freeCodeCamp/curriculum/challenges/german/10-coding-interview-prep/rosetta-code/knapsack-problem-bounded.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc7ed2	Knapsack problem/Bounded	1	323652	knapsack-problembounded

--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 pieces times.

--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.

--hints--

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) sollte 755 zurückgeben.

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
);

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) sollte 875 zurückgeben.

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
);

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) sollte 1015 zurückgeben.

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
);

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) sollte 1120 zurückgeben.

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
);

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) sollte 1225 zurückgeben.

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
);

--seed--

--seed-contents--

function findBestPack(data, maxweight) {

}

--solutions--

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;
}