170 lines
6.5 KiB
Markdown
170 lines
6.5 KiB
Markdown
---
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id: 5a23c84252665b21eecc7ed3
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title: Knapsack problem/Continuous
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challengeType: 5
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forumTopicId: 323654
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dashedName: knapsack-problemcontinuous
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---
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# --description--
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A thief burgles a butcher's shop, where he can select from some items.
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The thief knows the weights and prices of each items. Because he has a knapsack with a limit on the maximum weight that it can carry, he wants to select the items such that he would have his profit maximized. He may cut the items; the item has a reduced price after cutting that is proportional to the original price by the ratio of masses. That means: half of an item has half the price of the original.
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# --instructions--
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Write a function that takes an array of objects representing the items available in the shop. Each object has 3 attributes: name, weight, and value. The function also takes the maximum weight as a parameter. The function should return the maximum value possible, and the total weight of the selected items should not exceed the maximum weight.
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# --hints--
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`knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 10)` should return `257.875`.
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```js
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assert.equal(
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knapContinuous(
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[
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{ weight: 3.8, value: 36, name: 'beef' },
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{ weight: 5.4, value: 43, name: 'pork' },
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{ weight: 3.6, value: 90, name: 'ham' },
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{ weight: 2.4, value: 45, name: 'greaves' },
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{ weight: 4.0, value: 30, name: 'flitch' },
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{ weight: 2.5, value: 56, name: 'brawn' },
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{ weight: 3.7, value: 67, name: 'welt' },
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{ weight: 3.0, value: 95, name: 'salami' },
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{ weight: 5.9, value: 98, name: 'sausage' }
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],
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10
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),
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257.875
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);
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```
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`knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 12)` should return `295.05405405405406`.
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```js
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assert.equal(
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knapContinuous(
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[
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{ weight: 3.8, value: 36, name: 'beef' },
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{ weight: 5.4, value: 43, name: 'pork' },
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{ weight: 3.6, value: 90, name: 'ham' },
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{ weight: 2.4, value: 45, name: 'greaves' },
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{ weight: 4.0, value: 30, name: 'flitch' },
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{ weight: 2.5, value: 56, name: 'brawn' },
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{ weight: 3.7, value: 67, name: 'welt' },
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{ weight: 3.0, value: 95, name: 'salami' },
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{ weight: 5.9, value: 98, name: 'sausage' }
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],
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12
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),
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295.05405405405406
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);
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```
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`knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 15)` should return `349.3783783783784`.
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```js
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assert.equal(
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knapContinuous(
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[
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{ weight: 3.8, value: 36, name: 'beef' },
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{ weight: 5.4, value: 43, name: 'pork' },
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{ weight: 3.6, value: 90, name: 'ham' },
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{ weight: 2.4, value: 45, name: 'greaves' },
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{ weight: 4.0, value: 30, name: 'flitch' },
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{ weight: 2.5, value: 56, name: 'brawn' },
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{ weight: 3.7, value: 67, name: 'welt' },
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{ weight: 3.0, value: 95, name: 'salami' },
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{ weight: 5.9, value: 98, name: 'sausage' }
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],
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15
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),
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349.3783783783784
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);
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```
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`knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 22)` should return `459.5263157894737`.
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```js
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assert.equal(
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knapContinuous(
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[
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{ weight: 3.8, value: 36, name: 'beef' },
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{ weight: 5.4, value: 43, name: 'pork' },
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{ weight: 3.6, value: 90, name: 'ham' },
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{ weight: 2.4, value: 45, name: 'greaves' },
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{ weight: 4.0, value: 30, name: 'flitch' },
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{ weight: 2.5, value: 56, name: 'brawn' },
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{ weight: 3.7, value: 67, name: 'welt' },
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{ weight: 3.0, value: 95, name: 'salami' },
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{ weight: 5.9, value: 98, name: 'sausage' }
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],
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22
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),
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459.5263157894737
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);
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```
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`knapContinuous([{ "weight":3.8, "value":36, name:"beef" }, { "weight":5.4, "value":43, name:"pork" }, { "weight":3.6, "value":90, name:"ham" }, { "weight":2.4, "value":45, name:"greaves" }, { "weight":4.0, "value":30, name:"flitch" }, { "weight":2.5, "value":56, name:"brawn" }, { "weight":3.7, "value":67, name:"welt" }, { "weight":3.0, "value":95, name:"salami" }, { "weight":5.9, "value":98, name:"sausage" }], 24)` should return `478.4736842105263`.
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```js
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assert.equal(
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knapContinuous(
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[
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{ weight: 3.8, value: 36, name: 'beef' },
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{ weight: 5.4, value: 43, name: 'pork' },
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{ weight: 3.6, value: 90, name: 'ham' },
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{ weight: 2.4, value: 45, name: 'greaves' },
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{ weight: 4.0, value: 30, name: 'flitch' },
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{ weight: 2.5, value: 56, name: 'brawn' },
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{ weight: 3.7, value: 67, name: 'welt' },
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{ weight: 3.0, value: 95, name: 'salami' },
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{ weight: 5.9, value: 98, name: 'sausage' }
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],
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24
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),
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478.4736842105263
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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 knapContinuous(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 knapContinuous(items, maxweight) {
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function item_cmp(a, b) {
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const ua = a.unitVal,
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ub = b.unitVal;
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return ua < ub ? 1 : ua > ub ? -1 : 0;
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}
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items = items.map(({ value, weight }) => ({
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unitVal: value / weight,
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weight
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}));
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items.sort(item_cmp);
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let val = 0;
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let wt = 0;
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for (let { unitVal, weight } of items) {
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var portion = Math.min(maxweight - wt, weight);
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wt += portion;
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var addVal = portion * unitVal;
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val += addVal;
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if (wt >= maxweight) {
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break;
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}
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}
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return val;
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}
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```
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