Quickselect in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Quickselect in C++
//
// PURPOSE
// Quickselect finds a zero-based order statistic without fully sorting the input.
//
// METHOD
// Partition around the middle-position pivot using a three-way partition. Retain only the
// side containing rank k, or return the pivot when k lies in the equal region.
//
// COMPLEXITY
// O(n) expected time for random input; O(n squared) worst case for this deterministic pivot.
// O(1) auxiliary space.
//
// CONTRACT
// 0 <= k < n. Mutates input. Returns the kth smallest value, counting duplicates.
// 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: 5.
// Expected a after call: [2, 2, 5, 7, 9].
// 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 quickselect(std::vector<int>& a, int k) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    alg_require(((k >= 0) && (k < n)));
    int low = 0;
    int high = alg_sub(n, 1);
    int left = 0;
    int mid = 0;
    int right = 0;
    int pivot = 0;
    int temp = 0;
    while ((low <= high)) {
        pivot = a[alg_add(low, (alg_sub(high, low) / 2))];
        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 ((k < left)) {
            high = alg_sub(left, 1);
        } else {
            if ((k > right)) {
                low = alg_add(right, 1);
            } else {
                return pivot;
            }
        }
    }
    return alg_sub(0, 1);
}

int main(void) {
    std::vector<int> a = {7, 2, 9, 2, 5};
    int k = 2;
    int result = quickselect(a, k);
    printf("%d\n", result);
    // Expected a: [2, 2, 5, 7, 9]
    for (int alg_print = 0; alg_print < 5; alg_print++) printf("%d ", a[alg_print]);
    printf("\n");
    return 0;
}