2019-10-23 14:23:50 +00:00
---
id: 5a23c84252665b21eecc7ed1
title: Knapsack problem/0-1
challengeType: 5
2019-10-23 16:04:34 +00:00
forumTopicId: 323649
2019-10-23 14:23:50 +00:00
---
## Description
< section id = 'description' >
The 0-1 knapsack problem is defined as follows:
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.
< / section >
## Instructions
< section id = 'instructions' >
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.
< / section >
## Tests
< section id = 'tests' >
``` yml
tests:
- 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 > .
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, "< 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 > .");
- 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 > .
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, "< 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 > .");
- 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 > .
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, "< 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 > .");
- 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 > .
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, "< 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 > .");
- 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 > .
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, "< 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 > .");
- 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 > .'
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, "< 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 > .");
```
< / section >
## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
function knapsack(items, maxweight) {
// Good luck!
}
```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
function knapsack(items, maxweight) {
var _ = {
max: function (e) {
var mx = e[0];
e.forEach(function (f) {
if (mx < f )
mx = f;
})
return mx;
},
map: function (array, func) {
return array.map(func)
},
isUndefined: function (a) {
if (a) {
return false;
}
return true;
},
range: function (start, end, step) {
var a = []
var f = f = (i, end) => i < end
if (start > end)
f = (i, end) => i > end
for (var i = start; f(i, end); i += step)
a.push(i)
return a
}
}
var valuefn = (e) => e.value
var weightfn = (e) => e.weight
var _epsilon = 0.01;
var _p = _ .max(_.map(items, valuefn));
var _k = _epsilon * _p / items.length;
var _memo = (function () {
var _mem = {};
var _key = function (i, w) {
return i + '::' + w;
};
return {
get: function (i, w) {
return _mem[_key(i, w)];
},
put: function (i, w, r) {
_mem[_key(i, w)] = r;
return r;
}
};
})();
var _m = function (i, w) {
i = Math.round(i);
w = Math.round(w);
if (i < 0 | | w = == 0 ) {
// empty base case
return { items: [], totalWeight: 0, totalValue: 0 };
}
var mm = _memo.get(i, w);
if (!_.isUndefined(mm)) {
return mm;
}
var item = items[i];
if (weightfn(item) > w) {
//item does not fit, try the next item
return _memo.put(i, w, _m(i - 1, w));
}
// this item could fit.
// are we better off excluding it?
var excluded = _m(i - 1, w);
// or including it?
var included = _m(i - 1, w - weightfn(item));
if (included.totalValue + Math.floor(valuefn(item) / _k) > excluded.totalValue) {
// better off including it
// make a copy of the list
var i1 = included.items.slice();
i1.push(item);
return _memo.put(i, w,
{
items: i1,
totalWeight: included.totalWeight + weightfn(item),
totalValue: included.totalValue + Math.floor(valuefn(item) / _k)
});
}
//better off excluding it
return _memo.put(i, w, excluded);
};
var scaled = _m(items.length - 1, maxweight);
var val = 0;
scaled.items.forEach(function (e) {
val += e.value
})
return val;
}
```
< / section >