Sudoku Backtracking Solver in Java

// Sudoku Backtracking Solver in Java
//
// 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// 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: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

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

    static int sudoku_solve(int[] board) {
        java.util.Objects.requireNonNull(board, "board");
        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 = Math.addExact(Math.multiplyExact((r / 3), 3), (c / 3));
            digit = board[cell];
            if ((digit == 0)) {
                empty[count] = cell;
                count = Math.addExact(count, 1);
            } else {
                if (((rows[Math.addExact(Math.multiplyExact(r, 10), digit)] != 0) || (cols[Math.addExact(Math.multiplyExact(c, 10), digit)] != 0) || (boxes[Math.addExact(Math.multiplyExact(box, 10), digit)] != 0))) {
                    return Math.negateExact(1);
                }
                rows[Math.addExact(Math.multiplyExact(r, 10), digit)] = 1;
                cols[Math.addExact(Math.multiplyExact(c, 10), digit)] = 1;
                boxes[Math.addExact(Math.multiplyExact(box, 10), digit)] = 1;
            }
            cell = Math.addExact(cell, 1);
        }
        while (((position >= 0) && (position < count))) {
            cell = empty[position];
            r = (cell / 9);
            c = (cell % 9);
            box = Math.addExact(Math.multiplyExact((r / 3), 3), (c / 3));
            digit = board[cell];
            if ((digit != 0)) {
                rows[Math.addExact(Math.multiplyExact(r, 10), digit)] = 0;
                cols[Math.addExact(Math.multiplyExact(c, 10), digit)] = 0;
                boxes[Math.addExact(Math.multiplyExact(box, 10), digit)] = 0;
            }
            digit = Math.addExact(digit, 1);
            while (((digit <= 9) && ((rows[Math.addExact(Math.multiplyExact(r, 10), digit)] != 0) || (cols[Math.addExact(Math.multiplyExact(c, 10), digit)] != 0) || (boxes[Math.addExact(Math.multiplyExact(box, 10), digit)] != 0)))) {
                digit = Math.addExact(digit, 1);
            }
            if ((digit == 10)) {
                board[cell] = 0;
                position = Math.subtractExact(position, 1);
            } else {
                board[cell] = digit;
                rows[Math.addExact(Math.multiplyExact(r, 10), digit)] = 1;
                cols[Math.addExact(Math.multiplyExact(c, 10), digit)] = 1;
                boxes[Math.addExact(Math.multiplyExact(box, 10), digit)] = 1;
                position = Math.addExact(position, 1);
            }
        }
        if ((position == count)) {
            return 1;
        }
        return 0;
    }

    public static void main(String[] args) {
        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);
        System.out.println(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]
        System.out.println(java.util.Arrays.toString(board));
    }
}