Bipartite Graph Coloring in JavaScript

"use strict";
// Bipartite Graph Coloring in JavaScript
//
// PURPOSE
// A graph is bipartite when its vertices can be colored with two colors so that each edge
// joins opposite colors.
//
// METHOD
// BFS every uncolored component. Give neighbors the opposite color and reject any edge
// joining equal colors.
//
// COMPLEXITY
// O(n squared) time with this dense matrix, O(n) auxiliary space.
//
// CONTRACT
// Symmetric flattened n by n 0/1 matrix. Returns 1 or 0. Self-loops make a graph non-
// bipartite.
// 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_bipartite(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 queue = new Int32Array(alg_size(alg_add(n, 1)));
    let source = 0;
    let head = 0;
    let tail = 0;
    let u = 0;
    let v = 0;
    while ((source < n)) {
        if ((color[source] == 0)) {
            head = 0;
            tail = 1;
            queue[0] = source;
            color[source] = 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)) {
                        if ((color[v] == color[u])) {
                            return 0;
                        }
                        if ((color[v] == 0)) {
                            color[v] = alg_sub(3, color[u]);
                            queue[tail] = v;
                            tail = alg_add(tail, 1);
                        }
                    }
                    v = alg_add(v, 1);
                }
            }
        }
        source = alg_add(source, 1);
    }
    return 1;
}

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