N Queens Problem in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare the chessboard size variable.

DSA C

int [1] = 8;

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AN

BboardSize

Csize

Dchessboard

Attempts:

3 left

💡 Hint

Common Mistakes

Using variable names that are not standard or clear like 'boardSize' or 'chessboard'.

The standard variable name for the size of the chessboard in N Queens is N.

2fill in blank

medium

Complete the code to initialize the chessboard array with zeros.

DSA C

int board[[1]][[1]] = {0};

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AboardSize

B8

Csize

DN

Attempts:

3 left

💡 Hint

Common Mistakes

Using a fixed number like 8 instead of the variable N.

Using undefined variables like 'size' or 'boardSize'.

The board size variable N is used to declare the 2D array dimensions.

3fill in blank

hard

Fix the error in the function signature for checking if a queen can be placed.

DSA C

int isSafe(int board[[1]][[1]], int row, int col) {

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Asize

BN

C8

DboardSize

Attempts:

3 left

💡 Hint

Common Mistakes

Using a fixed number like 8 instead of the variable N.

Using undefined variables in the parameter.

The function uses the variable N to represent the board size in the parameter.

4fill in blank

hard

Fill both blanks to complete the loop that checks the left side of the current row for queens.

DSA C

for (int i = 0; i [1] col; i[2]) {
    if (board[row][i] == 1) {
        return 0;
    }
}

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

A<

B>

C++

D--

Attempts:

3 left

💡 Hint

Common Mistakes

Using > instead of < in the loop condition.

Using decrement instead of increment.

The loop runs from 0 to col - 1, so the condition is i < col and the increment is i++.

5fill in blank

hard

Fill all three blanks to complete the recursive function call and backtracking step.

DSA C

if (solveNQUtil(board, [1])) {
    return 1;
}
board[row][[2]] = [3]; // Backtrack

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

Acol + 1

Bcol

C0

Attempts:

3 left

💡 Hint

Common Mistakes

Not incrementing the column in the recursive call.

Setting the wrong cell to 0 during backtracking.

The recursive call moves to the next column col + 1. The backtracking resets the current cell board[row][col] to 0.

Practice

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

easy

A. Place N queens on an NxN chessboard so that all queens attack each other

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

C. Count the total number of queens on the board

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

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 D

4. Quick Check:

   Goal = Place queens safely [OK]

Hint: Remember: Queens must not attack each other [OK]

Common Mistakes:

• Thinking queens can attack each other
• Confusing the problem with counting queens
• Ignoring diagonal attacks

2. Which of the following is the correct way to declare a 2D array for the chessboard in C for the N Queens Problem with size N?

easy

A. int board[];

B. int board[N][N];

C. int board[N];

D. int board(N,N);

Solution

1. Step 1: Recall C syntax for 2D arrays

   In C, a 2D array is declared as type name[size1][size2]; where both sizes are specified.

2. Step 2: Match the correct declaration

   int board[N][N]; uses int board[N][N]; which correctly declares a 2D array for the chessboard.

3. Final Answer:

   int board[N][N]; -> Option B

4. Quick Check:

   2D array syntax = int board[N][N]; [OK]

Hint: Use int board[N][N] for 2D arrays in C [OK]

Common Mistakes:

• Using 1D array for 2D board
• Incorrect syntax like int board(N,N);
• Not specifying both dimensions

3. What will be the output of the following code snippet for N=4 when printing the board after placing queens at positions (0,1), (1,3), (2,0), (3,2)?

int board[4][4] = {0};
board[0][1] = 1;
board[1][3] = 1;
board[2][0] = 1;
board[3][2] = 1;
for(int i=0; i<4; i++) {
  for(int j=0; j<4; j++) {
    printf("%d ", board[i][j]);
  }
  printf("\n");
}

medium

A. 0 0 1 0
1 0 0 0
0 1 0 0
0 0 0 1

B. 1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

C. 0 1 0 0
0 0 0 1
1 0 0 0
0 0 1 0

D. 0 0 0 1
0 0 1 0
1 0 0 0
0 1 0 0

Solution

1. Step 1: Place queens on the board as per given positions

   Set board[0][1], board[1][3], board[2][0], board[3][2] to 1; others remain 0.

2. Step 2: Print the board row-wise

   Row 0: 0 1 0 0 Row 1: 0 0 0 1 Row 2: 1 0 0 0 Row 3: 0 0 1 0

3. Final Answer:

   0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 -> Option C

4. Quick Check:

   Positions match output [OK]

Hint: Map queen positions to 1s in 2D array [OK]

Common Mistakes:

• Mixing row and column indices
• Printing without spaces or newlines
• Incorrect initialization of board

4. Identify the error in this C function snippet for checking if a queen can be placed at board[row][col]:

int isSafe(int board[][N], int row, int col) {
  for(int i=0; i=0 && j>=0; i--, j--) {
    if(board[i][j] == 1) return 0;
  }
  for(int i=row, j=col; i>=0 && j

medium

A. The function assumes N is a global constant but it may not be

B. The function incorrectly checks columns beyond the current row

C. The function misses checking the lower diagonals

D. The function does not check the current row for queens

Solution

1. Step 1: Analyze the use of N in function parameter

   The function uses int board[][N] but N is not passed as a parameter or defined locally.

2. Step 2: Understand C array parameter rules

   In C, array sizes must be known or passed explicitly; assuming N as global can cause errors if not defined.

3. Final Answer:

   The function assumes N is a global constant but it may not be -> Option A

4. Quick Check:

   Array size N must be known [OK]

Hint: Always pass array size explicitly or define globally [OK]

Common Mistakes:

• Ignoring array size requirements in C
• Assuming N is always global
• Missing checks for diagonals

5. Given the backtracking approach to solve the N Queens Problem, which of the following best describes the role of recursion in the solution?

hard

A. Recursion tries to place queens row by row and backtracks when no safe position is found

B. Recursion counts the total number of queens placed on the board

C. Recursion moves queens randomly until all are placed

D. Recursion only checks if the board is full without placing queens

Solution

1. Step 1: Understand backtracking in N Queens

   Backtracking uses recursion to place queens one row at a time, checking safety.

2. Step 2: Identify recursion behavior

   If no safe position is found in a row, recursion backtracks to previous row to try other positions.

3. Final Answer:

   Recursion tries to place queens row by row and backtracks when no safe position is found -> Option A

4. Quick Check:

   Backtracking = recursive trial and error [OK]

Hint: Think recursion as trial and error with backtracking [OK]

Common Mistakes:

• Thinking recursion places queens randomly
• Confusing recursion with counting
• Ignoring backtracking step