Sudoku Backtracking Solver in C#

using System;
// 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# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// 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: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int sudoku_solve(Span<int> board) {
        checked {
            alg_require((board.Length == 81));
            for (int alg_i = 0; alg_i < board.Length; alg_i++) {
                int alg_value = board[alg_i];
                alg_require(((alg_value >= 0) && (alg_value <= 9)));
            }
            int[] rows = new int[alg_size(90)];
            int[] cols = new int[alg_size(90)];
            int[] boxes = new int[alg_size(90)];
            int[] empty = new int[alg_size(81)];
            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 = (((r / 3) * 3) + (c / 3));
                digit = board[cell];
                if ((digit == 0)) {
                    empty[count] = cell;
                    count = (count + 1);
                } else {
                    if (((rows[((r * 10) + digit)] != 0) || (cols[((c * 10) + digit)] != 0) || (boxes[((box * 10) + digit)] != 0))) {
                        return (-1);
                    }
                    rows[((r * 10) + digit)] = 1;
                    cols[((c * 10) + digit)] = 1;
                    boxes[((box * 10) + digit)] = 1;
                }
                cell = (cell + 1);
            }
            while (((position >= 0) && (position < count))) {
                cell = empty[position];
                r = (cell / 9);
                c = (cell % 9);
                box = (((r / 3) * 3) + (c / 3));
                digit = board[cell];
                if ((digit != 0)) {
                    rows[((r * 10) + digit)] = 0;
                    cols[((c * 10) + digit)] = 0;
                    boxes[((box * 10) + digit)] = 0;
                }
                digit = (digit + 1);
                while (((digit <= 9) && ((rows[((r * 10) + digit)] != 0) || (cols[((c * 10) + digit)] != 0) || (boxes[((box * 10) + digit)] != 0)))) {
                    digit = (digit + 1);
                }
                if ((digit == 10)) {
                    board[cell] = 0;
                    position = (position - 1);
                } else {
                    board[cell] = digit;
                    rows[((r * 10) + digit)] = 1;
                    cols[((c * 10) + digit)] = 1;
                    boxes[((box * 10) + digit)] = 1;
                    position = (position + 1);
                }
            }
            if ((position == count)) {
                return 1;
            }
            return 0;
        }
    }

    static void Main() {
        int[] board = new int[] {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);
        Console.WriteLine(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]
        Console.WriteLine("[" + string.Join(", ", board) + "]");
    }
}