This small script uses combinatory analysis to figure out the optimal denominations for given number of possible coins to minimize the coins required to produce any amount between 1 cent and 1 dollar. The candidate set of denominations is reduced to keep the combinatory possibilities within reason.
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August 29, 2015 14:04
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Optimal denominations
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| // Candidate denominations | |
| var candidates = [0.02,0.03,0.04,0.05,0.06,0.7,0.08,0.09,0.10,0.12,0.13,0.15,0.20,0.25,0.30,0.35,0.40,0.45,0.50,0.60,0.7,0.8,0.9,1]; | |
| // All amounts between one cent and a dollar | |
| var amounts = Array | |
| .apply(0, Array(100)) | |
| .map(function (element, i) { | |
| return (i+1)/100; | |
| }); | |
| // Standard combinatory function | |
| function comb(c) { | |
| var n = candidates.length; | |
| var s=[]; | |
| function bitprint(u) { | |
| var s=[]; | |
| for (var n=0; u; ++n, u>>=1) | |
| if (u&1) s.push(candidates[n]); | |
| return s; | |
| } | |
| function bitcount(u) { | |
| for (var n=0; u; ++n, u=u&(u-1)); | |
| return n; | |
| } | |
| for (var u=0; u<1<<n; u++) | |
| if (bitcount(u)==c) | |
| s.push(bitprint(u)); | |
| return s; | |
| } | |
| // Roll through all combinations and pick minimum score | |
| function denom(n) { | |
| return comb(n-1) | |
| .reduce(function(p,c) { | |
| c = c.sort().reverse().concat(0.01); | |
| var score = amounts.reduce(function(p,s) { | |
| return p + c.reduce(function(p,d) { | |
| if (s > 0) { | |
| p += Math.floor(s/d); | |
| s = s % d; | |
| } | |
| return p; | |
| },0); | |
| },0); | |
| return (p && p.score < score) ? p : { score: score, denom: c}; | |
| }); | |
| } |
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <h1>Optimal denominations for a dollar</h1> | |
| <script src="denom.js"></script> | |
| <script> | |
| var numCoins = [2,3,4,5,6]; | |
| function next() { | |
| var n = numCoins.shift(); | |
| if (!n) return; | |
| var result = denom(n); | |
| var res = document.createElement('p'); | |
| res.textContent = n+' coins is: '+JSON.stringify(result.denom)+' with a score of '+result.score; | |
| document.body.appendChild(res); | |
| setTimeout(next) | |
| } | |
| setTimeout(next) | |
| </script> | |
| </html> |
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