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Task/Knapsack-problem-0-1/JavaScript/knapsack-problem-0-1-1.js
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Task/Knapsack-problem-0-1/JavaScript/knapsack-problem-0-1-1.js
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/*global portviz:false, _:false */
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/*
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* 0-1 knapsack solution, recursive, memoized, approximate.
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*
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* credits:
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*
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* the Go implementation here:
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* http://rosettacode.org/mw/index.php?title=Knapsack_problem/0-1
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*
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* approximation details here:
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* http://math.mit.edu/~goemans/18434S06/knapsack-katherine.pdf
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*/
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portviz.knapsack = {};
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(function() {
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this.combiner = function(items, weightfn, valuefn) {
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// approximation guarantees result >= (1-e) * optimal
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var _epsilon = 0.01;
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var _p = _.max(_.map(items,valuefn));
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var _k = _epsilon * _p / items.length;
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var _memo = (function(){
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var _mem = {};
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var _key = function(i, w) {
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return i + '::' + w;
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};
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return {
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get: function(i, w) {
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return _mem[_key(i,w)];
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},
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put: function(i, w, r) {
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_mem[_key(i,w)]=r;
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return r;
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}
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};
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})();
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var _m = function(i, w) {
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i = Math.round(i);
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w = Math.round(w);
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if (i < 0 || w === 0) {
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// empty base case
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return {items: [], totalWeight: 0, totalValue: 0};
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}
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var mm = _memo.get(i,w);
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if (!_.isUndefined(mm)) {
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return mm;
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}
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var item = items[i];
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if (weightfn(item) > w) {
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//item does not fit, try the next item
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return _memo.put(i, w, _m(i-1, w));
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}
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// this item could fit.
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// are we better off excluding it?
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var excluded = _m(i-1, w);
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// or including it?
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var included = _m(i-1, w - weightfn(item));
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if (included.totalValue + Math.floor(valuefn(item)/_k) > excluded.totalValue) {
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// better off including it
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// make a copy of the list
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var i1 = included.items.slice();
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i1.push(item);
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return _memo.put(i, w,
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{items: i1,
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totalWeight: included.totalWeight + weightfn(item),
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totalValue: included.totalValue + Math.floor(valuefn(item)/_k)});
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}
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//better off excluding it
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return _memo.put(i,w, excluded);
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};
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return {
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/* one point */
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one: function(maxweight) {
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var scaled = _m(items.length - 1, maxweight);
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return {
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items: scaled.items,
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totalWeight: scaled.totalWeight,
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totalValue: scaled.totalValue * _k
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};
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},
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/* the entire EF */
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ef: function(maxweight, step) {
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return _.map(_.range(0, maxweight+1, step), function(weight) {
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var scaled = _m(items.length - 1, weight);
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return {
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items: scaled.items,
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totalWeight: scaled.totalWeight,
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totalValue: scaled.totalValue * _k
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};
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});
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}
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};
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};
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}).apply(portviz.knapsack);
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/*global portviz:false, _:false */
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/*
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* after rosettacode.org/mw/index.php?title=Knapsack_problem/0-1
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*/
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var allwants = [
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{name:"map", weight:9, value: 150},
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{name:"compass", weight:13, value: 35},
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{name:"water", weight:153, value: 200},
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{name:"sandwich", weight: 50, value: 160},
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{name:"glucose", weight:15, value: 60},
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{name:"tin", weight:68, value: 45},
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{name:"banana", weight:27, value: 60},
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{name:"apple", weight:39, value: 40},
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{name:"cheese", weight:23, value: 30},
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{name:"beer", weight:52, value: 10},
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{name:"suntan cream", weight:11, value: 70},
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{name:"camera", weight:32, value: 30},
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{name:"T-shirt", weight:24, value: 15},
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{name:"trousers", weight:48, value: 10},
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{name:"umbrella", weight:73, value: 40},
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{name:"waterproof trousers", weight:42, value: 70},
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{name:"waterproof overclothes", weight:43, value: 75},
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{name:"note-case", weight:22, value: 80},
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{name:"sunglasses", weight:7, value: 20},
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{name:"towel", weight:18, value: 12},
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{name:"socks", weight:4, value: 50},
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{name:"book", weight:30, value: 10}
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];
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var near = function(actual, expected, tolerance) {
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if (expected === 0 && actual === 0) return true;
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if (expected === 0) {
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return Math.abs(expected - actual) / actual < tolerance;
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}
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return Math.abs(expected - actual) / expected < tolerance;
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};
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test("one knapsack", function() {
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var combiner =
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portviz.knapsack.combiner(allwants,
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function(x){return x.weight;},
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function(x){return x.value;});
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var oneport = combiner.one(400);
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ok(near(oneport.totalValue, 1030, 0.01), "correct total value");
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ok(near(oneport.totalValue, 1030, 0.01), "correct total value");
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equal(oneport.totalWeight, 396, "correct total weight");
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});
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test("frontier", function() {
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var combiner =
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portviz.knapsack.combiner(allwants,
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function(x){return x.weight;},
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function(x){return x.value;});
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var ef = combiner.ef(400, 1);
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equal(ef.length, 401, "401 because it includes the endpoints");
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ef = combiner.ef(400, 40);
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equal(ef.length, 11, "11 because it includes the endpoints");
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var expectedTotalValue = [
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0,
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330,
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445,
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590,
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685,
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755,
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810,
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860,
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902,
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960,
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1030
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] ;
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_.each(ef, function(element, index) {
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// 15% error! bleah!
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ok(near(element.totalValue, expectedTotalValue[index], 0.15),
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'actual ' + element.totalValue + ' expected ' + expectedTotalValue[index]);
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});
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deepEqual(_.pluck(ef, 'totalWeight'), [
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0,
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39,
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74,
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118,
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158,
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200,
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236,
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266,
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316,
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354,
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396
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]);
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deepEqual(_.map(ef, function(x){return x.items.length;}), [
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0,
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4,
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6,
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7,
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9,
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10,
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10,
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12,
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14,
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11,
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12
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]);
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});
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@ -0,0 +1,68 @@
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<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<meta http-equiv="X-UA-Compatible" content="ie=edge">
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<title>KNAPSACK 22 JavaScript</title> </head> <body> <noscript>Vkluch JS</noscript>
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https://jdoodle.com/h/2Ut
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rextester.com/BQYV50962
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<script>
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var n=22; G=400; a = Math.pow(2,n+1); // KNAPSACKj.js
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var dec, i, h, k, max, m, s;
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var L=[n], C=[n], j=[n], q=[a], d=[a]; e=[a];
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document.write("<br><br># Kol Cena<br>")
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document.write("# Amo Price<br><br>")
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L=[ 9,13,153,50,15,68,27,39,23,52,11,32,24,48,73,42,43,22,7,18,4,30 ]
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C=[ 150,35,200,160,60,45,60,40,30,10,70,30,15,10,40,70,75,80,20,12,50,10 ]
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for (i=0; i<n; i++)
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{ // L[i]=1+Math.floor(Math.random()*3)
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// C[i]=10+Math.floor(Math.random()*9);
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j[i]=0;
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document.write( (i+1) +" "+ L[i] +" "+ C[i] +"<br>")
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}
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for (i=0; i<a; i++) { q[i]=0; d[i]=0;}
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document.write("<br>")
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document.write("Mx Kol St-st Schifr<br>")
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document.write("Mx Amo Price Cipher<br>")
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for (h = a-1; h>(a-1)/2; h--)
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{ dec=h; e[h]=""
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while (dec > 0)
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{ s = Math.floor(dec % 2);
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e[h] = s + e[h]; dec = Math.floor(dec/2);
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}
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if (e[h] == "") {e[h] = "0";}
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e[h]= e[h].substr(1, e[h].length-1);
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for (k=0; k<n; k++)
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{ j[k] = Number(e[h].substr(k,1));
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q[h]=q[h]+j[k]*C[k];
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d[h]=d[h]+L[k]*j[k];
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}
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// if (d[h] <= G)
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// document.write("<br>"+ G +" "+ d[h] +" "+ q[h] +" "+ e[h])
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} document.write("<br>")
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max=0; m=1;
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for (i=0; i<a; i++)
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{ if (d[i]<=G && q[i]>max){ max=q[i]; m=i;}
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}
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document.write("<br>"+ d[m] +" "+ q[m] +" "+ e[m] +"<br><br>")
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document.write("Mx St-st Schifr<br>")
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document.write("Mx Price Cipher<br><br>")
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</script>
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</body> </html>
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