Solving the Eight Queens Problem

The provided assignment content describes a Java class named `Queens` that solves the N-Queens problem, which involves placing N queens on an NxN chessboard in such a way that no queen attacks any other queen. The class includes methods for clearing the board, displaying the board, and placing queens in columns.

public class Queens {
// squares per row or per column
public static final int BOARD_SIZE = 8;
//used to indicate empty square
public static final int EMPTY = 0;
//used to indicate square contains a queen
public static final int QUEEN = 1;
private int board[][]; // chess board
public Queens() {
// --------------------------------------------------
// Constructor: Create an empty square board.
// --------------------------------------------------
board = new int[BOARD_SIZE][BOARD_SIZE];
} // end constructor
public void clearBoard(){
// --------------------------------------------------
// Clears the board.
// Precondition: None.
// Postcondition: Sets all squares to EMPTY
// --------------------------------------------------
// place your logic to implement this method here
} // end clearBoard
public void displayBoard(){
// --------------------------------------------------

// Displays the board.
// Precondition: None.
// Postcondition: Board is written to standartd
// output; zero is an EMPTY square, one is a square
// containing a queen (QUEEN)
// --------------------------------------------------
for (int i=0; i<BOARD_SIZE; i++) {
for (int j=0; j<BOARD_SIZE; j++) {
// place your logic to implement this method here
// that prints a single row of the chess board
// to the console window (i.e., standard output)
}
System.out.print("\n");
// this newline prints after a row
// of the chess board has been printed
}
} // end displayBoard
public boolean placeQueens(int column) {
// --------------------------------------------------
// Place queens in columns of the board beginning
// at the column specified.
// Precondition: Queens are placed correctly in
// columns 1 thro coulumn-1.
// Postcondition: If a solution is found, each
// column of the board contains one queen and method
// returns true; otherwise retruns false (no
// solution existis for a queen anywhere in column
// specified).

// --------------------------------------------------
if (column > BOARD_SIZE) {
return true; // base case
}
else {
boolean queenPlaced = false;
int row = 1; // number of square in column
while ( !queenPlaced && (row <= BOARD_SIZE) ) {
// if square can be attacked
if (isUnderAttack(row, column)) {
++row; // consider next square in column
} // end if
else { // place queen and consider next column
setQueen(row, column);
queenPlaced = placeQueens(column+1);
// if no queen is possible in the next column,
if (!queenPlaced) {
// backtrack: remove queen placed earliers
// and try next square in column
removeQueen(row, column);
++row;
} // end if
} // end if
} // end while
return queenPlaced;
} // end if
} // end placeQueens

private void setQueen(int row, int column) {
// --------------------------------------------------
// Set a queen at square indicated by row and
// column.
// Precondition: None.
// Postcondition: Sets the square on the board in a
// given row and column to QUEEN.
// --------------------------------------------------
board[row-1][column-1] = QUEEN;
} // end setQueen
private void removeQueen(int row, int column) {
// --------------------------------------------------
// Remove a queen at square indicated by row and
// column.
// Precondition: None.
// Postcondition: Sets the square on the board in a
// given row and column to EMPTY.
// --------------------------------------------------
board[row-1][column-1] = EMPTY;
} // end setQueen
private boolean isUnderAttack(int row, int column) {
// --------------------------------------------------
// Determines whether the square on the board at a
// given row and column is under attack by any queens
// in the columns 1 through column-1.
// Precondition: Each column between 1 and column-1

// has a queen placed in a square at a specific row.
// None of these queens can be attacked by any other
// queen.
// Postcondition: If the deignated square is under
// attack, returns true; otherwise, returns false.
// --------------------------------------------------
// check column
for (int i=0; i<row-1; i++){
if (board[i][column-1]==1){
return true;
}
}
// check row
for (int i=0; i<column-1; i++) {
if (board[row-1][i] == 1){
return true;
}
}
// check lower diagnal
int lower_dir_row = row-2;
int lower_dir_column = column-2;
while (lower_dir_row>=0 && lower_dir_column>=0){
if (board[lower_dir_row][lower_dir_column]==1){
return true;
} else {
lower_dir_row = lower_dir_row -1;
lower_dir_column = lower_dir_column -1;
}

}
// check upper diagnal
int upper_dir_row = row;
int upper_dir_column = column-2;
while (upper_dir_row<BOARD_SIZE && upper_dir_column>=0){
if(board[upper_dir_row][upper_dir_column] ==1){
return true;
}else{
upper_dir_row = upper_dir_row +1;
upper_dir_column = upper_dir_column -1;
}
}
return false;
} // end isUnderAttack
} // end Queens