N Queens Problem in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the chessboard with empty cells represented by '.'

DSA Python

board = [['.' for _ in range([1])] for _ in range([1])]

Drag options to blanks, or click blank then click option'

Asize

BN

Cn

Dlength

Attempts:

3 left

💡 Hint

Common Mistakes

Using a variable not defined for board size.

Using different variables for rows and columns.

The board size is n x n, so we use 'n' to create rows and columns.

2fill in blank

medium

Complete the code to check if a queen can be placed at row r and column c without conflicts.

DSA Python

for i in range(r):
    if board[i][c] == 'Q':
        return [1]

Drag options to blanks, or click blank then click option'

ANone

BFalse

C0

DTrue

Attempts:

3 left

💡 Hint

Common Mistakes

Returning True when conflict is found.

Returning None or 0 which do not indicate failure clearly.

If there is already a queen in the same column above, we cannot place another queen there, so return False.

3fill in blank

hard

Fix the error in the diagonal check to correctly detect conflicts for the upper left diagonal.

DSA Python

i, j = r, c
while i >= 0 and j >= 0:
    if board[i][j] == 'Q':
        return [1]
    i -= 1
    j -= 1

Drag options to blanks, or click blank then click option'

AFalse

BTrue

CNone

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Returning True instead of False on conflict.

Not decrementing i and j correctly.

If a queen is found on the upper left diagonal, placement is invalid, so return False.

4fill in blank

hard

Fill both blanks to check the upper right diagonal for conflicts.

DSA Python

i, j = r, c
while i >= 0 and j [1] n:
    if board[i][j] == 'Q':
        return [2]
    i -= 1
    j += 1

Drag options to blanks, or click blank then click option'

A<

B>

CFalse

DTrue

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' for the column boundary.

Returning True instead of False on conflict.

We check while j is less than n to stay inside the board, and return False if a queen is found.

5fill in blank

hard

Fill all three blanks to place a queen, recurse to next row, and backtrack by removing the queen.

DSA Python

board[r][c] = [1]
if solve(r [2] 1):
    return True
board[r][c] = [3]

Drag options to blanks, or click blank then click option'

A'Q'

B+

C'.'

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong symbols for queen or empty cell.

Using '-' instead of '.' to clear the cell.

Using subtraction instead of addition for next row.

Place 'Q' to mark queen, move to next row with r + 1, and remove queen by resetting to '.' on backtrack.

Practice

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

easy

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

B. Count the total number of queens on a chessboard

C. Move queens to capture all opponent pieces

D. Arrange queens in a single row on the chessboard

Solution

1. Step 1: Understand the problem statement

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

2. Step 2: Analyze the options

   Only Place N queens on an NxN chessboard so that no two queens attack each other correctly describes placing queens so none attack each other. Other options describe unrelated tasks.

3. Final Answer:

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

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 be in the same row or column
• Confusing the problem with counting queens
• Assuming queens can attack each other

2. Which of the following Python code snippets correctly initializes an empty chessboard for the N Queens Problem with size n?

easy

A. board = [[0 for _ in range(n)] for _ in range(n)]

B. board = [[0]*n]

C. board = [0]*n

D. board = [[0]*n]*n

Solution

1. Step 1: Understand board initialization

   We need a 2D list with independent rows to represent the chessboard.

2. Step 2: Analyze each option

   board = [[0]*n]*n creates rows referencing the same list, causing bugs. board = [[0 for _ in range(n)] for _ in range(n)] creates independent rows correctly. board = [0]*n creates a 1D list, not 2D. board = [[0]*n] creates a single row only.

3. Final Answer:

   board = [[0 for _ in range(n)] for _ in range(n)] -> Option A

4. Quick Check:

   Independent rows = board = [[0 for _ in range(n)] for _ in range(n)] [OK]

Hint: Use nested list comprehension for independent rows [OK]

Common Mistakes:

• Using [[0]*n]*n causing shared references
• Creating 1D list instead of 2D
• Forgetting to repeat for each row

3. What will be the output of the following Python code snippet for n = 4?

def is_safe(board, row, col):
    for i in range(col):
        if board[row][i] == 1:
            return False
    for i, j in zip(range(row, -1, -1), range(col, -1, -1)):
        if board[i][j] == 1:
            return False
    for i, j in zip(range(row, len(board), 1), range(col, -1, -1)):
        if board[i][j] == 1:
            return False
    return True

board = [[0]*4 for _ in range(4)]
board[1][0] = 1
print(is_safe(board, 1, 1))
print(is_safe(board, 0, 1))

medium

A. True\nFalse

B. False\nFalse

C. False\nTrue

D. True\nTrue

Solution

1. Step 1: Check is_safe for position (1,1)

   Column check: board[1][0] == 1, so returns False.

2. Step 2: Check is_safe for position (0,1)

   Row left: board[0][0] == 0. Upper diagonal: board[0][1] == 0. Lower diagonal: board[1][0] == 1, so returns False.

3. Final Answer:

   False\nFalse -> Option B

4. Quick Check:

   Check columns and diagonals = False, False [OK]

Hint: Check columns and diagonals left of position [OK]

Common Mistakes:

• Ignoring diagonal checks
• Confusing row and column indices
• Assuming safe if no queen in same row only

4. Identify the error in the following code snippet for solving the N Queens Problem:

def solve_n_queens(board, col):
    if col >= len(board):
        return True
    for row in range(len(board)):
        if is_safe(board, row, col):
            board[row][col] = 1
            if solve_n_queens(board, col + 1):
                return True
            board[row][col] = 0
    return False

board = [[0]*4 for _ in range(4)]
solve_n_queens(board, 0)
print(board)

medium

A. The base case condition is incorrect

B. The board is not reset properly after backtracking

C. The function returns True too early, missing all solutions

D. The is_safe function is not called

Solution

1. Step 1: Analyze the recursion and return statements

   The function returns True immediately after finding the first solution, so it stops searching further.

2. Step 2: Understand impact on solution finding

   This means it finds only one solution and does not explore all possible solutions.

3. Final Answer:

   The function returns True too early, missing all solutions -> Option C

4. Quick Check:

   Early return stops full search [OK]

Hint: Return True only after exploring all columns [OK]

Common Mistakes:

• Stopping recursion after first solution
• Not resetting board on backtrack
• Incorrect base case check

5. Given the N Queens Problem, which approach best improves efficiency by reducing unnecessary checks during queen placement?

hard

A. Place queens randomly and retry if conflicts occur

B. Check the entire board for conflicts every time before placing a queen

C. Use nested loops to try all possible board configurations without pruning

D. Use backtracking with arrays to track columns and diagonals already occupied

Solution

1. Step 1: Understand efficiency in N Queens

   Checking the entire board repeatedly wastes time; pruning reduces checks.

2. Step 2: Analyze options for pruning

   Using arrays to track columns and diagonals occupied avoids repeated scanning, improving speed.

3. Final Answer:

   Use backtracking with arrays to track columns and diagonals already occupied -> Option D

4. Quick Check:

   Pruning with tracking arrays = Use backtracking with arrays to track columns and diagonals already occupied [OK]

Hint: Track columns and diagonals to skip invalid spots fast [OK]

Common Mistakes:

• Checking full board every time
• Trying random placements without pruning
• Using brute force without backtracking