Matrix Chain Multiplication in JavaScript

"use strict";
// Matrix Chain Multiplication in JavaScript
//
// PURPOSE
// Matrix-chain DP chooses the parenthesization requiring the fewest scalar multiplications
// without changing matrix order.
//
// METHOD
// For each interval length, try every split and combine both subchain costs with the
// multiplication cost of their results.
//
// COMPLEXITY
// O(n cubed) time and O(n squared) space for n matrices.
//
// CONTRACT
// dimensions has n+1 positive entries; matrix i has dimensions[i] by dimensions[i+1]. n>=1.
// All candidate costs must be < 1000000000.
// 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: 4500.
// 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 matrix_chain(dimensions) {
    alg_require(dimensions instanceof Int32Array);
    let n = alg_sub(dimensions.length, 1);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((dimensions.length == alg_add(n, 1)));
    alg_require((n >= 1));
    for (let alg_i = 0; alg_i < dimensions.length; alg_i++) {
        let alg_value = dimensions[alg_i];
        alg_require(((alg_value > 0) && (alg_value <= 1000)));
    }
    let dp = new Int32Array(alg_size(alg_mul(n, n)));
    let length = 2;
    let left = 0;
    let right = 0;
    let split = 0;
    let candidate = 0;
    while ((length <= n)) {
        left = 0;
        while ((alg_add(left, length) <= n)) {
            right = alg_sub(alg_add(left, length), 1);
            dp[alg_add(alg_mul(left, n), right)] = 1000000000;
            split = left;
            while ((split < right)) {
                candidate = alg_add(alg_add(dp[alg_add(alg_mul(left, n), split)], dp[alg_add(alg_mul(alg_add(split, 1), n), right)]), alg_mul(alg_mul(dimensions[left], dimensions[alg_add(split, 1)]), dimensions[alg_add(right, 1)]));
                dp[alg_add(alg_mul(left, n), right)] = Math.min(dp[alg_add(alg_mul(left, n), right)], candidate);
                split = alg_add(split, 1);
            }
            left = alg_add(left, 1);
        }
        length = alg_add(length, 1);
    }
    return dp[alg_sub(n, 1)];
}

let dimensions = new Int32Array([10, 30, 5, 60]);
let result = matrix_chain(dimensions);
console.log(result);