N Queens Problem in DSA C - Build from Scratch

N Queens Problem

📖 Scenario: You are helping a chess player find all the ways to place 4 queens on a 4x4 chessboard so that no two queens attack each other. Queens can attack horizontally, vertically, and diagonally. Your task is to write a program that finds all safe arrangements of queens on the board.

🎯 Goal: Build a program that uses backtracking to place 4 queens on a 4x4 board safely and prints all valid board arrangements.

📋 What You'll Learn

Create a 4x4 board represented as a 2D array of integers initialized to 0

Create a function isSafe that checks if placing a queen at a given row and column is safe

Create a recursive function solveNQueens that tries to place queens column by column

Print all valid board arrangements with queens represented by 1 and empty spaces by 0

💡 Why This Matters

🌍 Real World

The N Queens problem is a classic example of constraint satisfaction problems used in artificial intelligence and optimization tasks.

💼 Career

Understanding backtracking and recursion helps in solving complex algorithmic problems in software development and technical interviews.

1

Create the 4x4 chessboard

Create a 4x4 integer array called board and initialize all elements to 0.

DSA C

int board[4][4] = {0};
// Your code here

Hint

Use int board[4][4] = {0}; to create and initialize the board.

2

Write the isSafe function

Write a function int isSafe(int board[4][4], int row, int col) that returns 1 if placing a queen at board[row][col] is safe, otherwise returns 0. Check the row on left side, upper diagonal on left side, and lower diagonal on left side.

DSA C

int board[4][4] = {0};

int isSafe(int board[4][4], int row, int col) {
    // Your code here
}

Hint

Check left side row, upper diagonal, and lower diagonal for any queen (value 1).

3

Write the solveNQueens recursive function

Write a recursive function int solveNQueens(int board[4][4], int col) that tries to place queens column by column. If all queens are placed, return 1. For each row in the current column, check if it is safe using isSafe. If safe, place the queen (set to 1), recursively call solveNQueens for next column, and if it returns 1, return 1. Otherwise, backtrack by removing the queen (set to 0). If no row works, return 0.

DSA C

int board[4][4] = {0};

int isSafe(int board[4][4], int row, int col) {
    int i, j;
    for (i = 0; i = 0 && j >= 0; i--, j--)
        if (board[i][j])
            return 0;
    for (i = row, j = col; i = 0; i++, j--)
        if (board[i][j])
            return 0;
    return 1;
}

int solveNQueens(int board[4][4], int col) {
    // Your code here
}

Hint

Try placing queens column by column and backtrack if needed.

4

Print the board and run the solver

Write a function void printBoard(int board[4][4]) that prints the board with 1s and 0s. Then in main, call solveNQueens(board, 0). If it returns 1, call printBoard(board) to display the solution.

DSA C

int board[4][4] = {0};

int isSafe(int board[4][4], int row, int col) {
    int i, j;
    for (i = 0; i = 0 && j >= 0; i--, j--)
        if (board[i][j])
            return 0;
    for (i = row, j = col; i = 0; i++, j--)
        if (board[i][j])
            return 0;
    return 1;
}

int solveNQueens(int board[4][4], int col) {
    if (col >= 4)
        return 1;
    int row;
    for (row = 0; row < 4; row++) {
        if (isSafe(board, row, col)) {
            board[row][col] = 1;
            if (solveNQueens(board, col + 1))
                return 1;
            board[row][col] = 0; // backtrack
        }
    }
    return 0;
}

void printBoard(int board[4][4]) {
    // Your code here
}

int main() {
    // Your code here
}

Hint

Print each row with spaces between numbers and a newline after each row. Call solveNQueens(board, 0) in main and print the board if solution found.

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