Directed Cycle Detection by DFS in JavaScript

"use strict";
// Directed Cycle Detection by DFS in JavaScript
//
// PURPOSE
// DFS detects a directed cycle when an edge points to a vertex still active in the current
// search path.
//
// METHOD
// Use an explicit stack and per-vertex next-neighbor positions. Mark vertices active on
// entry and finished on exit. An edge to an active vertex is a back edge.
//
// COMPLEXITY
// O(n squared) matrix traversal time and O(n) auxiliary space.
//
// CONTRACT
// Flattened n by n 0/1 directed adjacency matrix; returns 1 if a 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: 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 directed_cycle(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 color = new Int32Array(alg_size(alg_add(n, 1)));
    let stack = new Int32Array(alg_size(alg_add(n, 1)));
    let next_vertex = new Int32Array(alg_size(alg_add(n, 1)));
    let source = 0;
    let top = 0;
    let u = 0;
    let v = 0;
    while ((source < n)) {
        if ((color[source] == 0)) {
            top = 1;
            stack[0] = source;
            color[source] = 1;
            while ((top > 0)) {
                u = stack[alg_sub(top, 1)];
                if ((next_vertex[u] == n)) {
                    color[u] = 2;
                    top = alg_sub(top, 1);
                } else {
                    v = next_vertex[u];
                    next_vertex[u] = alg_add(next_vertex[u], 1);
                    if ((graph[alg_add(alg_mul(u, n), v)] != 0)) {
                        if ((color[v] == 1)) {
                            return 1;
                        }
                        if ((color[v] == 0)) {
                            color[v] = 1;
                            stack[top] = v;
                            top = alg_add(top, 1);
                        }
                    }
                }
            }
        }
        source = alg_add(source, 1);
    }
    return 0;
}

let graph = new Int32Array([0, 1, 1, 0]);
let n = 2;
let result = directed_cycle(graph, n);
console.log(result);