82. N Queens - Constraint Satisfaction

You're building a puzzle solver that needs to place N queens on an N×N chessboard such that no two queens attack each other. This is a classic constraint satisfaction problem used in scheduling, resource allocation, and optimization.

The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.

Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.

Requirements

1. Basic Functionality

• Place n queens on n×n board
• No two queens attack each other (same row, column, or diagonal)
• Return all distinct solutions
• Each solution is an array of strings representing the board

Example Usage

solveNQueens(4);
// [
//   [".Q..","...Q","Q...","..Q."],
//   ["..Q.","Q...","...Q",".Q.."]
// ]

solveNQueens(1);
// [["Q"]]

Real-World Context

This problem models real constraint satisfaction scenarios:

• Scheduling: Assign tasks without conflicts
• Resource allocation: Place resources without interference
• Optimization: Find valid configurations
• Puzzle solving: Classic backtracking problem