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Pascal's Triangle
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| /* | |
| Pascal's Triangle | |
| usage: | |
| triangle(<number of levels to display>) | |
| returns: | |
| one string for each level of pyramid followed by a newline | |
| */ | |
| // eg. sequence(4) returns [0,1,2,3,4] | |
| var sequence = (function() { | |
| var cache = {}; | |
| function seq(end) { | |
| if (cache[end] !== undefined) { | |
| return cache[end]; | |
| } | |
| var result = []; | |
| for (var i = 0; i <= end; i++) { | |
| result.push(i); | |
| cache[i] = Object.assign([], result); | |
| } | |
| return result; | |
| } | |
| return seq; | |
| })(); | |
| // eg. factorial(4) returns result of 1*2*3*4 | |
| var factorial = (function() { | |
| var cache = {}; | |
| function fac(number) { | |
| if (cache[number] !== undefined) { | |
| return cache[number]; | |
| } | |
| var result = sequence(number) | |
| .filter(function(item) { | |
| return item > 1; | |
| }) | |
| .reduce(function(prev, next) { | |
| return prev * next; | |
| }, 1); | |
| cache[number] = result; | |
| return result; | |
| } | |
| return fac; | |
| })(); | |
| function nChooseK(n, k) { | |
| var num = factorial(n); | |
| var denom = factorial(k) * factorial(n - k); | |
| return num / denom; | |
| } | |
| function row(number) { | |
| var result = sequence(number) | |
| .map(function(item) { | |
| return nChooseK(number, item); | |
| }, '') | |
| .join(' '); | |
| return result; | |
| } | |
| function triangle(height) { | |
| var result = sequence(height) | |
| .reduce(function(prev, next) { | |
| return prev + row(next) + '\n' | |
| }, ''); | |
| return result; | |
| } |
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