Dutch National Flag Partition in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Dutch National Flag Partition in C++
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and 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: [0, 0, 1, 2, 2].
// 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 dutch_flag(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));
    for (int alg_i = 0; alg_i < (int)a.size(); alg_i++) {
        int alg_value = a[alg_i];
        alg_require(((alg_value >= 0) && (alg_value <= 2)));
    }
    int low = 0;
    int mid = 0;
    int high = alg_sub(n, 1);
    int temp = 0;
    while ((mid <= high)) {
        if ((a[mid] == 0)) {
            temp = a[low];
            a[low] = a[mid];
            a[mid] = temp;
            low = alg_add(low, 1);
            mid = alg_add(mid, 1);
        } else {
            if ((a[mid] == 1)) {
                mid = alg_add(mid, 1);
            } else {
                temp = a[mid];
                a[mid] = a[high];
                a[high] = temp;
                high = alg_sub(high, 1);
            }
        }
    }
    return 0;
}

int main(void) {
    std::vector<int> a = {2, 0, 1, 2, 0};
    int result = dutch_flag(a);
    printf("%d\n", result);
    for (int z = 0; z < 5; z++) printf("%d ", a[z]);
    printf("\n");
    // Expected a: [0, 0, 1, 2, 2]
    return 0;
}