N Queens Problem in DSA Java - Build from Scratch

N Queens Problem

📖 Scenario: You are helping a chess player place n queens on an n x n chessboard. The queens must be placed so that no two queens can attack each other. This means no two queens share the same row, column, or diagonal.This classic problem helps understand how to use backtracking to explore all possible safe placements.

🎯 Goal: Build a Java program that finds one valid way to place n queens on the board so that none attack each other. You will create the board, set the size n, write the backtracking logic to place queens safely, and print the final board.

📋 What You'll Learn

Create a 2D array to represent the chessboard

Add a variable n to set the board size

Write a method to check if placing a queen is safe

Write a recursive method to place queens using backtracking

Print the board showing queen positions as 'Q' and empty spaces as '.'

💡 Why This Matters

🌍 Real World

The N Queens problem is a classic example of constraint satisfaction and backtracking algorithms used in puzzle solving, scheduling, and resource allocation.

💼 Career

Understanding backtracking and recursion is essential for software engineers working on complex problem solving, AI, and optimization tasks.

1

Create the chessboard

Create a 2D char array called board of size 4 x 4. Initialize all positions with the character '.' to represent empty spaces.

DSA Java

// Create a 4x4 board filled with '.'
// Your code here

Hint

Use nested for loops to fill the 2D array with '.' characters.

2

Set the board size variable

Add a static integer variable called n and set it to 4 to represent the size of the chessboard.

DSA Java

public class NQueens {
    static char[][] board = new char[4][4];
    // Add static int n = 4 below
    // Your code here

    public static void main(String[] args) {
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                board[i][j] = '.';
            }
        }
    }
}

Hint

Declare n as a static integer variable and use it to define the board size.

3

Write the backtracking logic to place queens

Write a static method called solve that takes an integer col and returns a boolean. This method tries to place queens column by column using backtracking. Also write a helper method isSafe that checks if placing a queen at board[row][col] is safe (no other queen attacks it). Use these methods to place queens safely on the board.

DSA Java

public class NQueens {
    static int n = 4;
    static char[][] board = new char[n][n];

    // Write isSafe method here
    // Write solve method here

    public static void main(String[] args) {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                board[i][j] = '.';
            }
        }
    }
}

Hint

Check rows, upper-left diagonal, and lower-left diagonal in isSafe. Use recursion and backtracking in solve.

4

Print the final board

Add code in the main method to print the board after calling solve(0). Print each row on a new line, showing 'Q' for queens and '.' for empty spaces.

DSA Java

Hint

Use nested loops to print each row and column of the board. Print a space after each character for clarity.

Practice

1. What is the main goal of the N Queens Problem?

easy

A. Place queens only on the diagonal cells of the board

B. Place N queens on an NxN chessboard so that no two queens attack each other

C. Count the total number of queens on the board

D. Find the shortest path for a queen to move across the board

Solution

1. Step 1: Understand the problem statement

   The N Queens Problem requires placing N queens on an NxN chessboard so that no two queens threaten each other.

2. Step 2: Identify the correct goal

   This means no two queens share the same row, column, or diagonal.

3. Final Answer:

   Place N queens on an NxN chessboard so that no two queens attack each other -> Option B

4. Quick Check:

   Goal = Place queens safely [OK]

Hint: Remember: no two queens can share row, column, or diagonal [OK]

Common Mistakes:

• Thinking queens can share the same row or column
• Confusing the problem with counting queens
• Assuming queens only attack diagonally

2. Which of the following Java method signatures is correct for a recursive function solving the N Queens Problem?

easy

A. static int solveNQueens(int[][] board, int n, int row)

B. public void solveNQueens(int n, int row, int[][] board)

C. public static boolean solveNQueens(int row, int n, int[][] board)

D. boolean solveNQueens(int n, int[][] board, int row)

Solution

1. Step 1: Check method signature correctness

   The recursive method should return a boolean indicating success/failure, take current row, board size, and board state.

2. Step 2: Validate parameter order and modifiers

   public static boolean solveNQueens(int row, int n, int[][] board) matches this: public static boolean solveNQueens(int row, int n, int[][] board)

3. Final Answer:

   public static boolean solveNQueens(int row, int n, int[][] board) -> Option C

4. Quick Check:

   Correct signature = public static boolean solveNQueens(int row, int n, int[][] board) [OK]

Hint: Recursive method returns boolean and takes current row first [OK]

Common Mistakes:

• Wrong return type (e.g., void instead of boolean)
• Incorrect parameter order
• Missing static keyword if required

3. What will be the output of the following Java code snippet for N=4?

public class NQueensTest {
    static int count = 0;
    public static void main(String[] args) {
        int n = 4;
        int[][] board = new int[n][n];
        solveNQueens(0, n, board);
        System.out.println(count);
    }
    static boolean solveNQueens(int row, int n, int[][] board) {
        if (row == n) {
            count++;
            return true;
        }
        boolean res = false;
        for (int col = 0; col < n; col++) {
            if (isSafe(row, col, board, n)) {
                board[row][col] = 1;
                res = solveNQueens(row + 1, n, board) || res;
                board[row][col] = 0;
            }
        }
        return res;
    }
    static boolean isSafe(int row, int col, int[][] board, int n) {
        for (int i = 0; i < row; i++) {
            if (board[i][col] == 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 >= 0 && j < n; i--, j++) {
            if (board[i][j] == 1) return false;
        }
        return true;
    }
}

medium

A. 2

B. 4

C. 1

D. 0

Solution

1. Step 1: Understand the code logic

   The code counts all valid solutions for 4 queens on a 4x4 board using backtracking.

2. Step 2: Recall known result for 4 queens

   It is a well-known fact that there are 2 valid solutions for the 4 queens problem.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Number of solutions for N=4 = 2 [OK]

Hint: Remember: 4 queens have exactly 2 solutions [OK]

Common Mistakes:

• Assuming only 1 solution exists
• Confusing number of solutions with board size
• Ignoring backtracking resets

4. Identify the bug in this snippet of the N Queens solver:

static boolean isSafe(int row, int col, int[][] board, int n) {
    for (int i = 0; i < row; i++) {
        if (board[i][col] == 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 >= 0 && j <= n; i--, j++) {
        if (board[i][j] == 1) return false;
    }
    return true;
}

medium

A. It incorrectly checks columns beyond the board size

B. It does not check the left diagonal upwards

C. It does not check the current row for other queens

D. It misses checking the lower diagonals for threats

Solution

1. Step 1: Analyze the safety checks

   The column check and upper-left diagonal are correct.

2. Step 2: Identify the bug in upper-right diagonal

   The loop condition 'i >= 0 && j <= n' allows j to reach n (e.g., when col = n-1, after first iteration j = n), causing ArrayIndexOutOfBoundsException on board[i][n].

3. Final Answer:

   It incorrectly checks columns beyond the board size -> Option A

4. Quick Check:

   Upper-right diagonal: j <= n causes out-of-bounds [OK]

Hint: Always verify loop bounds in diagonal checks to avoid index errors [OK]

Common Mistakes:

• Forgetting off-by-one errors in diagonal loop conditions
• Overlooking array bounds in upper-right diagonal traversal
• Confusing upper vs lower diagonal checks

5. You want to modify the N Queens solver to print all distinct solutions for N=4. Which approach is best to achieve this?

hard

A. Stop recursion as soon as the first solution is found to save time

B. Place all queens in the first row and check if they attack each other

C. Use a greedy algorithm to place queens in the first available safe spot in each row

D. Modify the recursive function to store each valid board configuration in a list instead of returning after first success

Solution

1. Step 1: Understand the requirement

   We want to find and print all distinct solutions, not just one.

2. Step 2: Choose the correct approach

   Modifying the recursive function to continue searching after finding a solution and storing each valid board is the correct approach.

3. Step 3: Eliminate wrong options

   Stopping after first solution won't find all solutions. Greedy algorithm to place queens in the first available safe spot in each row and placing all queens in the first row and check if they attack each other are incorrect strategies.

4. Final Answer:

   Modify the recursive function to store each valid board configuration in a list instead of returning after first success -> Option D

5. Quick Check:

   Store all solutions by continuing recursion [OK]

Hint: Keep searching after each solution to collect all boards [OK]

Common Mistakes:

• Stopping recursion after first solution
• Using greedy instead of backtracking
• Placing multiple queens in one row