Iterative Quick Sort in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Iterative Quick Sort in C++
//
// PURPOSE
// Quick sort partitions around a pivot and sorts the two resulting regions. This iterative
// version stores pending intervals explicitly instead of using recursion.
//
// METHOD
// Choose a median-of-three pivot and partition into less-than, equal-to, and greater-than
// regions. Process the smaller region immediately and defer the larger one to keep the
// explicit stack bounded.
//
// COMPLEXITY
// O(n log n) average time, O(n squared) adversarial worst case. Equal-key input takes O(n).
// O(log n) pending intervals; 64 stack slots cover the supported bounded input lengths. Not
// stable.
//
// CONTRACT
// Sorts ascending in place and returns 0. Three-way partition handles repeated keys
// efficiently. Median-of-three reduces common fixed-endpoint pivot problems but does not
// provide introsort's worst-case guarantee.
// 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 quick_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));
    std::vector<int> lefts(alg_size(64), 0);
    std::vector<int> rights(alg_size(64), 0);
    int top = 0;
    int low = 0;
    int high = alg_sub(n, 1);
    int left = 0;
    int right = 0;
    int mid = 0;
    int pivot = 0;
    int temp = 0;
    while (((low < high) || (top > 0))) {
        if ((low >= high)) {
            top = alg_sub(top, 1);
            low = lefts[top];
            high = rights[top];
        }
        mid = alg_add(low, (alg_sub(high, low) / 2));
        pivot = alg_max(alg_min(a[low], a[mid]), alg_min(alg_max(a[low], a[mid]), a[high]));
        left = low;
        mid = low;
        right = high;
        while ((mid <= right)) {
            if ((a[mid] < pivot)) {
                temp = a[left];
                a[left] = a[mid];
                a[mid] = temp;
                left = alg_add(left, 1);
                mid = alg_add(mid, 1);
            } else {
                if ((a[mid] > pivot)) {
                    temp = a[mid];
                    a[mid] = a[right];
                    a[right] = temp;
                    right = alg_sub(right, 1);
                } else {
                    mid = alg_add(mid, 1);
                }
            }
        }
        if ((alg_sub(left, low) < alg_sub(high, right))) {
            if ((alg_add(right, 1) < high)) {
                lefts[top] = alg_add(right, 1);
                rights[top] = high;
                top = alg_add(top, 1);
            }
            high = alg_sub(left, 1);
        } else {
            if ((low < alg_sub(left, 1))) {
                lefts[top] = low;
                rights[top] = alg_sub(left, 1);
                top = alg_add(top, 1);
            }
            low = alg_add(right, 1);
        }
    }
    return 0;
}

int main(void) {
    std::vector<int> a = {5, 1, 3, 1};
    int result = quick_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;
}