freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/knapsack-problem-bounded.md

---
id: 5a23c84252665b21eecc7ed2
title: Knapsack problem/Bounded
challengeType: 5
---

## Description
<section id='description'>
The bounded knapsack problem is defined as follows:
You are given an array of objects representing items to be put in a knapsack. The objects have 4 attributes: name, pieces (the number of the particular item), 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.  Keep in mind that each item can appear between 0 and <code>pieces</code> times.
</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>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 300)</code> should return <code>755</code>.
    testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 300), 755, "<code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 300)</code> should return <code>755</code>.");
  - text: <code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 400)</code> should return <code>875</code>.
    testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 400), 875, "<code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 400)</code> should return <code>875</code>.");
  - text: <code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 500)</code> should return <code>1015</code>.
    testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 500), 1015, "<code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 500)</code> should return <code>1015</code>.");
  - text: <code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 600)</code> should return <code>1120</code>.
    testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 600), 1120, "<code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 600)</code> should return <code>1120</code>.");
  - text: <code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 700)</code> should return <code>1225</code>.
    testString: assert.equal(findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 700), 1225, "<code>findBestPack([{ name:'map', weight:9, value:150, pieces:1 }, { name:'compass', weight:13, value:35, pieces:1 }, { name:'water', weight:153, value:200, pieces:2 }, { name:'sandwich', weight:50, value:60, pieces:2 }, { name:'glucose', weight:15, value:60, pieces:2 }, { name:'tin', weight:68, value:45, pieces:3 }, { name:'banana', weight:27, value:60, pieces:3 }, { name:'apple', weight:39, value:40, pieces:3 }, { name:'cheese', weight:23, value:30, pieces:1 }, { name:'beer', weight:52, value:10, pieces:3 }, { name:'suntan, cream', weight:11, value:70, pieces:1 }, { name:'camera', weight:32, value:30, pieces:1 }, { name:'T-shirt', weight:24, value:15, pieces:2 }], 700)</code> should return <code>1225</code>.");
```

</section>

## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>

```js
function findBestPack(data, maxweight) {
  // Good luck!
}
```

</div>
</section>

## Solution
<section id='solution'>

```js
function findBestPack(data, maxweight) {
  var m = [
    [0]
  ]; // maximum pack value found so far
  var b = [
    [0]
  ]; // best combination found so far
  var opts = [0]; // item index for 0 of item 0
  var P = [1]; // item encoding for 0 of item 0
  var choose = 0;
  for (var j = 0; j < data.length; j++) {
    opts[j + 1] = opts[j] + data[j].pieces; // item index for 0 of item j+1
    P[j + 1] = P[j] * (1 + data[j].pieces); // item encoding for 0 of item j+1
  }
  for (var j = 0; j < opts[data.length]; j++) {
    m[0][j + 1] = b[0][j + 1] = 0; // best values and combos for empty pack: nothing
  }
  for (var w = 1; w <= maxweight; w++) {
    m[w] = [0];
    b[w] = [0];
    for (var j = 0; j < data.length; j++) {
      var N = data[j].pieces; // how many of these can we have?
      var base = opts[j]; // what is the item index for 0 of these?
      for (var n = 1; n <= N; n++) {
        var W = n * data[j].weight; // how much do these items weigh?
        var s = w >= W ? 1 : 0; // can we carry this many?
        var v = s * n * data[j].value; // how much are they worth?
        var I = base + n; // what is the item number for this many?
        var wN = w - s * W; // how much other stuff can we be carrying?
        var C = n * P[j] + b[wN][base]; // encoded combination
        m[w][I] = Math.max(m[w][I - 1], v + m[wN][base]); // best value
        choose = b[w][I] = m[w][I] > m[w][I - 1] ? C : b[w][I - 1];
      }
    }
  }

  var best = [];
  for (var j = data.length - 1; j >= 0; j--) {
    best[j] = Math.floor(choose / P[j]);
    choose -= best[j] * P[j];
  }

  var wgt = 0;
  var val = 0;
  for (var i = 0; i < best.length; i++) {
    if (0 == best[i]) continue;
    wgt += best[i] * data[i].weight;
    val += best[i] * data[i].value;
  }

  return val;
}
```

</section>