Rod Cutting in JavaScript

"use strict";
// Rod Cutting in JavaScript
//
// PURPOSE
// Rod cutting chooses cuts that maximize the sale value of a rod. It considers every first
// piece and reuses the optimal solution for the remaining length.
//
// METHOD
// Set the value of length zero to zero. For each length, try each possible first cut and
// combine its price with the already computed remainder value.
//
// COMPLEXITY
// O(n squared) time and O(n) auxiliary space.
//
// CONTRACT
// prices[i] is the nonnegative price for length i+1 and contains n entries. Returns maximum
// revenue for length n. Revenue 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: 10.
// 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 rod_cutting(prices, n) {
    alg_require(prices instanceof Int32Array);
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    let dp = new Int32Array(alg_size(alg_add(n, 1)));
    let length = 1;
    let cut = 0;
    while ((length <= n)) {
        cut = 1;
        while ((cut <= length)) {
            dp[length] = Math.max(dp[length], alg_add(prices[alg_sub(cut, 1)], dp[alg_sub(length, cut)]));
            cut = alg_add(cut, 1);
        }
        length = alg_add(length, 1);
    }
    return dp[n];
}

let prices = new Int32Array([1, 5, 8, 9]);
let n = 4;
let result = rod_cutting(prices, n);
console.log(result);