Solving the N-Queens Problem

The N-Queens problem is a classic problem in computer science, which involves placing N queens on an NxN chessboard in such a way that no two queens threaten each other. In other words, the goal is to find a configuration in which no two queens share the same row, column, or diagonal.

This problem can be solved using the backtracking technique, which is well-suited for situations where we need to explore all possible solutions by making a series of choices and undoing them when necessary.

To solve the N-Queens problem using backtracking, we start with an empty chessboard and try to place a queen in each column, one by one. We recursively explore all possible placements for the current column and backtrack if we encounter a situation where no queen can be placed without conflicting with the existing queens.

Let's take a look at an example implementation of the N-Queens problem in C++:

xxxxxxxxxx

}

#include <iostream>

using namespace std;

​

int main() {

  // N: The number of queens

  int N;

  cout << "Enter the number of queens: ";

  cin >> N;

​

  // Create an empty chessboard of size N x N

  char board[N][N];

  for (int i = 0; i < N; i++) {

    for (int j = 0; j < N; j++) {

      board[i][j] = '.';

    }

  }

​

  // Function to check if a queen can be placed at a given position

  auto isSafe = [&](int row, int col) -> bool {

    // Check if there is any queen in the same row

    for (int i = 0; i < col; i++) {

      if (board[row][i] == 'Q')

        return false;

    }

​

    // Check if there is any queen in the upper diagonal

    for (int i = row, j = col; i >= 0 && j >= 0; i--, j--) {

      if (board[i][j] == 'Q')

        return false;