Monotonic Deque Sliding Maximum in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Monotonic Deque Sliding Maximum in C++
//
// PURPOSE
// A monotonic deque returns every fixed-window maximum in linear time.
//
// METHOD
// Keep candidate indices in decreasing value order. Discard expired indices from the front
// and dominated candidates from the back; the front is the current maximum.
//
// COMPLEXITY
// O(n) time; O(n) allocated index-buffer space in this linear-buffer implementation, with at
// most k live candidates.
//
// CONTRACT
// 1 <= k <= n. output has n-k+1 entries. Writes maximum values and returns output length.
// 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: 6.
// Expected output after call: [3, 3, 5, 5, 6, 7].
// 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 sliding_maximum(const std::vector<int>& a, int k, std::vector<int>& output) {
    alg_require(a.size() <= 1000000);
    alg_require(output.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    alg_require(((int)output.size() == alg_add(alg_sub(n, k), 1)));
    alg_require(((k >= 1) && (k <= n)));
    std::vector<int> queue(alg_size(n), 0);
    int head = 0;
    int tail = 0;
    int i = 0;
    while ((i < n)) {
        while (((head < tail) && (queue[head] <= alg_sub(i, k)))) {
            head = alg_add(head, 1);
        }
        while (((head < tail) && (a[queue[alg_sub(tail, 1)]] <= a[i]))) {
            tail = alg_sub(tail, 1);
        }
        queue[tail] = i;
        tail = alg_add(tail, 1);
        if ((i >= alg_sub(k, 1))) {
            output[alg_add(alg_sub(i, k), 1)] = a[queue[head]];
        }
        i = alg_add(i, 1);
    }
    return alg_add(alg_sub(n, k), 1);
}

int main(void) {
    std::vector<int> a = {1, 3, -1, -3, 5, 3, 6, 7};
    int k = 3;
    std::vector<int> output = {0, 0, 0, 0, 0, 0};
    int result = sliding_maximum(a, k, output);
    printf("%d\n", result);
    // Expected output: [3, 3, 5, 5, 6, 7]
    for (int alg_print = 0; alg_print < 6; alg_print++) printf("%d ", output[alg_print]);
    printf("\n");
    return 0;
}