Beginner Exercism • javascript

Knapsack

Challenge Overview

Your task is to determine which items to take so that the total value of her selection is maximized, taking into account the knapsack's carrying capacity.

Introduction

Lhakpa is a Sherpa mountain guide and porter. After months of careful planning, the expedition Lhakpa works for is about to leave. She will be paid the value she carried to the base camp.

In front of her are many items, each with a value and weight. Lhakpa would gladly take all of the items, but her knapsack can only hold so much weight.

Instructions

Your task is to determine which items to take so that the total value of her selection is maximized, taking into account the knapsack’s carrying capacity.

Items will be represented as a list of items. Each item will have a weight and value. All values given will be strictly positive. Lhakpa can take only one of each item.

For example:

Items: [
  { "weight": 5, "value": 10 },
  { "weight": 4, "value": 40 },
  { "weight": 6, "value": 30 },
  { "weight": 4, "value": 50 }
]

Knapsack Maximum Weight: 10

For the above, the first item has weight 5 and value 10, the second item has weight 4 and value 40, and so on. In this example, Lhakpa should take the second and fourth item to maximize her value, which, in this case, is 90. She cannot get more than 90 as her knapsack has a weight limit of 10.

Source: Exercism javascript/knapsack

💡 View Solution

export const knapsack = (maximumWeight, items) => {
  const n = items.length;
  const dp = Array.from({ length: n + 1 }, () => Array(maximumWeight + 1).fill(0));

  for (let i = 1; i <= n; i++) {
    const { weight, value } = items[i - 1];
    for (let w = 0; w <= maximumWeight; w++) {
      if (weight <= w) {
        dp[i][w] = Math.max(dp[i - 1][w], dp[i - 1][w - weight] + value);
      } else {
        dp[i][w] = dp[i - 1][w];
      }
    }
  }

  return dp[n][maximumWeight];
};