Idea from http://blog.stevenlevithan.com/archives/algebra-with-regexes. The function returns only one of the solutions, and returns an empty string if there are no solutions. I had never thought that RegExp is so powerful...
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solveAlgebraicEquation (using RegExp)
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| function( | |
| a, // the set of variables | |
| b, // the sum | |
| c, // placeholder | |
| d, // placeholder | |
| e // placeholder | |
| ){ | |
| c = '^'; | |
| for (d = 0; e = a[d++];) | |
| c += '(,*)\\' + d + '{' + ~-e + '}' // part of the RegExp pattern. | |
| return ( | |
| ( | |
| Array(-~b) + '' // let b plus one and coerce the array into a string that consists of commas. | |
| ).match(c + '$') | |
| || | |
| '' // if no matches, go to an empty string. | |
| ).slice(1) // shift the matched whole substring or do nothing when no matches. | |
| } |
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| function(a,b,c,d,e){c="^";for(d=0;e=a[d++];)c+="(,*)\\"+d+"{"+~-e+"}";return((Array(-~b)+"").match(c+"$")||"").slice(1)} |
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| DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE | |
| Version 2, December 2004 | |
| Copyright (C) 2011 YOUR_NAME_HERE <YOUR_URL_HERE> | |
| Everyone is permitted to copy and distribute verbatim or modified | |
| copies of this license document, and changing it is allowed as long | |
| as the name is changed. | |
| DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE | |
| TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION | |
| 0. You just DO WHAT THE FUCK YOU WANT TO. |
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| { | |
| "name": "solveAlgebraicEquation", | |
| "description": "Solve algebraic equation with RegExp", | |
| "keywords": [ | |
| "solveAlgebraicEquation", | |
| "algebraic equation", | |
| "RegExp" | |
| ] | |
| } |
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| <!DOCTYPE html> | |
| <title>solveAlgebraicEquation</title> | |
| <div>Output: <b id="ret"></b></div> | |
| <script> | |
| var myFunction = function(a,b,c,d,e){c="^";for(d=0;e=a[d++];)c+="(,*)\\"+d+"{"+~-e+"}";return((Array(-~b)+"").match(c+"$")||"").slice(1)}; | |
| // The input should be ([a, b, c, ...], sum) | |
| // e.g. Solve 11x + 2y + 5z = 115 | |
| var solution = myFunction([11, 2, 5], 115); | |
| document.getElementById( "ret" ).innerHTML = 'One of the solutions of 11x + 2y + 5z = 115 is x = ' + | |
| solution[0].length + ', y = ' + | |
| solution[1].length + ', z = ' + | |
| solution[2].length; | |
| </script> |
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You can leave out the "RegExp", since the arguments of match get coerced to RegExp anyway. So it is:
function(a,b,c,d,e){c="^";for(d=0;e=a[d++];)c+="(,*)\\"+d+"{"+~-e+"}";return((Array(-~b)+"").match(c+"$")||"").slice(1)};