Warshall Transitive Closure in JavaScript

"use strict";
// Warshall Transitive Closure in JavaScript
//
// PURPOSE
// Transitive closure records whether every vertex can reach every other vertex. Warshall is
// the Boolean counterpart of Floyd-Warshall.
//
// METHOD
// Mark each vertex reachable from itself. For every intermediate k, mark i-to-j reachable
// whenever i reaches k and k reaches j. The matrix accumulates reachability through the
// processed intermediates.
//
// COMPLEXITY
// O(n cubed) time and O(1) auxiliary space beyond the caller-owned matrix.
//
// CONTRACT
// Mutates a flattened n by n 0/1 adjacency matrix to reflexive transitive closure. Returns
// 0. A vertex reaches itself via a path of zero edges.
// 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 graph after call: [1, 1, 1, 0, 1, 1, 0, 0, 1].
// 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 transitive_closure(graph, n) {
    alg_require(graph instanceof Int32Array);
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((graph.length == alg_mul(n, n)));
    let i = 0;
    let j = 0;
    let k = 0;
    while ((i < n)) {
        graph[alg_add(alg_mul(i, n), i)] = 1;
        i = alg_add(i, 1);
    }
    while ((k < n)) {
        i = 0;
        while ((i < n)) {
            j = 0;
            while ((j < n)) {
                if (((graph[alg_add(alg_mul(i, n), k)] != 0) && (graph[alg_add(alg_mul(k, n), j)] != 0))) {
                    graph[alg_add(alg_mul(i, n), j)] = 1;
                }
                j = alg_add(j, 1);
            }
            i = alg_add(i, 1);
        }
        k = alg_add(k, 1);
    }
    return 0;
}

let graph = new Int32Array([0, 1, 0, 0, 0, 1, 0, 0, 0]);
let n = 3;
let result = transitive_closure(graph, n);
console.log(result);
console.log(graph);
// Expected graph: [1, 1, 1, 0, 1, 1, 0, 0, 1]