0-1 Knapsack in JavaScript

"use strict";
// 0-1 Knapsack in JavaScript
//
// PURPOSE
// Knapsack chooses items with maximum total value under a weight limit, using each item at
// most once. The one-dimensional table stores the best value for each capacity.
//
// METHOD
// Process items one at a time and capacities downward. Compare skipping the item with adding
// its value to the previous best at the remaining capacity. Descending capacities prevent
// reusing the current item.
//
// COMPLEXITY
// O(n * capacity) time and O(capacity) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Weights are positive, values nonnegative, capacity >= 0. Both arrays have n entries.
// Returns best value, not the chosen item set.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic
// lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or
// overflow throw RangeError.
//
// EXAMPLE
// Expected return: 9.
// Run: node example.js
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); }
function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; }
function alg_add(a,b) { return alg_checked(a+b); }
function alg_sub(a,b) { return alg_checked(a-b); }
function alg_mul(a,b) { return alg_checked(a*b); }
function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; }

function knapsack(weights, values, capacity) {
    alg_require(weights instanceof Int32Array);
    alg_require(values instanceof Int32Array);
    alg_require(Number.isInteger(capacity) && capacity >= -2147483648 && capacity <= 2147483647);
    let n = weights.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((weights.length == n));
    alg_require((values.length == n));
    alg_require(((capacity >= 0) && (capacity <= 1000000)));
    for (let alg_i = 0; alg_i < weights.length; alg_i++) {
        let alg_value = weights[alg_i];
        alg_require((alg_value > 0));
    }
    for (let alg_i = 0; alg_i < values.length; alg_i++) {
        let alg_value = values[alg_i];
        alg_require((alg_value >= 0));
    }
    let dp = new Int32Array(alg_size(alg_add(capacity, 1)));
    let i = 0;
    let c = 0;
    while ((i < n)) {
        c = capacity;
        while ((c >= weights[i])) {
            dp[c] = Math.max(dp[c], alg_add(dp[alg_sub(c, weights[i])], values[i]));
            c = alg_sub(c, 1);
        }
        i = alg_add(i, 1);
    }
    return dp[capacity];
}

let weights = new Int32Array([2, 3, 4]);
let values = new Int32Array([4, 5, 7]);
let capacity = 5;
let result = knapsack(weights, values, capacity);
console.log(result);