Added n-queen problem

README.md

@@ -151,6 +151,11 @@ This category should be reorganized.
 - number_theory/modular_arithmetics.cc
 - number_theory/primes.cc
 
+
+## Backtracking
+
+- n_queen_problem
+
 ## Other
 
 This category should be reorganized.

backtracking/n_queen_problem.cc

@@ -0,0 +1,75 @@
+/*
+** Provide the value of n
+** This program will print one of the solution of N-Queen problem if possible for given n.
+** N-Queen problem is a great example of backtracking.
+** where you chose a path and if the solution is not found you backtrack to choose a different path.
+*/
+
+#include<iostream>
+using namespace std;
+bool grid[10001][10001];
+int n;
+bool isAttacked(int x, int y)
+{
+    for(int i = 0; i < n; i++)
+    {
+        if(grid[i][y] || grid[x][i])
+            return true;
+    }
+    for(int i = x-1, j = y-1; i >= 0; i--, j--)
+    {
+        if(grid[i][j])
+            return true;
+    }
+    for(int i = x-1, j = y+1; i >= 0; i--, j++)
+    {
+        if(grid[i][j])
+            return true;
+    }
+    return false;
+}
+bool nQueen(int row)
+{
+    if(row >= n)
+        return true;
+    for(int i = 0; i < n; i++)
+    {
+        if(!isAttacked(row, i))
+        {
+            grid[row][i] = true;
+            if(nQueen(row + 1))
+                return true;
+            grid[row][i] = false;   //BACKTRACKING
+        }
+    }
+    return false;
+}
+int main()
+{
+    cout<<"Enter number of queens : ";
+    cin>>n;
+    for(int i =0; i < n; i++)
+        for(int j = 0; j < n; j++)
+            grid[i][j] =false;
+    if(nQueen(0))
+    {
+        cout<<"Solution :-\n";
+        for(int i = 0; i < n; i++)
+        {
+            for(int j = 0; j < n; j++)
+            {
+                if(grid[i][j])
+                    cout<<"Q ";
+                else
+                    cout<<"- ";
+            }
+            cout<<endl;
+        }
+    }
+    else
+    {
+        cout<<"No Answer.\n";
+    }
+
+    return 0;
+}