Disjoint Set Union in JavaScript

"use strict";
// Disjoint Set Union in JavaScript
//
// PURPOSE
// Disjoint set union maintains connected components as a forest of parent links. Union by
// size and path compression keep repeated operations nearly constant in amortized time.
//
// METHOD
// Start with each vertex as its own component. Find each edge endpoint root with path
// halving. If roots differ, attach the smaller tree to the larger and decrease the component
// count.
//
// COMPLEXITY
// O(n + m alpha(n)) amortized time and O(n) auxiliary space, where alpha is the inverse
// Ackermann function.
//
// CONTRACT
// n >= 0; edge arrays u_edges and v_edges have m valid vertex indices each. Treats edges as
// undirected. Returns component count; isolated vertices count separately.
// 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 component_count(u_edges, v_edges, n) {
    alg_require(u_edges instanceof Int32Array);
    alg_require(v_edges instanceof Int32Array);
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    let m = u_edges.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require((u_edges.length == m));
    alg_require((v_edges.length == m));
    for (let alg_i = 0; alg_i < u_edges.length; alg_i++) {
        let alg_value = u_edges[alg_i];
        alg_require(((alg_value >= 0) && (alg_value < n)));
    }
    for (let alg_i = 0; alg_i < v_edges.length; alg_i++) {
        let alg_value = v_edges[alg_i];
        alg_require(((alg_value >= 0) && (alg_value < n)));
    }
    let parent = new Int32Array(alg_size(alg_add(n, 1)));
    let size = new Int32Array(alg_size(alg_add(n, 1)));
    let i = 0;
    let edge = 0;
    let u = 0;
    let v = 0;
    let temp = 0;
    let count = n;
    while ((i < n)) {
        parent[i] = i;
        size[i] = 1;
        i = alg_add(i, 1);
    }
    while ((edge < m)) {
        u = u_edges[edge];
        v = v_edges[edge];
        while ((parent[u] != u)) {
            parent[u] = parent[parent[u]];
            u = parent[u];
        }
        while ((parent[v] != v)) {
            parent[v] = parent[parent[v]];
            v = parent[v];
        }
        if ((u != v)) {
            if ((size[u] < size[v])) {
                temp = u;
                u = v;
                v = temp;
            }
            parent[v] = u;
            size[u] = alg_add(size[u], size[v]);
            count = alg_sub(count, 1);
        }
        edge = alg_add(edge, 1);
    }
    return count;
}

let u_edges = new Int32Array([0, 1, 3]);
let v_edges = new Int32Array([1, 2, 4]);
let n = 5;
let result = component_count(u_edges, v_edges, n);
console.log(result);