Sudoku Backtracking Solver in JavaScript

"use strict";
// Sudoku Backtracking Solver in JavaScript
//
// 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
// Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic
// lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or
// overflow throw RangeError.
//
// 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: node example.js
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); }
function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; }
function alg_add(a,b) { return alg_checked(a+b); }
function alg_sub(a,b) { return alg_checked(a-b); }
function alg_mul(a,b) { return alg_checked(a*b); }
function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; }

function sudoku_solve(board) {
    alg_require(board instanceof Int32Array);
    alg_require((board.length == 81));
    for (let alg_i = 0; alg_i < board.length; alg_i++) {
        let alg_value = board[alg_i];
        alg_require(((alg_value >= 0) && (alg_value <= 9)));
    }
    let rows = new Int32Array(alg_size(90));
    let cols = new Int32Array(alg_size(90));
    let boxes = new Int32Array(alg_size(90));
    let empty = new Int32Array(alg_size(81));
    let count = 0;
    let position = 0;
    let cell = 0;
    let r = 0;
    let c = 0;
    let box = 0;
    let digit = 0;
    while ((cell < 81)) {
        r = Math.floor(cell / 9);
        c = (cell % 9);
        box = alg_add(alg_mul(Math.floor(r / 3), 3), Math.floor(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 = Math.floor(cell / 9);
        c = (cell % 9);
        box = alg_add(alg_mul(Math.floor(r / 3), 3), Math.floor(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;
}

let board = new Int32Array([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]);
let result = sudoku_solve(board);
console.log(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.log(Array.from(board));