Breadth First Search Shortest Path in JavaScript

"use strict";
// Breadth First Search Shortest Path in JavaScript
//
// PURPOSE
// BFS explores an unweighted graph one distance layer at a time. The first discovery of a
// vertex gives its shortest number of edges from the source.
//
// METHOD
// Put the source into a FIFO queue and mark its distance zero. Remove vertices in order and
// enqueue each undiscovered neighbor with distance one greater. Mark on enqueue so each
// vertex enters at most once.
//
// COMPLEXITY
// O(n squared) time with this adjacency matrix and O(n) auxiliary space. An adjacency-list
// implementation is O(V+E).
//
// CONTRACT
// graph is a flattened n by n 0/1 adjacency matrix, n >= 1, source and target are valid
// vertices. Directed edges are supported. Returns distance or -1.
// 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: 2.
// 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 bfs_distance(graph, n, source, target) {
    alg_require(graph instanceof Int32Array);
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(Number.isInteger(source) && source >= -2147483648 && source <= 2147483647);
    alg_require(Number.isInteger(target) && target >= -2147483648 && target <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((graph.length == alg_mul(n, n)));
    alg_require(((n >= 1) && (source >= 0) && (source < n)));
    alg_require(((target >= 0) && (target < n)));
    let distance = new Int32Array(alg_size(n));
    let queue = new Int32Array(alg_size(n));
    let v = 0;
    let u = 0;
    let head = 0;
    let tail = 1;
    while ((v < n)) {
        distance[v] = alg_sub(0, 1);
        v = alg_add(v, 1);
    }
    distance[source] = 0;
    queue[0] = source;
    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) && (distance[v] == alg_sub(0, 1)))) {
                distance[v] = alg_add(distance[u], 1);
                queue[tail] = v;
                tail = alg_add(tail, 1);
            }
            v = alg_add(v, 1);
        }
    }
    return distance[target];
}

let graph = new Int32Array([0, 1, 0, 0, 0, 1, 0, 0, 0]);
let n = 3;
let source = 0;
let target = 2;
let result = bfs_distance(graph, n, source, target);
console.log(result);