Heap Sort in JavaScript

"use strict";
// Heap Sort in JavaScript
//
// PURPOSE
// Heap sort uses a max heap so the largest remaining value can be moved to the end. It gives
// a worst-case time guarantee without a second array.
//
// METHOD
// Build a max heap from the bottom up. Swap its root with the last active element, shrink
// the heap, and sift the new root downward. The suffix is sorted after every extraction.
//
// COMPLEXITY
// O(n log n) time, O(1) auxiliary space; heap construction is O(n). Not stable.
//
// CONTRACT
// Sorts n elements ascending in place; returns 0.
// 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: 0.
// Expected a after call: [1, 1, 3, 5].
// 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 heap_sort(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let start = alg_sub(Math.floor(n / 2), 1);
    let end = alg_sub(n, 1);
    let root = 0;
    let child = 0;
    let temp = 0;
    while ((start >= 0)) {
        root = start;
        while ((alg_add(alg_mul(2, root), 1) < n)) {
            child = alg_add(alg_mul(2, root), 1);
            if (((alg_add(child, 1) < n) && (a[child] < a[alg_add(child, 1)]))) {
                child = alg_add(child, 1);
            }
            if ((a[root] >= a[child])) {
                break;
            }
            temp = a[root];
            a[root] = a[child];
            a[child] = temp;
            root = child;
        }
        start = alg_sub(start, 1);
    }
    while ((end > 0)) {
        temp = a[0];
        a[0] = a[end];
        a[end] = temp;
        root = 0;
        while ((alg_add(alg_mul(2, root), 1) < end)) {
            child = alg_add(alg_mul(2, root), 1);
            if (((alg_add(child, 1) < end) && (a[child] < a[alg_add(child, 1)]))) {
                child = alg_add(child, 1);
            }
            if ((a[root] >= a[child])) {
                break;
            }
            temp = a[root];
            a[root] = a[child];
            a[child] = temp;
            root = child;
        }
        end = alg_sub(end, 1);
    }
    return 0;
}

let a = new Int32Array([5, 1, 3, 1]);
let result = heap_sort(a);
console.log(result);
console.log(a);
// Expected a: [1, 1, 3, 5]