Stem-and-leaf plot
You are encouraged to solve this task according to the task description, using any language you may know.
Create a well-formatted stem-and-leaf plot from the following data set, where the leaves are the last digits:
12 127 28 42 39 113 42 18 44 118 44 37 113 124 37 48 127 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58 114 126 53 114 96 25 109 7 31 141 46 13 27 43 117 116 27 7 68 40 31 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30 127 31 116 146
The primary intent of this task is the presentation of information. It is acceptable to hardcode the data set or characteristics of it (such as what the stems are) in the example, insofar as it is impractical to make the example generic to any data set. For example, in a computation-less language like HTML the data set may be entirely prearranged within the example; the interesting characteristics are how the proper visual formatting is arranged.
If possible, the output should not be a bitmap image. Monospaced plain text is acceptable, but do better if you can. It may be a window, i.e. not a file.
Note: If you wish to try multiple data sets, you might try this generator.
Ada
GNAT used for sorting, could use any other sorting method. Does not handle negative stems properly. <lang Ada> with Ada.Text_IO; use Ada.Text_IO; with Ada.Integer_Text_IO; use Ada.Integer_Text_IO; with Gnat.Heap_Sort_G; procedure stemleaf is data : array(Natural Range <>) of Integer := ( 0,12,127,28,42,39,113, 42,18,44,118,44,37,113,124,37,48,127,36,29,31, 125,139,131,115,105,132,104,123,35,113,122,42,117,119,58,109,23,105, 63,27,44,105,99,41,128,121,116,125,32,61,37,127,29,113,121,58,114,126, 53,114,96,25,109,7,31,141,46,13,27,43,117,116,27,7,68,40,31,115,124,42, 128,52,71,118,117,38,27,106,33,117,116,111,40,119,47,105,57,122,109, 124,115,43,120,43,27,27,18,28,48,125,107,114,34,133,45,120, 30,127, 31,116,146); -- Position 0 is used for storage during sorting, initialized as 0
procedure Move (from, to : in Natural) is begin data(to) := data(from); end Move;
function Cmp (p1, p2 : Natural) return Boolean is begin return data(p1)<data(p2); end Cmp;
package Sorty is new GNAT.Heap_Sort_G(Move,Cmp); min,max,p,stemw: Integer; begin Sorty.Sort(data'Last); min := data(1); max := data(data'Last); stemw := Integer'Image(max)'Length; p := 1; for stem in min/10..max/10 loop put(stem,Width=>stemw); put(" |"); Leaf_Loop: while data(p)/10=stem loop put(" "); put(data(p) mod 10,Width=>1); exit Leaf_loop when p=data'Last; p := p+1; end loop Leaf_Loop; new_line; end loop; end stemleaf; </lang> Output:
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
C
<lang c>#include <stdio.h>
- include <stdlib.h>
int dataset[] = {
12,127, 28, 42, 39,113, 42, 18, 44,118, 44, 37,113,124, 37, 48,127, 36,
29, 31,125,139,131,115,105,132,104,123, 35,113,122, 42,117,119, 58,109,
23,105, 63, 27, 44,105, 99, 41,128,121,116,125, 32, 61, 37,127, 29,113,
121, 58,114,126, 53,114, 96, 25,109, 7, 31,141, 46, 13, 27, 43,117,116,
27, 7, 68, 40, 31,115,124, 42,128, 52, 71,118,117, 38, 27,106, 33,117,
116,111, 40,119, 47,105, 57,122,109,124,115, 43,120, 43, 27, 27, 18, 28,
48,125,107,114, 34,133, 45,120, 30,127, 31,116,146
};
- define DATA_SIZE (sizeof(dataset)/sizeof(dataset[0]))
typedef struct valueNodeStruct *ValueNode;
struct valueNodeStruct {
int value; ValueNode left, right;
};
FILE *fout;
void DspyNodeList( ValueNode node, const char *fmat) {
if (NULL==node) return; DspyNodeList(node->left,fmat); fprintf(fout, fmat, node->value); DspyNodeList(node->right,fmat);
}
void doStemLeaf( int *dataset, int dssize, int dp) {
int ix; int maxd, mind, ngroups, x; int divsr = 1; ValueNode * groups; char fmat[16]; sprintf(fmat," %%%dd", dp );
mind = maxd= dataset[0];
for (ix=1; ix<dssize; ix++) {
if (maxd < dataset[ix]) maxd = dataset[ix];
if (mind > dataset[ix]) mind = dataset[ix];
}
x =(mind < 0) ? -1 : 0;
for (ix=dp; ix; ix--) {
maxd /= 10;
mind /= 10;
divsr *= 10;
}
mind += x;
ngroups = maxd - mind + 1;
groups = calloc(ngroups , sizeof(ValueNode));
for (ix=0; ix<dssize; ix++) {
int stemval, leafval;
ValueNode node, *np;
stemval = dataset[ix]/divsr;
leafval = dataset[ix]%divsr;
if (leafval < 0) { leafval += divsr; stemval -=1; } // fix broken % & / operators
node = malloc(sizeof(struct valueNodeStruct));
node->value = leafval;
node->left = node->right = NULL;
for (np = &groups[stemval-mind]; (*np);
np = (*np)->value < leafval? &((*np)->right) : &((*np)->left) );
*np = node;
}
for (ix=0; ix<ngroups; ix++) {
fprintf(fout,"\n%3d |", ix+mind);
DspyNodeList( groups[ix], fmat );
}
fprintf(fout,"\n\n");
}
int main()
{
fout = fopen("stemleaf.out", "w");
// fout = stdout;
doStemLeaf(dataset, DATA_SIZE, 1);
// doStemLeaf(dataset, DATA_SIZE, 2);
fclose(fout); return 0;
}
</lang>
Output:
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
D
<lang d>import std.stdio;
uint[] dataset = [ 111, 107, 100, 107, 115, 111, 97, 112, 104, 106, 113, 109, 113, 128, 128, 118, 113, 124, 127, 136, 106,123, 124,126, 116, 127, 119, 97, 102, 110, 120, 103, 115, 93, 123, 79, 119, 110, 110, 107, 105, 105, 110, 77, 90, 114, 106];
uint[][] plot; void main() {
uint stem;
foreach(number; dataset)
{
stem = number / 10;
if(plot.length <= stem)
plot.length = stem + 1; // could use an associative array, but this handles the blank stems for us
plot[stem] ~= number - stem * 10; // this discards all but the last digit
}
foreach(i, row; plot)
{
writef("%2d |", i);
foreach(leaf; row.sort)
writef(" %d", leaf);
writefln();
}
}</lang>
Output:
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
Forth
<lang forth>create data
12 , 127 , 28 , 42 , 39 , 113 , 42 , 18 , 44 , 118 , 44 , 37 , 113 , 124 , 37 , 48 , 127 , 36 , 29 , 31 , 125 , 139 , 131 , 115 , 105 , 132 , 104 , 123 , 35 , 113 , 122 , 42 , 117 , 119 , 58 , 109 , 23 , 105 , 63 , 27 , 44 , 105 , 99 , 41 , 128 , 121 , 116 , 125 , 32 , 61 , 37 , 127 , 29 , 113 , 121 , 58 , 114 , 126 , 53 , 114 , 96 , 25 , 109 , 7 , 31 , 141 , 46 , 13 , 27 , 43 , 117 , 116 , 27 , 7 , 68 , 40 , 31 , 115 , 124 , 42 , 128 , 52 , 71 , 118 , 117 , 38 , 27 , 106 , 33 , 117 , 116 , 111 , 40 , 119 , 47 , 105 , 57 , 122 , 109 , 124 , 115 , 43 , 120 , 43 , 27 , 27 , 18 , 28 , 48 , 125 , 107 , 114 , 34 , 133 , 45 , 120 , 30 , 127 , 31 , 116 , 146 ,
here constant data-end
- sort ( end start -- )
over cell - swap do
dup i cell+ do
i @ j @ < if
i @ j @ i ! j !
then
cell +loop
cell +loop drop ;
- plot
data-end data sort
data
data-end cell - @ 10 / 1+
data @ 10 /
do
cr i 2 u.r ." | "
begin dup @ 10 /mod i = while . cell+ dup data-end = until else drop then
loop
drop ;
plot</lang> Output:
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
Haskell
<lang haskell>import Data.List import Control.Arrow import Control.Monad
nlsRaw = "12 127 28 42 39 113 42 18 44 118 44 37 113 124 37 48 127 36 29 31"
++ " 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109 23 105 63" ++ " 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58 114 126 53" ++ " 114 96 25 109 7 31 141 46 13 27 43 117 116 27 7 68 40 31 115 124 42 128" ++ " 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 122 109 124 115" ++ " 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30 127 31 116 146"
nls :: [Int] nls = map read $ words nlsRaw
groupWith f = takeWhile(not.null). unfoldr(Just. (partition =<< (. f). (==). f. head)) justifyR = foldl ((. return) . (++) . tail) . flip replicate ' '
task ds = mapM_ (putStrLn. showStemLeaves justifyR fb. (head *** sort.concat). unzip)
$ groupWith fst $ stems ++ map (second return) stemLeaf where stemLeaf = map (`quotRem` 10) ds
stems = map (flip(,)[]) $ uncurry enumFromTo $ minimum &&& maximum $ fst $ unzip stemLeaf showStemLeaves f w (a,b) = f w (show a) ++ " |" ++ concatMap (f w. show) b fb = length $ show $ maximum $ map abs ds</lang> Output:
*Main> task nls 0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
HicEst
The dialog prompts for bitmap or a text image, and for the stem base. Data are read in from clipboard. <lang HicEst>REAL :: workspace(1000), base=16
DLG(CHeckbox=bitmap, NameEdit=base, DNum, MIn=1, MAx=16) ! 1 <= stem base <= 16 READ(ClipBoard, ItemS=nData) workspace ! get raw data
ALIAS(workspace,1, dataset,nData, stems,nData) SORT(Vector=dataset, Sorted=dataset) stems = (dataset - MOD(dataset,base)) / base dataset = dataset - base*stems max_stem = MAX(stems)
IF( bitmap ) AXIS() printed = 0 DO stem = 0, max_stem
last = INDEX(stems, stem, 4) ! option 4: search backward
IF( last > printed ) THEN
nLeaves = last - printed
IF(bitmap) THEN
LINE(PenUp=1,W=8, x=0, y=stem, x=nLeaves, y=stem)
ELSE
ALIAS(dataset,printed+1, leaves,nLeaves)
WRITE(Format="i3, ':', 100Z2") stem, leaves
ENDIF
printed = printed + nLeaves
ELSE
WRITE(Format="i3, ':'") stem
ENDIF
ENDDO</lang> Shown is the given example for bitmap=0 and base 16
0 : 7 7 C D 1 : 2 2 7 9 B B B B B B C C D D E F F F F 2 : 0 1 2 3 4 5 5 5 6 7 8 8 9 A A A A B B B C C C D E F 3 : 0 0 4 5 9 A A D F 4 : 4 7 5 : 6 : 0 3 8 9 9 9 9 A B D D D F 7 : 1 1 1 1 2 2 2 3 3 3 4 4 4 4 5 5 5 5 6 6 7 7 8 8 9 9 A A B C C C D D D E F F F F 8 : 0 0 3 4 5 B D 9 : 2
J
Solution: (Tacit) <lang j>stem =: <.@(%&10) leaf =: 10&| stemleaf =: (stem@{. ; leaf)/.~ stem expandStems =: <./ ([ + i.@>:@-~) >./ expandLeaves=: (expandStems e. ])@[ #inv ]
showStemLeaf=: (":@,.@expandStems@[ ; ":&>@expandLeaves)&>/@(>@{. ; <@{:)@|:@stemleaf@/:~</lang>
Solution: (Explicit) <lang j>stemleafX=: monad define
leaves=. 10 | y stems=. y <.@:% 10 leaves=. stems </. leaves NB. group leaves by stem (<"0 ~.stems),.leaves
)
showStemLeafX=: monad define
'stems leaves'=. (>@{. ; <@{:)@|: stemleafX /:~ y
xstems=. (<./ ([ + i.@>:@-~ ) >./) stems NB. stems including those with no leaves
xleaves=. (xstems e. stems) #inv leaves NB. expand leaves to match xstems
(": ,.xstems) ; ":&> xleaves
)</lang>
Example: <lang j> nls =: ; <@(_&".);._2 noun define 12 127 28 42 39 113 42 18 44 118 44 37 113 124 37 48 127 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58 114 126 53 114 96 25 109 7 31 141 46 13 27 43 117 116 27 7 68 40 31 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30 127 31 116 146 )
stemleaf nls NB. display has been abbreviated
┌──┬─────────────────────────────────────────────┐ │1 │2 8 3 8 │ ├──┼─────────────────────────────────────────────┤ │12│7 4 7 5 3 2 8 1 5 7 1 6 4 8 2 4 0 5 0 7 │ ├──┼─────────────────────────────────────────────┤ │2 │8 9 3 7 9 5 7 7 7 7 7 8 │ ...
showStemLeaf nls
┌──┬─────────────────────────────────────────────┐ │ 0│7 7 │ │ 1│2 3 8 8 │ │ 2│3 5 7 7 7 7 7 7 8 8 9 9 │ │ 3│0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 │ │ 4│0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 │ │ 5│2 3 7 8 8 │ │ 6│1 3 8 │ │ 7│1 │ │ 8│ │ │ 9│6 9 │ │10│4 5 5 5 5 6 7 9 9 9 │ │11│1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9│ │12│0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 │ │13│1 2 3 9 │ │14│1 6 │ └──┴─────────────────────────────────────────────┘
(showStemLeaf -: showStemLeafX) nls NB. both solutions give same result
1</lang>
JavaScript
It turns out that HTML+CSS renders the plot quite attractively.
<lang html4strict><!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <head> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" > <title>stem and leaf plot</title> <script type='text/javascript'>
function has_property(obj, propname) {
return typeof(obj[propname]) == "undefined" ? false : true;
}
function compare_numbers(a, b) {return a-b;}
function stemplot(data, target) {
var stem_data = {};
var all_stems = [];
for (var i = 0; i < data.length; i++) {
var stem = Math.floor(data[i] / 10);
var leaf = Math.round(data[i] % 10);
if (has_property(stem_data, stem)) {
stem_data[stem].push(leaf);
} else {
stem_data[stem] = [leaf];
all_stems.push(stem);
}
}
all_stems.sort(compare_numbers);
var min_stem = all_stems[0];
var max_stem = all_stems[all_stems.length - 1];
var table = document.createElement('table');
for (var stem = min_stem; stem <= max_stem; stem++) {
var row = document.createElement('tr');
var label = document.createElement('th');
row.appendChild(label);
label.appendChild(document.createTextNode(stem));
if (has_property(stem_data, stem)) {
stem_data[stem].sort(compare_numbers);
for (var i = 0; i < stem_data[stem].length; i++) {
var cell = document.createElement('td');
cell.appendChild(document.createTextNode(stem_data[stem][i]));
row.appendChild(cell);
}
}
table.appendChild(row);
}
target.appendChild(table);
}
</script> <style type='text/css'>
body {font-family: monospace;}
table {border-collapse: collapse;}
th {border-right: 1px solid black; text-align: right;}
td {text-align: right;}
</style> </head> <body>
<script type='text/javascript'>
var data = [
12,127,28,42,39,113,42,18,44,118,44,37,113,124,37,48,127,36,29,31,125,139,131,
115,105,132,104,123,35,113,122,42,117,119,58,109,23,105,63,27,44,105,99,41,128,
121,116,125,32,61,37,127,29,113,121,58,114,126,53,114,96,25,109,7,31,141,46,13,
27,43,117,116,27,7,68,40,31,115,124,42,128,52,71,118,117,38,27,106,33,117,116,
111,40,119,47,105,57,122,109,124,115,43,120,43,27,27,18,28,48,125,107,114,34,
133,45,120,30,127,31,116,146
];
stemplot(data, document.getElementById('target'));
</script>
</body> </html></lang>
The output looks like:
OCaml
The definition of the function unique below can be omited if one uses the extlib.
<lang ocaml>let unique li =
let rec aux acc = function
| [] -> (List.rev acc)
| x::xs ->
if List.mem x acc
then aux acc xs
else aux (x::acc) xs
in
aux [] li</lang>
<lang ocaml>let data =
[ 12; 127; 28; 42; 39; 113; 42; 18; 44; 118; 44; 37; 113; 124; 37; 48; 127; 36; 29; 31; 125; 139; 131; 115; 105; 132; 104; 123; 35; 113; 122; 42; 117; 119; 58; 109; 23; 105; 63; 27; 44; 105; 99; 41; 128; 121; 116; 125; 32; 61; 37; 127; 29; 113; 121; 58; 114; 126; 53; 114; 96; 25; 109; 7; 31; 141; 46; 13; 27; 43; 117; 116; 27; 7; 68; 40; 31; 115; 124; 42; 128; 52; 71; 118; 117; 38; 27; 106; 33; 117; 116; 111; 40; 119; 47; 105; 57; 122; 109; 124; 115; 43; 120; 43; 27; 27; 18; 28; 48; 125; 107; 114; 34; 133; 45; 120; 30; 127; 31; 116; 146 ]
let data =
List.map (fun d -> let a = d / 10 in let b = d mod 10 in (a, b) ) data
let keys =
List.sort compare (unique (List.map fst data))
let () =
List.iter (fun key -> Printf.printf " %2d |" key; let vs = List.filter (fun (a,_) -> a = key) data in let vs = List.sort compare (List.map snd vs) in List.iter (Printf.printf " %d") vs; print_newline() ) keys</lang>
we can output the same latex code than the Perl example replacing the main function as follow:
<lang ocaml>let () =
print_endline "\
\\documentclass{report} \\usepackage{fullpage} \\begin{document}
\\begin{tabular}{ r | *{120}{c} }";
List.iter (fun key -> Printf.printf " %d" key; let vs = List.filter (fun (a,_) -> a = key) data in let vs = List.sort compare (List.map snd vs) in List.iter (Printf.printf " & %d") vs; print_endline " \\\\" ) keys;
print_endline "\
\\end{tabular}
\\end{document}"</lang>
Perl generating LaTeX
<lang perl>#!/usr/bin/perl -w
my @data = sort {$a <=> $b} qw( 12 127 28 42 39 113 42 18 44 118 44 37 113 124 37 48 127 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58 114 126 53 114 96 25 109 7 31 141 46 13 27 43 117 116 27 7 68 40 31 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30 127 31 116 );
- FIXME: This should count the maximum number of leaves in any one stem;
- instead it takes the total number of data items, which is usually
- a massive overestimate.
my $columns = @data;
print <<"EOT"; \\documentclass{report} \\usepackage{fullpage} \\begin{document}
\\begin{tabular}{ r | *{$columns}{c} }
EOT
my $laststem = undef;
for my $value (@data) {
my $stem = int($value / 10);
my $leaf = $value % 10;
while (not defined $laststem or $stem > $laststem) {
if (not defined $laststem) {
$laststem = $stem - 1;
} else {
print " \\\\\n";
}
$laststem++;
print " $laststem";
}
printf " & $leaf";
} print <<'EOT';
\end{tabular}
\end{document} EOT</lang>
LaTeX output of the Perl program:
<lang latex>\documentclass{report} \usepackage{fullpage} \begin{document}
\begin{tabular}{ r | *{120}{c} }
0 & 7 & 7 \\
1 & 2 & 3 & 8 & 8 \\
2 & 3 & 5 & 7 & 7 & 7 & 7 & 7 & 7 & 8 & 8 & 9 & 9 \\
...
13 & 1 & 2 & 3 & 9 \\
14 & 1
\end{tabular}
\end{document}</lang>
The parameter to the tabular environment defines the columns of the table. “r” and “c” are right- and center-aligned columns, “|” is a vertical rule, and “*{count}{cols}” repeats a column definition count times.
To get from the program above to a rendered PDF,
perl ./Stem-perl.pl > plot.tex && pdflatex plot.tex
and the output will be in plot.pdf. Output.
Perl 6
Handles negative stems properly. <lang perl6>my @data = <
12 127 28 42 39 113 42 18 44 118 44
37 113 124 37 48 127 36 29 31 125 139
131 115 105 132 104 123 35 113 122 42 117
119 58 109 23 105 63 27 44 105 99 41
128 121 116 125 32 61 37 127 29 113 121
58 114 126 53 114 96 25 109 7 31 141
46 13 27 43 117 116 27 7 68 40 31
115 124 42 128 52 71 118 117 38 27 106
33 117 116 111 40 119 47 105 57 122 109
124 115 43 120 43 27 27 18 28 48 125
107 114 34 133 45 120 30 127 31 116 146
>».Int.sort;
my Int $stem_unit = 10; my %h = @data.classify: * div $stem_unit;
my $range = [minmax] %h.keys».Int; my $stem_format = "%{$range.from.chars max $range.to.chars}d";
for $range.list -> $stem {
my $leafs = %h{$stem} // [];
say $stem.fmt($stem_format), ' | ', ~$leafs.map: * % $stem_unit;
}</lang>
Output:
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
PicoLisp
<lang PicoLisp>(de *Data
12 127 28 42 39 113 42 18 44 118 44 37 113 124 37 48 127 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58 114 126 53 114 96 25 109 7 31 141 46 13 27 43 117 116 27 7 68 40 31 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30 127 31 116 146 )
(let L
(group
(mapcar
'((N)
(cons
(or (format (head -1 (setq N (chop N)))) 0)
(last N) ) )
(sort *Data) ) )
(for I (range (caar L) (car (last L)))
(prinl (align 3 I) " | " (glue " " (cdr (assoc I L)))) ) )</lang>
Output:
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
PureBasic
PureBasic Code <lang PureBasic>If OpenConsole()
Dim MyList(120)
Define i, j, StemMax, StemMin
Restore MyData ; Get the address of MyData, e.g. the data to print as a Stem-and-leaf plot
For a=0 To 120
Read.i MyList(a) ; Read the data into the used Array
If MyList(a)>StemMax
StemMax=MyList(a) ; Find the largest Stem layer at the same time
EndIf
If MyList(a)<StemMin
StemMin=MyList(a) ; Find the smallest Stem layer at the same time
EndIf
Next
StemMax/10: StemMin/10 ; Remove the leafs from the Stem limits
SortArray(MyList(),#PB_Sort_Ascending) ; Sort the data
For i=StemMin To StemMax
Print(RSet(Str(i),3)+" | ") ; Print the Stem
For j=0 To 120
If MyList(j)<10*i ; Skip all smaller then current
Continue
ElseIf MyList(j)>=10*(i+1) ; Break current print if a new Stem layer is reached
Break
Else
Print(Str(MyList(j)%10)+" ") ; Print all Leafs on this current Stem layer
EndIf
Next j
PrintN("")
Next i
Print(#CRLF$+#CRLF$+"Press ENTER to exit")
Input()
CloseConsole()
EndIf
DataSection MyData:
Data.i 12,127, 28, 42, 39,113, 42, 18, 44,118, 44, 37,113,124, 37, 48,127, 36, 29, 31,125,139,131,115 Data.i 105,132,104,123, 35,113,122, 42,117,119, 58,109, 23,105, 63, 27, 44,105, 99, 41,128,121,116,125 Data.i 32, 61, 37,127, 29,113,121, 58,114,126, 53,114, 96, 25,109, 7, 31,141, 46, 13, 27, 43,117,116 Data.i 27, 7, 68, 40, 31,115,124, 42,128, 52, 71,118,117, 38, 27,106, 33,117,116,111, 40,119, 47,105 Data.i 57,122,109,124,115, 43,120, 43, 27, 27, 18, 28, 48,125,107,114, 34,133, 45,120, 30,127, 31,116,146
EndDataSection</lang>
Output
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
Python
Adjusting Stem.leafdigits allows you to modify how many digits of a value are used in the leaf, with the stem intervals adjusted accordingly.
<lang python>from collections import namedtuple
from pprint import pprint as pp
from math import floor
Stem = namedtuple('Stem', 'data, leafdigits')
data0 = Stem((12, 127, 28, 42, 39, 113, 42, 18, 44, 118, 44, 37, 113, 124, 37,
48, 127, 36, 29, 31, 125, 139, 131, 115, 105, 132, 104, 123, 35,
113, 122, 42, 117, 119, 58, 109, 23, 105, 63, 27, 44, 105, 99,
41, 128, 121, 116, 125, 32, 61, 37, 127, 29, 113, 121, 58, 114,
126, 53, 114, 96, 25, 109, 7, 31, 141, 46, 13, 27, 43, 117, 116,
27, 7, 68, 40, 31, 115, 124, 42, 128, 52, 71, 118, 117, 38, 27,
106, 33, 117, 116, 111, 40, 119, 47, 105, 57, 122, 109, 124, 115,
43, 120, 43, 27, 27, 18, 28, 48, 125, 107, 114, 34, 133, 45, 120,
30, 127, 31, 116, 146),
1.0)
def stemplot(stem):
d = []
interval = int(10**int(stem.leafdigits))
for data in sorted(stem.data):
data = int(floor(data))
stm, lf = divmod(data,interval)
d.append( (int(stm), int(lf)) )
stems, leafs = list(zip(*d))
stemwidth = max(len(str(x)) for x in stems)
leafwidth = max(len(str(x)) for x in leafs)
laststem, out = min(stems) - 1, []
for s,l in d:
while laststem < s:
laststem += 1
out.append('\n%*i |' % ( stemwidth, laststem))
out.append(' %0*i' % (leafwidth, l))
out.append('\n\nKey:\n Stem multiplier: %i\n X | Y => %i*X+Y\n'
% (interval, interval))
return .join(out)
if __name__ == '__main__':
print( stemplot(data0) )</lang>
Sample Output
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6 Key: Stem multiplier: 10 X | Y => 10*X+Y
R
<lang R> x <- c(12, 127, 28, 42, 39, 113, 42, 18, 44, 118, 44, 37, 113, 124, 37, 48, 127, 36, 29, 31, 125, 139, 131, 115, 105, 132, 104, 123, 35, 113, 122, 42, 117, 119, 58, 109, 23, 105, 63, 27, 44, 105, 99, 41, 128, 121, 116, 125, 32, 61, 37, 127, 29, 113, 121, 58, 114, 126, 53, 114, 96, 25, 109, 7, 31, 141, 46, 13, 27, 43, 117, 116, 27, 7, 68, 40, 31, 115, 124, 42, 128, 52, 71, 118, 117, 38, 27, 106, 33, 117, 116, 111, 40, 119, 47, 105, 57, 122, 109, 124, 115, 43, 120, 43, 27, 27, 18, 28, 48, 125, 107, 114, 34, 133, 45, 120, 30, 127, 31, 116, 146)
stem(x) </lang>
Output :
0 | 77 1 | 2388 2 | 357777778899 3 | 011112345677789 4 | 001222233344456788 5 | 23788 6 | 138 7 | 1 8 | 9 | 69 10 | 4555567999 11 | 13333444555666677778899 12 | 00112234445556777788 13 | 1239 14 | 16
Ruby
This implementation will handle negative values. <lang ruby>class StemLeafPlot
def initialize(data, options = {})
opts = {:leaf_digits => 1}.merge(options)
@leaf_digits = opts[:leaf_digits]
@multiplier = 10 ** @leaf_digits
@plot = generate_structure(data)
end
private
def generate_structure(data)
plot = Hash.new {|h,k| h[k] = []}
data.sort.each do |value|
stem, leaf = parse(value)
plot[stem] << leaf
end
plot
end
def parse(value) stem, leaf = value.abs.divmod(@multiplier) [Stem.get(stem, value), leaf.round] end
public
def print
stem_width = Math.log10(@plot.keys.max_by {|s| s.value}.value).ceil + 1
Stem.get_range(@plot.keys).each do |stem|
leaves = @plot[stem].inject("") {|str,leaf| str << "%*d " % [@leaf_digits, leaf]}
puts "%*s | %s" % [stem_width, stem, leaves]
end
puts "key: 5|4=#{5 * @multiplier + 4}"
puts "leaf unit: 1"
puts "stem unit: #@multiplier"
end
end
class Stem
@@cache = {}
def self.get(stem_value, datum) sign = datum < 0 ? :- : :+ cache(stem_value, sign) end private def self.cache(value, sign) if @@cachevalue, sign.nil? @@cachevalue, sign = self.new(value, sign) end @@cachevalue, sign end
def initialize(value, sign) @value = value @sign = sign end public attr_accessor :value, :sign def negative? @sign == :- end
def <=>(other)
if self.negative?
if other.negative?
other.value <=> self.value
else
-1
end
else
if other.negative?
1
else
self.value <=> other.value
end
end
end
def to_s
"%s%d" % [(self.negative? ? '-' : ' '), @value]
end
def self.get_range(array_of_stems)
min, max = array_of_stems.minmax
if min.negative?
if max.negative?
min.value.downto(max.value).collect {|n| cache(n, :-)}
else
min.value.downto(0).collect {|n| cache(n, :-)} + 0.upto(max.value).collect {|n| cache(n, :+)}
end
else
min.value.upto(max.value).collect {|n| cache(n, :+)}
end
end
end
data = DATA.read.split.map {|s| Float(s)} StemLeafPlot.new(data).print
__END__ 12 127 28 42 39 113 42 18 44 118 44 37 113 124 37 48 127 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58 114 126 53 114 96 25 109 7 31 141 46 13 27 43 117 116 27 7 68 40 31 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30 127 31 116 146</lang>
outputs
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6 key: 5|4=54 leaf unit: 1 stem unit: 10
Scala
<lang scala>def stemAndLeaf(numbers: List[Int]) = {
val lineFormat = "%" + (numbers map (_.toString.length) max) + "d | %s"
val map = numbers groupBy (_ / 10)
for (stem <- numbers.min / 10 to numbers.max / 10) {
println(lineFormat format (stem, map.getOrElse(stem, Nil) map (_ % 10) sortBy identity mkString " "))
}
}</lang>
Example:
scala> val list = """12 127 28 42 39 113 42 18 44 118 44 37 113 124 37 48 127 36 29 31 125 139 131 115 105
132 104 123 35 113 122 42 117 119 58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121
58 114 126 53 114 96 25 109 7 31 141 46 13 27 43 117 116 27 7 68 40 31 115 124 42 128 52 71 118 117
38 27 106 33 117 116 111 40 119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45
120 30 127 31 116
| 146""" split "\\s+" map (_.toInt) toList
list: List[Int] = List(12, 127, 28, 42, 39, 113, 42, 18, 44, 118, 44, 37, 113, 124, 37, 48, 127, 36, 29, 31, 125, 139, 1
31, 115, 105, 132, 104, 123, 35, 113, 122, 42, 117, 119, 58, 109, 23, 105, 63, 27, 44, 105, 99, 41, 128, 121, 116, 125,
32, 61, 37, 127, 29, 113, 121, 58, 114, 126, 53, 114, 96, 25, 109, 7, 31, 141, 46, 13, 27, 43, 117, 116, 27, 7, 68, 40,
31, 115, 124, 42, 128, 52, 71, 118, 117, 38, 27, 106, 33, 117, 116, 111, 40, 119, 47, 105, 57, 122, 109, 124, 115, 43, 1
20, 43, 27, 27, 18, 28, 48, 125, 107, 114, 34, 133, 45, 120, 30, 127, 31, 116, 146)
scala> stemAndLeaf(list)
0 | 7 7
1 | 2 3 8 8
2 | 3 5 7 7 7 7 7 7 8 8 9 9
3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9
4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8
5 | 2 3 7 8 8
6 | 1 3 8
7 | 1
8 |
9 | 6 9
10 | 4 5 5 5 5 6 7 9 9 9
11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9
12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8
13 | 1 2 3 9
14 | 1 6
Tcl
<lang tcl>package require Tcl 8.5
- How to process a single value, adding it to the table mapping stems to
- leaves.
proc addSLValue {tblName value {splitFactor 10}} {
upvar 1 $tblName tbl
# Extract the stem and leaf
if {$value < 0} {
set value [expr {round(-$value)}] set stem -[expr {$value / $splitFactor}]
} else {
set value [expr {round($value)}] set stem [expr {$value / $splitFactor}]
}
if {![info exist tbl]} {
dict set tbl min $stem
}
dict set tbl max $stem
set leaf [expr {$value % $splitFactor}]
dict lappend tbl $stem $leaf
}
- How to do the actual output of the stem-and-leaf table, given that we have
- already done the splitting into stems and leaves.
proc printSLTable {tblName} {
upvar 1 $tblName tbl
# Get the range of stems
set min [dict get $tbl min]
set max [dict get $tbl max]
# Work out how much width the stems take so everything lines up
set l [expr {max([string length $min], [string length $max])}]
# Print out the table
for {set i $min} {$i <= $max} {incr i} {
if {![dict exist $tbl $i]} { puts [format " %*d |" $l $i] } else { puts [format " %*d | %s" $l $i [dict get $tbl $i]] }
}
}
- Assemble the parts into a full stem-and-leaf table printer.
proc printStemLeaf {dataList {splitFactor 10}} {
foreach value [lsort -real $dataList] {
addSLValue tbl $value $splitFactor
} printSLTable tbl
}
- Demo code
set data {
12 127 28 42 39 113 42 18 44 118 44 37 113 124 37 48 127 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58 114 126 53 114 96 25 109 7 31 141 46 13 27 43 117 116 27 7 68 40 31 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30 127 31 116 146
} printStemLeaf $data</lang> Output:
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6
Ursala
<lang Ursala>#import std
- import nat
data =
<
12,127,28,42,39,113,42,18,44,118,44,37,113,124,37,48,127,36,29,31,125,139,131, 115,105,132,104,123,35,113,122,42,117,119,58,109,23,105,63,27,44,105,99,41,128, 121,116,125,32,61,37,127,29,113,121,58,114,126,53,114,96,25,109,7,31,141,46,13, 27,43,117,116,27,7,68,40,31,115,124,42,128,52,71,118,117,38,27,106,33,117,116, 111,40,119,47,105,57,122,109,124,115,43,120,43,27,27,18,28,48,125,107,114,34, 133,45,120,30,127,31,116,146>
stemleaf_plot =
^|T(~&,' | '--)*+ -+
^p(pad` @hS; * ==` ~-rlT,mat` *tS)@hSS+ (%nP*)^|*H/~& ^lrNCT/iota ~&, ^(*+ ^C/~&+ -:0!,~&zl)+ ^|(~&,nleq-<)*+ nleq-<&l@lK2hlPrSXS+ * division\10+-
- show+
main = stemleaf_plot data</lang>
Reading from right to left on the bottom line of the stemleaf_plot function, we
obtain the quotient and remainder of every datum divided by ten, partition by
quotients, sort the partitions and sort within each partition,
make a note of the maximum quotient, and reify the table into a function.
From right to left on the line above, we apply the reified function to each number up to the maximum quotient (i.e., including 8 which wasn't in the original table), convert each number to a string, flatten each leaf list with spaces as separators, and right justify the stem list.
The remaining top line forms the concatenation of each stem with its flattened leaf list and a vertical bar between them.
output:
0 | 7 7 1 | 2 3 8 8 2 | 3 5 7 7 7 7 7 7 8 8 9 9 3 | 0 1 1 1 1 2 3 4 5 6 7 7 7 8 9 4 | 0 0 1 2 2 2 2 3 3 3 4 4 4 5 6 7 8 8 5 | 2 3 7 8 8 6 | 1 3 8 7 | 1 8 | 9 | 6 9 10 | 4 5 5 5 5 6 7 9 9 9 11 | 1 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 7 8 8 9 9 12 | 0 0 1 1 2 2 3 4 4 4 5 5 5 6 7 7 7 7 8 8 13 | 1 2 3 9 14 | 1 6