aureooms/js-knapsack

import assert from 'assert';

/**
 * Exact DP solution to the unbounded knapsack problem with integer weights.
 * Runs in O(nW) time.
 *
 * @param {Array} v Values.
 * @param {Array} w Weights.
 * @param {Number} n Size of the problem.
 * @param {Number} W Size of the knapsack.
 * @param {Array} m Memory buffer.
 * @return {Number} Objective value of the optimum.
 */
const integerWeightsKnapsackUnbounded = (
    v,
    w,
    n,
    W,
    m = new v.constructor(W + 1).fill(0),
) => {
    assert(v.length === n);
    assert(w.length === n);
    assert(Number.isInteger(W) && W >= 0);
    assert(m.length >= W + 1);
    for (let j = 1; j <= W; ++j) {
        let temporary = m[j];
        for (let i = 0; i < n; ++i) {
            const wi = w[i];
            const vi = v[i];
            assert(Number.isInteger(wi) && wi >= 0 && wi <= W);
            const k = j - wi;
            // TODO sort by weight to avoid branching
            // from larger to smaller so that m is scanned
            // from left to right
            if (k >= 0) temporary = Math.max(temporary, m[k] + vi);
        }

        m[j] = temporary;
    }

    return m[W];
};

export default integerWeightsKnapsackUnbounded;