✨ feat(knapsackApprox): First draft.

Author: make-github-pseudonymous-again

package.json

@@ -77,6 +77,7 @@
     "url": "https://github.com/aureooms/js-knapsack/issues"
   },
   "dependencies": {
+    "@aureooms/js-compare": "^1.4.8",
     "@aureooms/js-itertools": "^4.1.0"
   },
   "devDependencies": {

src/knapsackApprox.js

@@ -0,0 +1,41 @@
+import assert from 'assert';
+import {increasing} from '@aureooms/js-compare';
+import {max, map, filter, range} from '@aureooms/js-itertools';
+
+import integerValuesKnapsack from './integerValuesKnapsack';
+
+/**
+ * (1-eps)-approx for the knapsack problem. Runs in O(N^3/eps) time.
+ *
+ * @param {Array} v Values.
+ * @param {Array} w Weights.
+ * @param {Array} n Size of the problem.
+ * @param {Array} W Size of the knapsack.
+ * @param {Array} eps Approximation constant.
+ * @param {Number} P Any lower bound on OPT > 0.
+ */
+const knapsackApprox = (
+	v,
+	w,
+	n,
+	W,
+	eps,
+	P = max(
+		increasing,
+		map(
+			(i) => v[i],
+			filter((i) => w[i] <= W, range(n)),
+		),
+	),
+) => {
+	assert(eps > 0 && eps < 1);
+	assert(P > 0);
+	assert(v.length === n);
+	assert(w.length === n);
+	const K = (eps * P) / n;
+	const u = Uint32Array.from(v, (vi) => Math.floor(vi / K));
+	// TODO reconstruct solution
+	return K * integerValuesKnapsack(u, w, n, W);
+};
+
+export default knapsackApprox;

yarn.lock

@@ -9,6 +9,11 @@
   dependencies:
     "@aureooms/js-error" "^4.0.1"
 
+"@aureooms/js-compare@^1.4.8":
+  version "1.4.8"
+  resolved "https://registry.yarnpkg.com/@aureooms/js-compare/-/js-compare-1.4.8.tgz#c6bff1091f4a2e211f449299572d9f195146fc59"
+  integrity sha512-Z26PU6OmuhS7ZJsELTKImmipF7J+KCOyN70wBhhVIhmqUhXY6C3JpJHAev6wNBkC4ThlQt3zO6p/OmBFIq76Qg==
+
 "@aureooms/js-error@^4.0.1":
   version "4.0.1"
   resolved "https://registry.yarnpkg.com/@aureooms/js-error/-/js-error-4.0.1.tgz#be2740b3f31a337e0828930c9b70d38113b4dd77"