Floyd's triangle
Floyd's triangle lists the natural numbers in a right triangle aligned to the left where
- the first row is just 1
- 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
The task is to:
- 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 monospace font, the numbers line up in vertical columns as shown and that only one space separates numbers of the last row.
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
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>
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>
Python
<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>
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