164 lines
7.5 KiB
Markdown
164 lines
7.5 KiB
Markdown
---
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id: 5a23c84252665b21eecc7ed1
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title: Knapsack problem/0-1
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challengeType: 5
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forumTopicId: 323649
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---
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## Description
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<section id='description'>
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The 0-1 knapsack problem is defined as follows:
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You are given an array of objects representing items to be put in a knapsack. The objects have 3 attributes: name, weight, and value. The items need to be selected so that the total weight does not exceed the maximum weight and the value is maximized.
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</section>
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## Instructions
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<section id='instructions'>
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Write a function to solve the knapsack problem. The function is given the array of objects and the maximum weight as parameters. It should return the maximum total value possible.
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 100)</code> should return <code>405</code>.
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testString: assert.equal(knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 100), 405);
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- text: <code>knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 200)</code> should return <code>510</code>.
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testString: assert.equal(knapsack([{ name:'map', weight:9, value:150 }, { name:'compass', weight:13, value:35 }, { name:'water', weight:153, value:200 }, { name:'sandwich', weight:50, value:160 }, { name:'glucose', weight:15, value:60 }, { name:'tin', weight:68, value:45 }, { name:'banana', weight:27, value:60 }, { name:'apple', weight:39, value:40 }], 200), 510);
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- text: <code>knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 100)</code> should return <code>145</code>.
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testString: assert.equal(knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 100), 145);
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- text: <code>knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 200)</code> should return <code>185</code>.
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testString: assert.equal(knapsack([{ name:'cheese', weight:23, value:30 }, { name:'beer', weight:52, value:10 }, { name:'suntan cream', weight:11, value:70 }, { name:'camera', weight:32, value:30 }, { name:'T-shirt', weight:24, value:15 }, { name:'trousers', weight:48, value:10 }, { name:'umbrella', weight:73, value:40 }], 200), 185);
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- text: <code>knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 100)</code> should return <code>237</code>.
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testString: assert.equal(knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 100), 237);
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- text: <code>knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 200)</code> should return <code>317</code>.'
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testString: assert.equal(knapsack([{ name:'waterproof trousers', weight:42, value:70 }, { name:'waterproof overclothes', weight:43, value:75 }, { name:'note-case', weight:22, value:80 }, { name:'sunglasses', weight:7, value:20 }, { name:'towel', weight:18, value:12 }, { name:'socks', weight:4, value:50 }, { name:'book', weight:30, value:10 }], 200), 317);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function knapsack(items, maxweight) {
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function knapsack(items, maxweight) {
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var _ = {
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max: function(e) {
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var mx = e[0];
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e.forEach(function(f) {
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if (mx < f) mx = f;
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});
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return mx;
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},
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map: function(array, func) {
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return array.map(func);
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},
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isUndefined: function(a) {
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if (a) {
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return false;
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}
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return true;
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},
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range: function(start, end, step) {
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var a = [];
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var f = (f = (i, end) => i < end);
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if (start > end) f = (i, end) => i > end;
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for (var i = start; f(i, end); i += step) a.push(i);
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return a;
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}
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};
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var valuefn = e => e.value;
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var weightfn = e => e.weight;
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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 (
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included.totalValue + Math.floor(valuefn(item) / _k) >
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excluded.totalValue
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) {
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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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}
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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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var scaled = _m(items.length - 1, maxweight);
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var val = 0;
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scaled.items.forEach(function(e) {
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val += e.value;
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});
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return val;
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}
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```
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</section>
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