Prim Minimum Spanning Tree in JavaScript

"use strict";
// Prim Minimum Spanning Tree in JavaScript
//
// PURPOSE
// Prim grows a minimum spanning tree by choosing the cheapest edge that connects an
// unvisited vertex to the current tree. The cut property justifies each greedy choice.
//
// METHOD
// Keep the cheapest connection cost for every unvisited vertex. Select the cheapest one, add
// its cost, and update neighbors. If no finite connection remains before all vertices are
// added, the graph is disconnected.
//
// COMPLEXITY
// O(n squared) time and O(n) auxiliary space for a dense adjacency matrix.
//
// CONTRACT
// n >= 1; symmetric flattened matrix for an undirected graph. -1 means absent, weights are
// nonnegative and < 1,000,000,000. Total must fit. Returns MST weight or -1 if disconnected.
// 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: 6.
// 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 prim_mst(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)));
    alg_require((n >= 1));
    for (let alg_i = 0; alg_i < graph.length; alg_i++) {
        let alg_value = graph[alg_i];
        alg_require(((alg_value >= alg_sub(0, 1)) && (alg_value < 1000000000)));
    }
    let cost = new Int32Array(alg_size(n));
    let used = new Int32Array(alg_size(n));
    let i = 0;
    let v = 0;
    let u = 0;
    let best = 0;
    let total = 0;
    while ((i < n)) {
        cost[i] = 1000000000;
        i = alg_add(i, 1);
    }
    cost[0] = 0;
    i = 0;
    while ((i < n)) {
        u = alg_sub(0, 1);
        best = 1000000000;
        v = 0;
        while ((v < n)) {
            if (((used[v] == 0) && (cost[v] < best))) {
                best = cost[v];
                u = v;
            }
            v = alg_add(v, 1);
        }
        if ((u == alg_sub(0, 1))) {
            return alg_sub(0, 1);
        }
        used[u] = 1;
        total = alg_add(total, cost[u]);
        v = 0;
        while ((v < n)) {
            if ((graph[alg_add(alg_mul(u, n), v)] >= 0)) {
                cost[v] = Math.min(cost[v], graph[alg_add(alg_mul(u, n), v)]);
            }
            v = alg_add(v, 1);
        }
        i = alg_add(i, 1);
    }
    return total;
}

let graph = new Int32Array([0, 4, 10, 4, 0, 2, 10, 2, 0]);
let n = 3;
let result = prim_mst(graph, n);
console.log(result);