# Solving the N-Queens Problem in C# | Print all possible solutions to N–Queens problem in C#

The N–queens puzzle is the problem of placing `N` chess queens on an `N × N` chessboard so that no two queens threaten each other. Thus, the solution requires that no two queens share the same row, column, or diagonal.

N-Queens is a tricky problem. To solve this problem efficiently, it requires knowing the backtracking algorithm. Basically, the problem is to place N queens on an NxN chessboard. So in this article, we will discuss how to solve the N-Queens problem using a backtracking algorithm.

C# Code

 using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks;   namespace ConsoleApp1 {     class Program     {         const int N = 4;         static void Main(string[] args)         {             int count = 0;             int[,] board = new int[N, N];               //Initialize the board array to 0             for (int i = 0; i < N; i++)             {                 for (int j = 0; j < N; j++)                 {                     board[i, j] = 0;                 }             }               //Initialize the pointer array             int[] pointer = new int[N];             for (int i = 0; i < N; i++)             {                 pointer[i] = -1;             }               //Implementation of Back Tracking Algorithm             for (int j = 0; ;)             {                 pointer[j]++;                 //Reset and move one column back                 if (pointer[j] == N)                 {                     board[pointer[j] - 1, j] = 0;                     pointer[j] = -1;                     j--;                     if (j == -1)                     {                         Console.WriteLine("all possible solutions to N–Queens problem are done");                         break;                     }                 }                 else                 {                     board[pointer[j], j] = 1;                     if (pointer[j] != 0)                     {                         board[pointer[j] - 1, j] = 0;                     }                     if (SolutionCheck(board))                     {                         j++;//move to next column                         if (j == N)                         {                             j--;                             count++;                             Console.WriteLine("Solution" + count.ToString() + ":");                             for (int p = 0; p < N; p++)                             {                                 for (int q = 0; q < N; q++)                                 {                                     Console.Write(board[p, q] + " ");                                 }                                 Console.WriteLine();                             }                         }                     }                 }             }               Console.ReadLine();         }         public static bool SolutionCheck(int[,] board)         {             //Row check             for (int i = 0; i < N; i++)             {                 int sum = 0;                 for (int j = 0; j < N; j++)                 {                     sum = sum + board[i, j];                 }                 if (sum > 1)                 {                     return false;                 }             }             //Main diagonal check             //above             for (int i = 0, j = N - 2; j >= 0; j--)             {                 int sum = 0;                 for (int p = i, q = j; q < N; p++, q++)                 {                     sum = sum + board[p, q];                 }                 if (sum > 1)                 {                     return false;                 }             }             //below             for (int i = 1, j = 0; i < N - 1; i++)             {                 int sum = 0;                 for (int p = i, q = j; p < N; p++, q++)                 {                     sum = sum + board[p, q];                 }                 if (sum > 1)                 {                     return false;                 }             }             //Minor diagonal check             //above             for (int i = 0, j = 1; j < N; j++)             {                 int sum = 0;                 for (int p = i, q = j; q >= 0; p++, q--)                 {                     sum = sum + board[p, q];                 }                 if (sum > 1)                 {                     return false;                 }             }             //below             for (int i = 1, j = N - 1; i < N - 1; i++)             {                 int sum = 0;                 for (int p = i, q = j; p < N; p++, q--)                 {                     sum = sum + board[p, q];                 }                 if (sum > 1)                 {                     return false;                 }             }             return true;         }     }   }

Output