Pascal's triangle: Difference between revisions

Line 309:

[1, 9, 36, 84, 126, 126, 84, 36, 9, 1]]);

}</lang>

Functional style:

<lang d>import std.stdio, std.algorithm, std.range;

auto pascal(int n) {

auto p = [[1]];

foreach (_; 0 .. n)

p ~= array(map!q{a[0] + a[1]}(zip(p[$-1] ~ 0, 0 ~ p[$-1])));

return p;

}

void main() {

writeln(pascal(5));

}</lang>

Output:

There is similarity between Pascal's triangle and [[Sierpinski triangle]]. Their difference are the initial line and the operation that act on the line element to produce next line. The following is a generic pascal's triangle implementation for positive number of lines output (n).

<lang d>import std.stdio, std.string, std.format : fmx = format ;

<lang d>import std.stdio, std.string, std.format : fmx = format;

string Pascal(alias dg, T, T initValue)(int n) {

string output ;

string output;

void append(T[] l) {

output ~= repeat(" ", (n - l.length + 1)*2) ;

output ~= repeat(" ", (n - l.length + 1)*2);

foreach(e; l) output ~= fmx("%4s", fmx("%4s",e)) ;

foreach(e; l) output ~= fmx("%4s", fmx("%4s",e));

output ~= "\n" ;

output ~= "\n";

}

if(n > 0) {

T[][] lines = [[initValue]] ;

T[][] lines = [[initValue]];

append(lines[0]) ;

append(lines[0]);

for(int i = 1 ; i < n ; i++) {

for(int i = 1; i < n; i++) {

lines ~= lines[i-1] ~ initValue ; // length + 1

lines ~= lines[i-1] ~ initValue; // length + 1

for(int j = 1 ; j < lines[i-1].length ; j++)

for(int j = 1; j < lines[i-1].length; j++)

lines[i][j] = dg(lines[i-1][j], lines[i-1][j-1]) ;

lines[i][j] = dg(lines[i-1][j], lines[i-1][j-1]);

append(lines[i]) ;

append(lines[i]);

}

return output ;

return output;

}

string delegate(int n) GenericPascal(alias dg, T, T initValue)(){

mixin Pascal!(dg, T, initValue) ;

mixin Pascal!(dg, T, initValue);

return &Pascal ;

return &Pascal;

}

char xor(char a, char b) { return a == b ? '_' : '*' ; }

char xor(char a, char b) { return a == b ? '_' : '*'; }

void main() {

auto pascal = GenericPascal!((int a, int b) { return a + b; }, int, 1) ;

auto pascal = GenericPascal!((int a, int b){return a + b;}, int, 1);

auto sierpinski = GenericPascal!(xor, char, '*') ;

auto sierpinski = GenericPascal!(xor, char, '*');

foreach(i ; [1,5,9]) writef(pascal(i)) ;

foreach(i; [1,5,9]) writef(pascal(i));

// an order 4 sierpinski triangle is a 2^4 lines generic

// pascal triangle with xor operation

foreach(i ; [16]) writef(sierpinski(i)) ;

foreach(i; [16]) writef(sierpinski(i));

}</lang>

Output: