Subset Sum Decision in JavaScript

"use strict";
// Subset Sum Decision in JavaScript
//
// PURPOSE
// Subset sum asks whether some selection of items totals an exact target. A reachability
// table records which sums can be formed.
//
// METHOD
// Mark zero reachable. For each item, scan sums downward and mark a sum reachable if it
// already was or if the sum minus the item was reachable before this item.
//
// COMPLEXITY
// O(n * target) time and O(target) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Items and target are nonnegative integers. Each input position can be used once. Returns 1
// if reachable, otherwise 0.
// 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: 1.
// 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 subset_sum(a, target) {
    alg_require(a instanceof Int32Array);
    alg_require(Number.isInteger(target) && target >= -2147483648 && target <= 2147483647);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    alg_require(((target >= 0) && (target <= 1000000)));
    for (let alg_i = 0; alg_i < a.length; alg_i++) {
        let alg_value = a[alg_i];
        alg_require((alg_value >= 0));
    }
    let dp = new Int32Array(alg_size(alg_add(target, 1)));
    dp[0] = 1;
    let i = 0;
    let s = 0;
    while ((i < n)) {
        s = target;
        while ((s >= a[i])) {
            if ((dp[alg_sub(s, a[i])] != 0)) {
                dp[s] = 1;
            }
            s = alg_sub(s, 1);
        }
        i = alg_add(i, 1);
    }
    return dp[target];
}

let a = new Int32Array([3, 4, 5]);
let target = 9;
let result = subset_sum(a, target);
console.log(result);