256 lines
7.6 KiB
Markdown
256 lines
7.6 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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dashedName: knapsack-problem0-1
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---
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# --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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# --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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# --hints--
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`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)` should return `405`.
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```js
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assert.equal(
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knapsack(
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[
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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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],
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100
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),
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405
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);
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```
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`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)` should return `510`.
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```js
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assert.equal(
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knapsack(
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[
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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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],
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200
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),
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510
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);
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```
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`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)` should return `145`.
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```js
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assert.equal(
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knapsack(
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[
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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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],
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100
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),
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145
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);
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```
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`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)` should return `185`.
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```js
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assert.equal(
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knapsack(
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[
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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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],
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200
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),
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185
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);
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```
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`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)` should return `237`.
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```js
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assert.equal(
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knapsack(
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[
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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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100
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),
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237
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);
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```
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`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)` should return `317`.'
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```js
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assert.equal(
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knapsack(
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[
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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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200
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),
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317
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);
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```
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# --seed--
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## --seed-contents--
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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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# --solutions--
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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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