Bellman Ford Shortest Path in JavaScript

"use strict";
// Bellman Ford Shortest Path in JavaScript
//
// PURPOSE
// Bellman-Ford permits negative edge weights and detects negative cycles reachable from the
// source. Repeated edge relaxation finds progressively longer optimal paths.
//
// METHOD
// Relax every edge up to n-1 times, stopping early if nothing changes. Perform one extra
// pass to detect a reachable negative cycle. Guard unreachable endpoints before adding
// weights.
//
// COMPLEXITY
// O(VE) time and O(V) auxiliary space.
//
// CONTRACT
// Edge arrays from_vertex, to_vertex, weight each have m entries; n >= 1. Finite distances
// and all relaxed sums stay strictly between -1,000,000,000 and 1,000,000,000. Returns
// distance, INF if unreachable, or -INF for any reachable negative cycle (even if it cannot
// reach target).
// 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 bellman_ford(from_vertex, to_vertex, weight, n, source, target) {
    alg_require(from_vertex instanceof Int32Array);
    alg_require(to_vertex instanceof Int32Array);
    alg_require(weight instanceof Int32Array);
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(Number.isInteger(source) && source >= -2147483648 && source <= 2147483647);
    alg_require(Number.isInteger(target) && target >= -2147483648 && target <= 2147483647);
    let m = from_vertex.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require((from_vertex.length == m));
    alg_require((to_vertex.length == m));
    alg_require((weight.length == m));
    alg_require(((n >= 1) && (source >= 0) && (source < n)));
    alg_require(((target >= 0) && (target < n)));
    for (let alg_i = 0; alg_i < from_vertex.length; alg_i++) {
        let alg_value = from_vertex[alg_i];
        alg_require(((alg_value >= 0) && (alg_value < n)));
    }
    for (let alg_i = 0; alg_i < to_vertex.length; alg_i++) {
        let alg_value = to_vertex[alg_i];
        alg_require(((alg_value >= 0) && (alg_value < n)));
    }
    let distance = new Int32Array(alg_size(n));
    let i = 0;
    let edge = 0;
    let iteration = 0;
    let changed = 0;
    let u = 0;
    let v = 0;
    while ((i < n)) {
        distance[i] = 1000000000;
        i = alg_add(i, 1);
    }
    distance[source] = 0;
    while ((iteration < alg_sub(n, 1))) {
        changed = 0;
        edge = 0;
        while ((edge < m)) {
            u = from_vertex[edge];
            v = to_vertex[edge];
            if (((distance[u] != 1000000000) && (alg_add(distance[u], weight[edge]) < distance[v]))) {
                distance[v] = alg_add(distance[u], weight[edge]);
                changed = 1;
            }
            edge = alg_add(edge, 1);
        }
        if ((changed == 0)) {
            break;
        }
        iteration = alg_add(iteration, 1);
    }
    edge = 0;
    while ((edge < m)) {
        u = from_vertex[edge];
        v = to_vertex[edge];
        if (((distance[u] != 1000000000) && (alg_add(distance[u], weight[edge]) < distance[v]))) {
            return alg_sub(0, 1000000000);
        }
        edge = alg_add(edge, 1);
    }
    return distance[target];
}

let from_vertex = new Int32Array([0, 1, 0]);
let to_vertex = new Int32Array([1, 2, 2]);
let weight = new Int32Array([4, -2, 9]);
let n = 3;
let source = 0;
let target = 2;
let result = bellman_ford(from_vertex, to_vertex, weight, n, source, target);
console.log(result);