aureooms/js-knapsack

import assert from 'assert';

import {map} from '@iterable-iterator/map';
import {range} from '@iterable-iterator/range';
import {max} from '@iterable-iterator/reduce';
import {increasing} from '@total-order/primitive';

/**
 * Exact DP solution to the unbounded knapsack problem with integer values
 * given a known upper bound V on OPT. Runs in O(nV) time.
 *
 * @param {Array} v Values.
 * @param {Array} w Weights.
 * @param {Number} n Size of the problem.
 * @param {Number} W Size of the knapsack.
 * @param {Number|BigInt} zero The number 0.
 * @param {Number} V Any upper bound on OPT >= 0.
 * @param {Array} m Memory buffer.
 * @return {Number} Objective value of the optimum.
 */
const integerValuesKnapsackUnbounded = (
    v,
    w,
    n,
    W,
    zero = 0,
    V = Math.floor(
        W *
            max(
                increasing,
                map((i) => v[i] / w[i], range(n)),
                zero,
            ),
    ),
    m = new w.constructor(V + 1).fill(W + 1),
) => {
    assert(v.length === n);
    assert(w.length === n);
    assert(Number.isInteger(V) && V >= 0);
    assert(m.length >= V + 1);
    m[0] = 0;
    for (let j = 1; j <= V; ++j) {
        let temporary = m[j];
        for (let i = 0; i < n; ++i) {
            const wi = w[i];
            const vi = v[i];
            assert(Number.isInteger(vi) && vi >= 0);
            const k = j - vi;
            // TODO sort by value to avoid branching
            // from larger to smaller so that m is scanned
            // from left to right
            if (k >= 0) temporary = Math.min(temporary, m[k] + wi);
        }

        m[j] = temporary;
    }

    for (let j = V; j > 0; --j) {
        if (m[j] <= W) return j;
    }

    return 0;
};

export default integerValuesKnapsackUnbounded;