Merge pull request #198 from Venkatesh-24/master

Added NQueens Leetcode Solution

Author: SarthakKeshari

LeetCode/NQueens.java

@@ -0,0 +1,81 @@
+// link https://leetcode.com/problems/n-queens/
+
+// Approach : We use a recursive backtracking approach to solve 
+// this problem
+
+// To get the intuition behind the solution Watch this video
+// https://youtu.be/Ph95IHmRp5M
+
+import java.util.List;
+import java.util.ArrayList;
+class NQueens {
+    public List<List<String>> solveNQueens(int n) {
+        
+        List<List<String>> l = new ArrayList<List<String>>();
+        int a[] = new int[n];
+        
+        findNQueens(l,n,0,a);
+        return l;
+        
+    }
+    
+    public void findNQueens(List<List<String>> l, int n, int k, int a[])
+    {
+        // if k == n then it means we have successfully placed all
+        // the N Queens so we add it to the resultant list
+        if(k == n)
+        {
+            List<String> board = new ArrayList<String>();
+            for(int row = 0; row < n; row++)
+            {
+                StringBuilder sb = new StringBuilder(n);   
+                for(int col = 0; col < n; col++)
+                {
+                    if(col == a[row])
+                    {
+                        sb.append("Q");
+                    }
+                    else
+                    {
+                        sb.append(".");
+                    }
+                }
+                board.add(sb.toString());
+                
+            }
+            l.add(board);
+        }
+        
+        // The for loop traverses the entire matrix placing each 
+        // queen at a position and checking if it is valid
+        for(int i = k; i < n; i++)
+        {
+            for(int j = 0; j < n; j++)
+            {
+                
+                if(isValid(i,j,a))
+                {
+                    //System.out.println(i + " " + j);
+                    a[i] = j;
+                    findNQueens(l,n,i+1,a);
+                }
+            }
+            return;
+        }
+    }
+    
+    //This function checks whether placing Queen at a particular 
+    // position affects previously placed Queens
+    public boolean isValid(int i, int j, int a[])
+    {
+        for(int k = 0; k < i; k++)
+        {
+            int diff = j - a[k];
+            if(a[k] == j || i - k == diff || i - k == -diff)
+            {
+                return false;
+            }
+        }
+        return true;
+    }
+}