Sudoku Backtracking Solver in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Sudoku Backtracking Solver in C++
//
// PURPOSE
// A Sudoku solver fills a 9 by 9 grid while respecting row, column, and box uniqueness.
//
// METHOD
// Validate givens into three occupancy tables, collect empty cells, then try candidate
// digits with iterative backtracking. On exhaustion restore each original empty cell to
// zero.
//
// COMPLEXITY
// Exponential worst-case search in the number of empty cells; O(81) bounded workspace.
//
// CONTRACT
// board has 81 values in [0,9], where 0 means empty. Returns 1 after solving, 0 if
// unsatisfiable, -1 for conflicting givens. On failure leaves board unchanged.
// 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: 1.
// Expected board after call: [5, 3, 4, 6, 7, 8, 9, 1, 2, 6, 7, 2, 1, 9, 5, 3, 4, 8, 1, 9, 8,
// 3, 4, 2, 5, 6, 7, 8, 5, 9, 7, 6, 1, 4, 2, 3, 4, 2, 6, 8, 5, 3, 7, 9, 1, 7, 1, 3, 9, 2, 4,
// 8, 5, 6, 9, 6, 1, 5, 3, 7, 2, 8, 4, 2, 8, 7, 4, 1, 9, 6, 3, 5, 3, 4, 5, 2, 8, 6, 1, 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 sudoku_solve(std::vector<int>& board) {
    alg_require(board.size() <= 1000000);
    alg_require(((int)board.size() == 81));
    for (int alg_i = 0; alg_i < (int)board.size(); alg_i++) {
        int alg_value = board[alg_i];
        alg_require(((alg_value >= 0) && (alg_value <= 9)));
    }
    std::vector<int> rows(alg_size(90), 0);
    std::vector<int> cols(alg_size(90), 0);
    std::vector<int> boxes(alg_size(90), 0);
    std::vector<int> empty(alg_size(81), 0);
    int count = 0;
    int position = 0;
    int cell = 0;
    int r = 0;
    int c = 0;
    int box = 0;
    int digit = 0;
    while ((cell < 81)) {
        r = (cell / 9);
        c = (cell % 9);
        box = alg_add(alg_mul((r / 3), 3), (c / 3));
        digit = board[cell];
        if ((digit == 0)) {
            empty[count] = cell;
            count = alg_add(count, 1);
        } else {
            if (((rows[alg_add(alg_mul(r, 10), digit)] != 0) || (cols[alg_add(alg_mul(c, 10), digit)] != 0) || (boxes[alg_add(alg_mul(box, 10), digit)] != 0))) {
                return alg_sub(0, 1);
            }
            rows[alg_add(alg_mul(r, 10), digit)] = 1;
            cols[alg_add(alg_mul(c, 10), digit)] = 1;
            boxes[alg_add(alg_mul(box, 10), digit)] = 1;
        }
        cell = alg_add(cell, 1);
    }
    while (((position >= 0) && (position < count))) {
        cell = empty[position];
        r = (cell / 9);
        c = (cell % 9);
        box = alg_add(alg_mul((r / 3), 3), (c / 3));
        digit = board[cell];
        if ((digit != 0)) {
            rows[alg_add(alg_mul(r, 10), digit)] = 0;
            cols[alg_add(alg_mul(c, 10), digit)] = 0;
            boxes[alg_add(alg_mul(box, 10), digit)] = 0;
        }
        digit = alg_add(digit, 1);
        while (((digit <= 9) && ((rows[alg_add(alg_mul(r, 10), digit)] != 0) || (cols[alg_add(alg_mul(c, 10), digit)] != 0) || (boxes[alg_add(alg_mul(box, 10), digit)] != 0)))) {
            digit = alg_add(digit, 1);
        }
        if ((digit == 10)) {
            board[cell] = 0;
            position = alg_sub(position, 1);
        } else {
            board[cell] = digit;
            rows[alg_add(alg_mul(r, 10), digit)] = 1;
            cols[alg_add(alg_mul(c, 10), digit)] = 1;
            boxes[alg_add(alg_mul(box, 10), digit)] = 1;
            position = alg_add(position, 1);
        }
    }
    if ((position == count)) {
        return 1;
    }
    return 0;
}

int main(void) {
    std::vector<int> board = {5, 3, 4, 6, 7, 8, 9, 1, 2, 6, 7, 2, 1, 9, 5, 3, 4, 8, 1, 9, 8, 3, 4, 2, 5, 6, 7, 8, 5, 9, 7, 6, 1, 4, 2, 3, 4, 2, 6, 8, 5, 3, 7, 9, 1, 7, 1, 3, 9, 2, 4, 8, 5, 6, 9, 6, 1, 5, 3, 7, 2, 8, 4, 2, 8, 7, 4, 1, 9, 6, 3, 5, 3, 4, 5, 2, 8, 6, 1, 7, 0};
    int result = sudoku_solve(board);
    printf("%d\n", result);
    // Expected board: [5, 3, 4, 6, 7, 8, 9, 1, 2, 6, 7, 2, 1, 9, 5, 3, 4, 8, 1, 9, 8, 3, 4, 2, 5, 6, 7, 8, 5, 9, 7, 6, 1, 4, 2, 3, 4, 2, 6, 8, 5, 3, 7, 9, 1, 7, 1, 3, 9, 2, 4, 8, 5, 6, 9, 6, 1, 5, 3, 7, 2, 8, 4, 2, 8, 7, 4, 1, 9, 6, 3, 5, 3, 4, 5, 2, 8, 6, 1, 7, 9]
    for (int alg_print = 0; alg_print < 81; alg_print++) printf("%d ", board[alg_print]);
    printf("\n");
    return 0;
}