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import java.util.ArrayList;

public class Recursion2 {

public static void main(String[] args) {

System.out.println(count(3, 3));

path("", 3, 3);

//2

boolean [] [] board = {

{true ,true , true},

{true ,true , true},

{true ,true , true}

};

allpaths("", board, 0, 0);

// N QUEEN QUESTION

int n = 4 ;

boolean [] [] board1 = new boolean[n][n];

Queen q = new Queen();

System.out.println(q.queens(board1,0));

}

// mase path question

static int count (int r ,int c){

if (r==1 || c==1){

return 1 ;

}

int left = count(r-1, c);

int right = count(r ,c-1);

return left+ right ;

}

static void path (String p , int r , int c){

if (r==1 && c==1){

System.out.println(p);

return ;

}

if (r>1){

path(p + 'D', r-1, c);

}

if (c>1){

path(p + 'R', r, c-1);

}

}

// in all dirtion :=

static void allpaths(String p , boolean maze [] [] , int r , int c){

if (r == maze.length-1 && c == maze[0].length-1){

System.out.println(p);

return;

}

if (!maze[r][c]){

return ;

}

// to mark visited place false and not go to them

maze [r] [c] = false ;

if (r < maze.length-1){

allpaths(p+'D', maze, r+1, c);

}

if (c < maze[0].length-1){

allpaths(p+'R', maze, r, c+1);

}

if (r>0){

allpaths(p+'U', maze, r-1, c);

}

if (c>0){

allpaths(p+'L', maze, r, c-1);

}

// to reverse the changes that made to allow the next recursion call happen

maze [r] [c] = true ;

}

}

class Queen {

static int queens(boolean [] [] board , int r){

if (r== board.length){

display (board);

System.out.println( );

return 1 ;

}

int count = 0 ;

// place for Queen

for (int c = 0; c < board.length; c++) {

if (isSafe(board , r , c)){

board[r][c] = true ;

count += queens(board, r+1);

board[r][c] = false;

}

}

return count ;

}

static boolean isSafe (boolean board[][] , int r , int c){

// vertical row check

for (int i = 0; i < r; i++) {

if (board[i][c] ){

return false ;

}

}

int maxLeft = Math.min(r, c);

// left diagonal

for (int i = 1; i <= maxLeft; i++) {

if (board[r-i][c-i]){

return false ;

}

}

// right diagonal

int maxRight = Math.min(r, board.length -c-1);

for (int i = 1; i <= maxRight; i++) {

if (board[r-i][c+i]){

return false ;

}

}

return true ;

}

static void display (boolean [][] board){

for (boolean[] r : board){

for(boolean element : r){

if (element){

System.out.print("Q ");

}

else{

System.out.print("X ");

}

}

System.out.println( );

}

}

}