Added the N-queen solver by using Backtracting(Recursion)

src/main/java/datastructures/Backtracking/nqueen.java

@@ -0,0 +1,109 @@
+// in this question queen are placed in level and boxes are choice for queen
+class nqueen{
+public static boolean isQueensafe(boolean[][] chess,int r,int c){
+   for(int j=c-1;j>=0;j--){
+     if(chess[r][j]==true){
+       return false;
+     }
+   }
+    for(int i=r-1;i>=0;i--){
+     if(chess[i][c]==true){
+       return false;
+     }
+   }
+  for(int i=r-1,j=c-1 ;i>=0 && j>=0; i-- ,j--){
+
+     if(chess[i][j]==true){
+       return false;
+     }
+
+  }
+
+   for(int i=r-1 ,j=c+1;i>=0 && j<chess[0].length ; i-- ,j++){
+
+     if(chess[i][j]==true){
+       return false;
+     }
+
+   }
+
+
+   return true;
+
+}
+// for combination with no kill queen
+  public static int count=0; 
+  public static void path(boolean[][] chess,int cq,int lqi,int lqj,String asf){
+
+      if(cq==chess.length){
+        System.out.println(asf);
+        return;
+      }
+
+      for(int i=lqi;i<chess.length;i++){
+        /*int j=lqj+1;
+        if(i>lqi){
+          j=0;
+        }*/
+        for(int j=(i==lqi?lqj+1:0) ;j<chess[0].length;j++){
+        if(chess[i][j]==false && isQueensafe(chess,i,j)==true){
+          chess[i][j]=true;
+          path(chess,cq+1,i,j,asf+i+j+"-");
+          chess[i][j]=false;  
+         }
+      }
+
+      }
+    }
+
+
+
+
+//only for permutation of 16 boxes for 4 queen = total permuuataion is 43680
+public static void pathpermu(boolean[][] chess ,int cq,String asf){
+   if(cq>chess.length){
+      System.out.println(++count+"-"+asf);
+      return;
+   }
+   for(int i=0;i<chess.length;i++){
+     for(int j=0;j<chess.length;j++){
+       if(chess[i][j]==false){
+         chess[i][j]=true;
+         pathpermu(chess,cq+1,asf+i+j+"-");
+         chess[i][j]=false;
+       }
+     }
+   }
+
+}
+//only for combination of 16 boxes for 4 queen = total combination is 1820
+public static void pathcombi(boolean[][] chess ,int cq,int lqi,int lqj,String asf){
+   if(cq==chess.length){
+      System.out.println(++count+"-"+asf);
+      return;
+   }
+   for(int i=lqi;i<chess.length;i++){
+
+      int j=lqj+1;
+        if(i>lqi){
+          j=0;
+        }
+     for(;j<chess.length;j++){
+       if(chess[i][j]==false){
+         chess[i][j]=true;
+         pathcombi(chess,cq+1,i,j,asf+i+j+"-");
+         chess[i][j]=false;
+       }
+     }
+   }
+
+   }
+public static void main(String[] args){
+        boolean[][] chess=new boolean[4][4];
+
+        path(chess,0,0,-1,"");//parameters chess array,current queen,initial index for row,initial index for col. -1 because int function +1 usefor j
+        //pathpermu(chess,1,"");
+        //pathcombi(chess,0,0,-1,"");
+
+    }
+}