)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Seed7
<lang seed7>$ include "seed7_05.s7i";
const proc: writeFloyd (in integer: rows) is func
local
var integer: number is 1;
var integer: numBeforeLastLine is 0;
var integer: line is 0;
var integer: column is 0;
begin
numBeforeLastLine := rows * pred(rows) div 2;
for line range 1 to rows do
for column range 1 to line do
if column <> 1 then
write(" ");
end if;
write(number lpad length(str(numBeforeLastLine + column)));
incr(number);
end for;
writeln;
end for;
end func;
const proc: main is func
begin writeFloyd(5); writeFloyd(14); end func;</lang>
Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Sidef
<lang ruby>func floyd(rows, n=1) {
var max = Math.range_sum(1, rows)
var widths = (max-rows .. max-1 -> map{.+n->to_s.len})
{ |r|
say %'#{1..r -> map{|i| "%#{widths[i-1]}d" % n++}.join(" ")}'
} << 1..rows
}
floyd(5) # or: floyd(5, 88) floyd(14) # or: floyd(14, 900)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
SPL
<lang spl>floyd(5) floyd(14)
floyd(n)=
k = 0
> r, 1..n
s = ""
> j, 1..r
k += 1
f = ">"+#.upper(#.log10((n-1)*n/2+j+1)+1)+">"
s += #.str(k,f)
<
#.output(s)
<
.</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Tcl
<lang tcl>proc floydTriangle n {
# Compute the column widths
for {set i [expr {$n*($n-1)/2+1}]} {$i <= $n*($n+1)/2} {incr i} {
lappend w [string length $i]
}
# Print the triangle
for {set i 0; set j 1} {$j <= $n} {incr j} {
for {set p -1; set k 0} {$k < $j} {incr k} { puts -nonewline [format "%*d " [lindex $w [incr p]] [incr i]] } puts ""
}
}
- Demonstration
puts "Floyd 5:" floydTriangle 5 puts "Floyd 14:" floydTriangle 14</lang>
- Output:
Floyd 5: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Floyd 14: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
TXR
<lang txrlisp>(defun flotri (n)
(let* ((last (trunc (* n (+ n 1)) 2))
(colw (mapcar [chain tostring length]
(range (- last n -1) last)))
(x 0))
(each ((r (range* 0 n)))
(each ((c (range 0 r)))
(format t " ~*a" [colw c] (inc x)))
(put-line))))
(defun usage (msg)
(put-line `error: @msg`) (put-line `usage:\n@(ldiff *full-args* *args*) <smallish-positive-integer>`) (exit 1))
(tree-case *args*
((num blah . etc) (usage "too many arguments")) ((num) (flotri (int-str num))) (() (usage "need an argument")))</lang>
- Output:
$ txr floyds-triangle.tl error: need an argument usage: txr floyds-triangle.tl <smallish-positive-integer> $ txr floyds-triangle.txr 1 2 error: too many arguments usage: txr floyds-triangle.tl <smallish-positive-integer> $ txr floyds-triangle.tl 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 $ txr floyds-triangle.tl 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
VBA
Solution in Microsoft Office Word. Based on VBScript <lang VB>Option Explicit Dim o As String Sub floyd(L As Integer)
Dim r, c, m, n As Integer
n = L * (L - 1) / 2
m = 1
For r = 1 To L
o = o & vbCrLf
For c = 1 To r
o = o & Space(Len(CStr(n + c)) - Len(CStr(m))) & m & " "
m = m + 1
Next
Next
End Sub Sub triangle()
o = "5 lines"
Call floyd(5)
o = o & vbCrLf & "14 lines"
Call floyd(14)
With Selection
.Font.Name = "Courier New"
.TypeText Text:=o
End With
End Sub</lang>
- Output:
<lang>5 lines
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15
14 lines
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105</lang>
VBScript
<lang VBScript> ' Read the number of rows to use.. intRows = WScript.StdIn.ReadLine
' Get the first number of the final row so we can calculate widths... intLastRowStart = (intRows ^ 2 - intRows) \ 2 + 1
For i = 1 To intRows intLastRow = intLastRowStart For j = 1 To i k = k + 1 WScript.StdOut.Write Space(Len(intLastRow) - Len(k)) & k & " " intLastRow = intLastRow + 1 Next WScript.StdOut.WriteLine "" Next </lang>
Visual Basic .NET
<lang vbnet>Imports System.Text
Module Module1
Function MakeTriangle(rows As Integer) As String
Dim maxValue As Integer = (rows * (rows + 1)) / 2
Dim digit = 0
Dim output As New StringBuilder
For row = 1 To rows
For column = 0 To row - 1
Dim colMaxDigit = (maxValue - rows) + column + 1
If column > 0 Then
output.Append(" ")
End If
digit = digit + 1
output.Append(digit.ToString().PadLeft(colMaxDigit.ToString().Length))
Next
output.AppendLine()
Next
Return output.ToString() End Function
Sub Main()
Dim args = Environment.GetCommandLineArgs()
Dim count As Integer
If args.Length > 1 AndAlso Integer.TryParse(args(1), count) AndAlso count > 0 Then
Console.WriteLine(MakeTriangle(count))
Else
Console.WriteLine(MakeTriangle(5))
Console.WriteLine()
Console.WriteLine(MakeTriangle(14))
End If
End Sub
End Module</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
Wren
<lang ecmascript>import "/fmt" for Fmt
var floyd = Fn.new { |n|
var k = 1
for (i in 1..n) {
for (j in 1..i) {
Fmt.write("$*d ", (j < 9) ? 2 : 3, k)
k = k + 1
}
System.print()
}
}
System.print("Floyd(5):") floyd.call(5) System.print("\nFloyd(14):") floyd.call(14)</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Floyd(14): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
XPL0
<lang XPL0>include c:\cxpl\codes; \include 'code' declarations
func IntLen(N); \Return number of digits in a positive integer int N; int I; for I:= 1 to 20 do
[N:= N/10; if N=0 then return I];
proc Floyd(N); \Display Floyd's triangle int N; int M, Row, Col; real F; [M:= (N-1+1)*(N-1)/2; \last Floyd number on second to last row F:= 1.0; \Floyd number counter for Row:= 1 to N do
[for Col:= 1 to Row do
[Format(IntLen(M+Col)+1, 0); RlOut(0, F); F:= F+1.0];
CrLf(0);
];
]; \Floyd
[Floyd(5); Floyd(14); ]</lang>
Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
zkl
Format last line and then fit each line to that format (which is wider than terminal width before formating breaks down (at 10 digit numbers)): <lang zkl>fcn lcNum(row){(row*(row+1)/2+1)} // lazy caterer's sequence fcn floydsTriangle(rows){
fmt:=[lcNum(rows-1)..lcNum(rows)-1].pump(String,fcn(n){
String("%",n.toString().len(),"d ")}); // eg "%2d %2d %3d %3d"
foreach row in (rows){
ns:=[lcNum(row)..lcNum(row+1)-1].walk(); // eg L(4.5,6)
fmt[0,ns.len()*4].fmt(ns.xplode()).println(); // eg "%2d %2d %2d ".fmt(4,5,6)
}
} floydsTriangle(5); println(); floydsTriangle(14);</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
ZX Spectrum Basic
<lang zxbasic>10 LET n=10: LET j=1: LET col=1 20 FOR r=1 TO n 30 FOR j=j TO j+r-1 40 PRINT TAB (col);j; 50 LET col=col+3 60 NEXT j 70 PRINT 80 LET col=1 90 NEXT r</lang>
- Programming Tasks
- Solutions by Programming Task
- 11l
- 360 Assembly
- 360 Assembly examples needing attention
- Examples needing attention
- Action!
- Ada
- ALGOL 68
- ALGOL W
- AppleScript
- Arturo
- Arturo examples needing attention
- AutoHotkey
- AWK
- BASIC
- Applesoft BASIC
- BASIC256
- BBC BASIC
- Commodore BASIC
- IS-BASIC
- IS-BASIC examples needing attention
- MasmBasic
- QBasic
- Yabasic
- Batch File
- BCPL
- Befunge
- Bracmat
- C
- C sharp
- C++
- Clojure
- CLU
- COBOL
- CoffeeScript
- Common Lisp
- Cowgol
- D
- Elixir
- Erlang
- ERRE
- Excel
- F Sharp
- Factor
- Forth
- Fortran
- FreeBASIC
- Gambas
- Go
- Groovy
- Haskell
- Icon
- Unicon
- J
- Java
- JavaScript
- Jq
- Julia
- Kotlin
- Lasso
- Lasso examples needing attention
- Liberty BASIC
- Lua
- Maple
- Mathematica
- Wolfram Language
- MATLAB
- Octave
- Modula-2
- NetRexx
- Nim
- OCaml
- OxygenBasic
- OxygenBasic examples needing attention
- PARI/GP
- Pascal
- Perl
- Phix
- PHP
- PicoLisp
- PL/I
- Prolog
- PureBasic
- Python
- Q
- Quackery
- R
- Racket
- Raku
- REXX
- Ring
- Ruby
- Run BASIC
- Rust
- Scala
- Seed7
- Sidef
- SPL
- Tcl
- TXR
- VBA
- VBScript
- Visual Basic .NET
- Wren
- Wren-fmt
- XPL0
- Zkl
- ZX Spectrum Basic