Coin Change Combination Count in JavaScript

"use strict";
// Coin Change Combination Count in JavaScript
//
// PURPOSE
// This algorithm counts unordered combinations of reusable denominations. Putting the coin
// loop outside the amount loop prevents counting different orders as different combinations.
//
// METHOD
// There is one way to make zero: choose no coins. Process each denomination once and update
// amounts upward so that the same denomination can be reused.
//
// COMPLEXITY
// O(m * amount) time and O(amount) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Denominations are distinct positive integers, amount >= 0. Counts and array sizes must
// fit. Duplicate denominations would overcount.
// 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: 4.
// 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 coin_combinations(coins, amount) {
    alg_require(coins instanceof Int32Array);
    alg_require(Number.isInteger(amount) && amount >= -2147483648 && amount <= 2147483647);
    let m = coins.length;
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require((coins.length == m));
    alg_require(((amount >= 0) && (amount <= 1000000)));
    for (let alg_i = 0; alg_i < coins.length; alg_i++) {
        let alg_value = coins[alg_i];
        alg_require((alg_value > 0));
    }
    let dp = new Int32Array(alg_size(alg_add(amount, 1)));
    dp[0] = 1;
    let j = 0;
    let x = 0;
    while ((j < m)) {
        x = coins[j];
        while ((x <= amount)) {
            dp[x] = alg_add(dp[x], dp[alg_sub(x, coins[j])]);
            x = alg_add(x, 1);
        }
        j = alg_add(j, 1);
    }
    return dp[amount];
}

let coins = new Int32Array([1, 2, 5]);
let amount = 5;
let result = coin_combinations(coins, amount);
console.log(result);