✨ feat(integerWeightKnapsackUnbounded): First draft.

Author: make-github-pseudonymous-again

src/index.js

@@ -1,12 +1,19 @@
 import integerValuesKnapsack from './integerValuesKnapsack';
 import integerWeightsKnapsack from './integerWeightsKnapsack';
+import integerWeightsKnapsackUnbounded from './integerWeightsKnapsackUnbounded';
 import knapsackApprox from './knapsackApprox';
 
 /* eslint import/no-anonymous-default-export: [2, {"allowObject": true}] */
 export default {
 	integerValuesKnapsack,
 	integerWeightsKnapsack,
+	integerWeightsKnapsackUnbounded,
 	knapsackApprox,
 };
 
-export {integerValuesKnapsack, integerWeightsKnapsack, knapsackApprox};
+export {
+	integerValuesKnapsack,
+	integerWeightsKnapsack,
+	integerWeightsKnapsackUnbounded,
+	knapsackApprox,
+};

src/integerWeightsKnapsackUnbounded.js

@@ -0,0 +1,33 @@
+import assert from 'assert';
+
+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;

test/src/unbounded-knapsack-problem.js

@@ -0,0 +1,53 @@
+import test from 'ava';
+
+import {all, map} from '@aureooms/js-itertools';
+
+import {integerWeightsKnapsackUnbounded} from '../../src';
+
+const macro = (t, solve, _name, v, w, n, W, opt, approx) => {
+	t.is(n, v.length);
+	t.is(n, w.length);
+	const result = solve(v, w, n, W);
+	if (approx === undefined) {
+		t.is(opt, result);
+	} else {
+		t.true(result >= approx * opt);
+	}
+};
+
+macro.title = (title, solve, name, v, w, n, W, opt, approx) =>
+	title
+		? `${title} (${name || solve.name})`
+		: approx === undefined
+		? `${name || solve.name}(${JSON.stringify(v)}, ${JSON.stringify(
+				w,
+		  )}, ${n}, ${W}) = ${opt}`
+		: `${name || solve.name}(${JSON.stringify(v)}, ${JSON.stringify(
+				w,
+		  )}, ${n}, ${W}) >= ${approx} * ${opt}`;
+
+const solvers = [
+	{
+		solve: integerWeightsKnapsackUnbounded,
+		hypothesis: (_, w) => all(map((x) => Number.isInteger(x), w)),
+	},
+];
+
+const instances = [
+	{
+		title: 'wikipedia illustration',
+		v: [4, 2, 2, 1, 10],
+		w: [12, 2, 1, 1, 4],
+		n: 5,
+		W: 15,
+		opt: 36,
+	},
+];
+
+for (const {title, v, w, n, W, opt} of instances) {
+	for (const {solve, name, hypothesis, approx} of solvers) {
+		if (!hypothesis || hypothesis(v, w, n, W)) {
+			test(title, macro, solve, name, v, w, n, W, opt, approx);
+		}
+	}
+}