Minimum Coin Change in JavaScript

"use strict";
// Minimum Coin Change in JavaScript
//
// PURPOSE
// Minimum coin change finds the fewest coins needed to make an exact amount when each
// denomination can be reused. Greedy selection fails for arbitrary denominations.
//
// METHOD
// Set the zero amount to zero coins and other amounts to an unreachable sentinel. For each
// amount, consider every coin and extend a reachable smaller amount by one coin.
//
// COMPLEXITY
// O(amount * m) time and O(amount) auxiliary space for m denominations; pseudo-polynomial in
// the numeric amount.
//
// CONTRACT
// amount >= 0, all coins > 0, m is their count. Returns -1 if impossible. The sentinel
// amount+1 must fit.
// 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: 2.
// 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 minimum_coins(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)));
    let x = 1;
    let j = 0;
    while ((x <= amount)) {
        dp[x] = alg_add(amount, 1);
        j = 0;
        while ((j < m)) {
            if ((coins[j] <= x)) {
                dp[x] = Math.min(dp[x], alg_add(dp[alg_sub(x, coins[j])], 1));
            }
            j = alg_add(j, 1);
        }
        x = alg_add(x, 1);
    }
    if ((dp[amount] > amount)) {
        return alg_sub(0, 1);
    }
    return dp[amount];
}

let coins = new Int32Array([1, 3, 4]);
let amount = 6;
let result = minimum_coins(coins, amount);
console.log(result);