In this tutorial, we will learn about Backtracking algorithm in Java and its approach to solve crosswords and puzzles problem

Backtracking algorithm resolves a problem by incrementally building candidates to the solution and abandoning a candidate as soon as it can not satisfy the constraint

## The N-Queen puzzle problem

Write an algorithm to place N chess queens on an NxN chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column or diagonal

## Backtracking approach

```
public class NQueens {
private void printBoard(int[][] board){
for (int i = 0; i < board.length; i++) {
for (int j = 0; j < board.length; j++) {
System.out.printf(" %d", board[i][j]);
}
System.out.println();
}
}
private boolean isValid(int[][] board, int row, int col) {
for (int i = 0; i < col; i++) {
if (board[row][i] == 1) return false;
}
for (int i = row, j = col; i >= 0 && j >= 0; i--, j--) {
if (board[i][j] == 1) return false;
}
for (int i = row, j = col; i < board.length && j >= 0 ; i++, j--) {
if (board[i][j] == 1) return false;
}
return true;
}
public boolean enumerate(int[][] board, int col) {
if (col == board.length) return true;
for (int i = 0; i < board.length; i++) {
if (isValid(board, i, col)) {
board[i][col] = 1;
if (enumerate(board, col+1)) return true;
board[i][col] = 0; //backtracking
}
}
return false;
}
public static void main(String[] args){
NQueens nQueens = new NQueens();
int[][] board = new int[8][8];
if (!nQueens.enumerate(board, 0)) {
System.out.println("Solution not found!");
}
nQueens.printBoard(board);
}
}
```

`int[][] board = new int[8][8]`

all cells default value are 0

`isValid(board, row, col)`

ensures no two queens share the same row, column or diagonal

`enumerate(board, col)`

tries all possible candidates starting from column 0 to 7, backtracks to remove the queen from the board as soon as can not build the solution

`col == board.length`

means all queen are placed on the board

`board[i][col] = 1`

places a queen on the board at rows `i`

and column `col`

`board[i][col] = 0`

removes the queen at rows `i`

and column `col`

from the board