Heap Sort in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Heap Sort in C++
//
// 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
// C++17: const vector references for inputs, mutable references for outputs, RAII workspace,
// standard lower_bound for LIS. Invalid inputs throw invalid_argument; overflow throws
// overflow_error; allocation failure propagates bad_alloc.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [1, 1, 3, 5].
// Run: g++ -std=c++17 -O2 example.cpp -o example && ./example
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

static int alg_min(int a, int b) { return a < b ? a : b; }
static int alg_max(int a, int b) { return a > b ? a : b; }
static void alg_require(bool valid) { if (!valid) throw std::invalid_argument("invalid algorithm input"); }
static int alg_checked(int64_t v) { if (v < INT32_MIN || v > INT32_MAX) throw std::overflow_error("32-bit result overflow"); return (int)v; }
static int alg_add(int a,int b) { return alg_checked((int64_t)a+b); }
static int alg_sub(int a,int b) { return alg_checked((int64_t)a-b); }
static int alg_mul(int a,int b) { return alg_checked((int64_t)a*b); }
static size_t alg_size(int n) { alg_require(n>=0 && n<=4000000); return (size_t)n; }

int heap_sort(std::vector<int>& a) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    int start = alg_sub((n / 2), 1);
    int end = alg_sub(n, 1);
    int root = 0;
    int child = 0;
    int 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;
}

int main(void) {
    std::vector<int> a = {5, 1, 3, 1};
    int result = heap_sort(a);
    printf("%d\n", result);
    for (int z = 0; z < 4; z++) printf("%d ", a[z]);
    printf("\n");
    // Expected a: [1, 1, 3, 5]
    return 0;
}