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BackTracking_NQueensProblem.java
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BackTracking_NQueensProblem.java
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public class BackTracking_NQueensProblem {
static int count = 0;
public static void print_board(char[][] board){
for (int i=0; i<board.length; i++){
for (int j=0; j<board.length; j++){
System.out.print(board[i][j] + " ");
}
System.out.println();
}
}
public static boolean is_safe(char[][] board, int row, int col){
// vertical up
for (int i=row-1; i>=0; i--){
if (board[i][col] == 'Q') return false;
}
// left diagonal up
for (int i=row-1, j = col-1; i>=0 && j>=0; i--,j--){
if (board[i][j]=='Q') return false;
}
// right diagonal up
for (int i=row-1, j=col+1; i>=0 && j<board.length; i--,j++){
if (board[i][j]=='Q') return false;
}
return true;
}
public static void N_Queens_all_sols(char[][] board, int row){
// base case
if (row==board.length) {
System.out.println("__________BOARD___________");
print_board(board);
count++;
return;
}
// recursion call
for (int j=0; j<board.length; j++){ // loop for cols bcz only one queen in one row
if (is_safe(board, row, j)){
board[row][j] = 'Q';
N_Queens_all_sols(board, row+1);
board[row][j] = 'X'; // backtracking step
}
}
}
public static boolean N_Queens_only_one(char[][] board, int row){
// base case
if (row==board.length) {
// System.out.println("__________BOARD___________");
// print_board(board);
return true;
}
// recursion call
for (int j=0; j<board.length; j++){ // loop for cols bcz only one queen in one row
if (is_safe(board, row, j)){
board[row][j] = 'Q';
if (N_Queens_only_one(board, row+1)){
return true;
}
board[row][j] = 'X'; // backtracking step
}
}
return false;
}
public static void main(String[] args) {
int n = 4;
char[][] board = new char[n][n];
for (int i=0; i<n; i++){
for (int j=0; j<n; j++){
board[i][j] = 'X';
}
}
// // Print all the solutions
// N_Queens_all_sols(board, 0);
//
//
// // Count solutions
// System.out.println("\nTotal ways to solve : " + count);
// Print only one solution if exists
if (N_Queens_only_one(board,0)){
System.out.println("Solution exists");
N_Queens_only_one(board, 0);
print_board(board);
}else {
System.out.println("Solution do not exist");
}
}
}