✨ feat(knapsackUnboundedGreedy): First draft.

Progress towards #3.

Author: make-github-pseudonymous-again

src/index.js

@@ -3,6 +3,7 @@ import integerValuesKnapsackUnbounded from './integerValuesKnapsackUnbounded';
 import integerWeightsKnapsack from './integerWeightsKnapsack';
 import integerWeightsKnapsackUnbounded from './integerWeightsKnapsackUnbounded';
 import knapsackApprox from './knapsackApprox';
+import knapsackUnboundedGreedy from './knapsackUnboundedGreedy';
 
 /* eslint import/no-anonymous-default-export: [2, {"allowObject": true}] */
 export default {
@@ -11,6 +12,7 @@ export default {
 	integerWeightsKnapsack,
 	integerWeightsKnapsackUnbounded,
 	knapsackApprox,
+	knapsackUnboundedGreedy,
 };
 
 export {
@@ -19,4 +21,5 @@ export {
 	integerWeightsKnapsack,
 	integerWeightsKnapsackUnbounded,
 	knapsackApprox,
+	knapsackUnboundedGreedy,
 };

src/knapsackUnboundedGreedy.js

@@ -0,0 +1,47 @@
+import assert from 'assert';
+import {fn, decreasing} from '@aureooms/js-compare';
+import {map, range, sorted} from '@aureooms/js-itertools';
+
+/**
+ * 1/2-approximation to the unbounded knapsack problem.
+ * Runs in O(n log n) time.
+ *
+ * @param {Array} v Values.
+ * @param {Array} w Weights.
+ * @param {Number} n Size of the problem.
+ * @param {Number} W Size of the knapsack.
+ */
+const knapsackUnboundedGreedy = (v, w, n, W) => {
+	assert(v.length === n);
+	assert(w.length === n);
+	assert(W >= 0);
+
+	const items = sorted(
+		orderedByDecreasingUtility,
+		map((i) => new Item(w[i], v[i]), range(n)),
+	);
+	return subroutine(W, items);
+};
+
+const subroutine = (W, items) => {
+	let value = 0;
+	let capacity = W;
+	for (const {v, w} of items) {
+		const copies = Math.floor(capacity / w);
+		capacity -= copies * w;
+		value += copies * v;
+	}
+
+	return value;
+};
+
+function Item(weight, value) {
+	assert(weight > 0);
+	this.w = weight;
+	this.v = value;
+}
+
+const utility = (x) => x.v / x.w;
+const orderedByDecreasingUtility = fn(decreasing, utility);
+
+export default knapsackUnboundedGreedy;

test/src/unbounded-knapsack-problem.js

@@ -5,6 +5,7 @@ import {all, map} from '@aureooms/js-itertools';
 import {
 	integerValuesKnapsackUnbounded,
 	integerWeightsKnapsackUnbounded,
+	knapsackUnboundedGreedy,
 } from '../../src';
 
 const macro = (t, solve, _name, v, w, n, W, opt, approx) => {
@@ -38,6 +39,10 @@ const solvers = [
 		solve: integerWeightsKnapsackUnbounded,
 		hypothesis: (_, w) => all(map((x) => Number.isInteger(x), w)),
 	},
+	{
+		solve: knapsackUnboundedGreedy,
+		approx: 1 / 2,
+	},
 ];
 
 const instances = [