Kahn Topological Cycle Detection in JavaScript

"use strict";
// Kahn Topological Cycle Detection in JavaScript
//
// PURPOSE
// Kahn algorithm repeatedly removes vertices with no incoming edges. A directed graph has a
// topological ordering exactly when all vertices can be removed this way.
//
// METHOD
// Compute indegrees, queue every zero-indegree vertex, then remove its outgoing edges.
// Enqueue a neighbor when its indegree becomes zero. Compare the number removed with n.
//
// COMPLEXITY
// O(n squared) time with an adjacency matrix and O(n) auxiliary space. Adjacency lists give
// O(V+E).
//
// CONTRACT
// Flattened n by n 0/1 directed matrix. Returns 1 for a DAG and 0 for a cycle. Empty graph
// is a DAG. This variant reports existence rather than returning an ordering.
// 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 is_dag(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 indegree = new Int32Array(alg_size(alg_add(n, 1)));
    let queue = new Int32Array(alg_size(alg_add(n, 1)));
    let u = 0;
    let v = 0;
    let head = 0;
    let tail = 0;
    while ((u < n)) {
        v = 0;
        while ((v < n)) {
            if ((graph[alg_add(alg_mul(u, n), v)] != 0)) {
                indegree[v] = alg_add(indegree[v], 1);
            }
            v = alg_add(v, 1);
        }
        u = alg_add(u, 1);
    }
    v = 0;
    while ((v < n)) {
        if ((indegree[v] == 0)) {
            queue[tail] = v;
            tail = alg_add(tail, 1);
        }
        v = alg_add(v, 1);
    }
    while ((head < tail)) {
        u = queue[head];
        head = alg_add(head, 1);
        v = 0;
        while ((v < n)) {
            if ((graph[alg_add(alg_mul(u, n), v)] != 0)) {
                indegree[v] = alg_sub(indegree[v], 1);
                if ((indegree[v] == 0)) {
                    queue[tail] = v;
                    tail = alg_add(tail, 1);
                }
            }
            v = alg_add(v, 1);
        }
    }
    if ((tail == n)) {
        return 1;
    }
    return 0;
}

let graph = new Int32Array([0, 1, 0, 0, 0, 1, 0, 0, 0]);
let n = 3;
let result = is_dag(graph, n);
console.log(result);