Added N-Queens to DP

DP/n_queens_problem.cpp

@@ -0,0 +1,65 @@
+#include<iostream>
+using namespace std;
+bool isSafe(int board[][10], int row, int col, int n) //This function is to check whether queen can be placed safely or not
+{
+ for(int i=0;i<col;i++)
+ {
+ if(board[row][i] == 1)
+ {
+ return false;
+ }
+ }
+ for(int i=row,j=col;i>=0 && j>=0;i--,j--)
+ {
+ if(board[i][j] ==1)
+ {
+ return false;
+ }
+ }
+ for(int i=row,j=col;i<n && j>=0;i++,j--)
+ {
+ if(board[i][j] ==1)
+ {
+ return false;
+ }
+ }
+ return true;
+}
+bool nQueen(int board[][10], int col, int n)
+{
+ if(col>=n)
+ {
+ for(int i=0;i<n;i++) //Simple printing of the board 
+ {
+ for(int j=0;j<n;j++)
+ {
+ cout<<board[i][j]<<" ";
+ }
+ cout<<endl;
+ }
+ return true;
+ }
+ for(int i=0;i<n;i++)
+ {
+ if(isSafe(board,i,col,n))
+ {
+ board[i][col]=1;
+ if(nQueen(board,col+1,n)) //Recursively calling the function to keep another queen
+ {
+ return true;
+ }
+ board[i][col]=0; //Backtracking
+ }
+ }
+ return false; //if control reaches over here that means there is no way to place queen on such a board
+}
+int main()
+{
+ int n;
+ int board[10][10]={0}; //Initially no queen on board
+ cin>>n;
+ bool check = nQueen(board,0,n); //function calling
+ if(check == false)
+ cout<<-1;
+ return 0;
+}