dsa.js/src/algorithms/knapsack-fractional.js

Data Structures & Algorithms in JS

/* eslint-disable no-mixed-operators */
// tag::snippet[]
/**
 * Solves Bounded Knapsack Problem (BKP)
 *  You can take fractions or whole part of items.
 * @param {Array} input array of objects with the shape {value, weight}
 * @param {Number} max maximum weight for knapsack
 */
function solveFractionalKnapsack(input, max) {
  let weight = 0;
  let value = 0;
  const items = [];

  // sort by value/weight ratio
  input.sort((a, b) => a.value / a.weight - b.value / b.weight);

  while (input.length && weight < max) {
    const bestRatioItem = input.pop();

    if (weight + bestRatioItem.weight <= max) {
      bestRatioItem.proportion = 1; // take item as a whole
    } else { // take a fraction of the item
      bestRatioItem.proportion = (max - weight) / bestRatioItem.weight;
    }

    items.push(bestRatioItem);
    weight += bestRatioItem.proportion * bestRatioItem.weight;
    value += bestRatioItem.proportion * bestRatioItem.value;
  }

  return { weight, value, items };
}
// end::snippet[]

module.exports = solveFractionalKnapsack;