Floyd Warshall All Pairs Shortest Paths in JavaScript

"use strict";
// Floyd Warshall All Pairs Shortest Paths in JavaScript
//
// PURPOSE
// Floyd-Warshall computes distances between every pair by gradually allowing more
// intermediate vertices. The ordering of the three loops expresses the dynamic programming
// recurrence.
//
// METHOD
// For each intermediate k, try improving every i-to-j path through k. Skip unreachable
// halves before adding distances. After pass k, paths may use only intermediates up to k.
//
// COMPLEXITY
// O(n cubed) time and O(1) auxiliary space beyond the caller-owned n squared distance
// matrix.
//
// CONTRACT
// Mutates flattened distance matrix. Diagonal starts at 0; missing edges use 1,000,000,000.
// Negative edges allowed. Finite path sums must fit and remain strictly between -INF and
// INF. Returns -1 if any negative cycle exists, otherwise 0.
// 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: 0.
// Expected distance after call: [0, 4, 6, 1000000000, 0, 2, 1000000000, 1000000000, 0].
// 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 floyd_warshall(distance, n) {
    alg_require(distance instanceof Int32Array);
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((distance.length == alg_mul(n, n)));
    let k = 0;
    let i = 0;
    let j = 0;
    while ((k < n)) {
        i = 0;
        while ((i < n)) {
            j = 0;
            while ((j < n)) {
                if (((distance[alg_add(alg_mul(i, n), k)] != 1000000000) && (distance[alg_add(alg_mul(k, n), j)] != 1000000000))) {
                    distance[alg_add(alg_mul(i, n), j)] = Math.min(distance[alg_add(alg_mul(i, n), j)], alg_add(distance[alg_add(alg_mul(i, n), k)], distance[alg_add(alg_mul(k, n), j)]));
                }
                j = alg_add(j, 1);
            }
            i = alg_add(i, 1);
        }
        k = alg_add(k, 1);
    }
    i = 0;
    while ((i < n)) {
        if ((distance[alg_add(alg_mul(i, n), i)] < 0)) {
            return alg_sub(0, 1);
        }
        i = alg_add(i, 1);
    }
    return 0;
}

let distance = new Int32Array([0, 4, 10, 1000000000, 0, 2, 1000000000, 1000000000, 0]);
let n = 3;
let result = floyd_warshall(distance, n);
console.log(result);
console.log(distance);
// Expected distance: [0, 4, 6, 1000000000, 0, 2, 1000000000, 1000000000, 0]