Create N-Queens_problem.cpp

Author: Lovecase

N-Queens_problem.cpp

@@ -0,0 +1,87 @@
+#include <iostream>
+#include <vector>
+using namespace std;
+
+bool isSafe(vector<vector<bool> > grid, int curr_row, int y, int n)
+{
+    for(int row=0; row<curr_row; row++)
+    {
+        if(grid[row][y]==1)                            //  checking for a row
+        {
+            return false;
+        }
+    }
+
+    int row=curr_row, col=y; 
+    while(row>=0  &&  col>=0)
+    {
+        if(grid[row][col]==1)                          //  checking for upper left diagonal
+        {
+            return false;
+        }
+        row--;
+        col--;
+    }
+
+    row=curr_row, col=y;
+    while(row>=0  &&  col<=n)
+    {
+        if(grid[row][col]==1)                          //  checking for upper right diagonal
+        {
+            return false;
+        }
+        row--;
+        col++;
+    }
+
+    return true;
+}
+
+void display(vector<vector<bool> > grid, int n)
+{
+    for(int i=0; i<n; i++)
+    {
+        for(int j=0; j<n; j++)
+        {
+            if(grid[i][j])
+            cout<<"1";
+
+            else
+            cout<<"0";
+        }
+        cout<<endl;
+    }   
+}
+
+// to count the no. of solutions possible
+int count=0;
+void countnQueen(vector<vector<bool> > &grid, int curr_row, int n)
+{
+    if(curr_row==n){
+        count++;
+        display(grid, n);
+        cout<<endl;
+        return;
+    }
+
+    for(int col=0; col<n; col++){
+        if(isSafe(grid, curr_row, col, n)){
+            grid[curr_row][col]=1;
+            countnQueen(grid, curr_row+1, n);
+            grid[curr_row][col]=0;                    // backtracking
+        }
+    }
+}
+
+int main()
+{
+    int n;
+    cin>>n;
+
+    vector<vector<bool> > grid(n, vector<bool>(n, false));
+
+    countnQueen(grid,0,n);
+    cout<<count;
+
+    return 0;
+}