N Queens Backtracking in JavaScript

"use strict";
// N Queens Backtracking in JavaScript
//
// PURPOSE
// N-queens places one queen in each row with no shared columns or diagonals.
//
// METHOD
// Try columns row by row. Keep occupied-column and diagonal marker arrays for constant-time
// safety checks. Backtrack when no column remains and count complete placements.
//
// COMPLEXITY
// Exponential search, bounded by O(n!) candidate placements with additional column-scan
// overhead; O(n) auxiliary space.
//
// CONTRACT
// 0<=n<=12. Returns solution count. The empty board has one placement. This implementation
// avoids recursion.
// 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.
// 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 n_queens(n) {
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((n >= 0) && (n <= 12)));
    let columns = new Int32Array(alg_size(alg_add(n, 1)));
    let rising = new Int32Array(alg_size(alg_add(alg_mul(2, n), 1)));
    let falling = new Int32Array(alg_size(alg_add(alg_mul(2, n), 1)));
    let placement = new Int32Array(alg_size(alg_add(n, 1)));
    let row = 0;
    let col = 0;
    let count = 0;
    if ((n == 0)) {
        return 1;
    }
    while ((row >= 0)) {
        col = placement[row];
        if ((col > 0)) {
            columns[alg_sub(col, 1)] = 0;
            rising[alg_sub(alg_add(row, col), 1)] = 0;
            falling[alg_add(alg_sub(row, col), n)] = 0;
        }
        while (((col < n) && ((columns[col] != 0) || (rising[alg_add(row, col)] != 0) || (falling[alg_sub(alg_add(alg_sub(row, col), n), 1)] != 0)))) {
            col = alg_add(col, 1);
        }
        if ((col == n)) {
            placement[row] = 0;
            row = alg_sub(row, 1);
        } else {
            placement[row] = alg_add(col, 1);
            columns[col] = 1;
            rising[alg_add(row, col)] = 1;
            falling[alg_sub(alg_add(alg_sub(row, col), n), 1)] = 1;
            if ((row == alg_sub(n, 1))) {
                count = alg_add(count, 1);
            } else {
                row = alg_add(row, 1);
                placement[row] = 0;
            }
        }
    }
    return count;
}

let n = 0;
let result = n_queens(n);
console.log(result);