Sudoku Solver Using Backtracking in DSA C++ - Build from Scratch

Sudoku Solver Using Backtracking

📋 What You'll Learn

💡 Why This Matters

🌍 Real World

Sudoku solvers are examples of constraint satisfaction problems used in AI and logic programming. They help understand backtracking and recursive problem solving.

💼 Career

Understanding backtracking algorithms and constraint checking is useful in software development, especially in fields like game development, AI, and solving complex puzzles or scheduling problems.

1

Create the Sudoku board

Create a 9x9 2D vector of integers called board with the exact values below, where 0 represents empty cells:

{
  {5, 3, 0, 0, 7, 0, 0, 0, 0},
  {6, 0, 0, 1, 9, 5, 0, 0, 0},
  {0, 9, 8, 0, 0, 0, 0, 6, 0},
  {8, 0, 0, 0, 6, 0, 0, 0, 3},
  {4, 0, 0, 8, 0, 3, 0, 0, 1},
  {7, 0, 0, 0, 2, 0, 0, 0, 6},
  {0, 6, 0, 0, 0, 0, 2, 8, 0},
  {0, 0, 0, 4, 1, 9, 0, 0, 5},
  {0, 0, 0, 0, 8, 0, 0, 7, 9}
}

DSA C++

# Create the 9x9 Sudoku board vector with the given values
# Your code here

Hint

Use std::vector> to create a 2D vector named board with the exact Sudoku puzzle values.

2

Create the isSafe function

Create a function called isSafe that takes three parameters: row, col, and num. It should return true if placing num in board[row][col] does not break Sudoku rules (no duplicates in the same row, column, or 3x3 box), otherwise false.

DSA C++

#include 
#include 

std::vector> board = {
    {5, 3, 0, 0, 7, 0, 0, 0, 0},
    {6, 0, 0, 1, 9, 5, 0, 0, 0},
    {0, 9, 8, 0, 0, 0, 0, 6, 0},
    {8, 0, 0, 0, 6, 0, 0, 0, 3},
    {4, 0, 0, 8, 0, 3, 0, 0, 1},
    {7, 0, 0, 0, 2, 0, 0, 0, 6},
    {0, 6, 0, 0, 0, 0, 2, 8, 0},
    {0, 0, 0, 4, 1, 9, 0, 0, 5},
    {0, 0, 0, 0, 8, 0, 0, 7, 9}
};

// Create the isSafe function below
// Your code here

Hint

Check the row, column, and 3x3 box for the number num. Return false if found, otherwise true.

3

Create the solveSudoku function using backtracking

Create a function called solveSudoku that returns true if the Sudoku puzzle is solved, otherwise false. Use nested loops to find an empty cell (value 0). For each empty cell, try numbers 1 to 9. Use isSafe to check if the number can be placed. If yes, place the number and recursively call solveSudoku. If recursion returns true, return true. Otherwise, reset the cell to 0 and try the next number. If no number fits, return false.

DSA C++

#include 
#include 

std::vector> board = {
    {5, 3, 0, 0, 7, 0, 0, 0, 0},
    {6, 0, 0, 1, 9, 5, 0, 0, 0},
    {0, 9, 8, 0, 0, 0, 0, 6, 0},
    {8, 0, 0, 0, 6, 0, 0, 0, 3},
    {4, 0, 0, 8, 0, 3, 0, 0, 1},
    {7, 0, 0, 0, 2, 0, 0, 0, 6},
    {0, 6, 0, 0, 0, 0, 2, 8, 0},
    {0, 0, 0, 4, 1, 9, 0, 0, 5},
    {0, 0, 0, 0, 8, 0, 0, 7, 9}
};

bool isSafe(int row, int col, int num) {
    for (int x = 0; x < 9; x++) {
        if (board[row][x] == num) return false;
        if (board[x][col] == num) return false;
    }
    int startRow = row - row % 3;
    int startCol = col - col % 3;
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            if (board[startRow + i][startCol + j] == num) return false;
        }
    }
    return true;
}

// Create the solveSudoku function below
// Your code here

Hint

Use nested loops to find empty cells and try numbers 1 to 9. Use recursion to solve the puzzle step-by-step.

4

Print the solved Sudoku board

Call solveSudoku() to solve the puzzle. Then print the board row by row, with spaces between numbers. Each row should be printed on a new line.

DSA C++

#include 
#include 

std::vector> board = {
    {5, 3, 0, 0, 7, 0, 0, 0, 0},
    {6, 0, 0, 1, 9, 5, 0, 0, 0},
    {0, 9, 8, 0, 0, 0, 0, 6, 0},
    {8, 0, 0, 0, 6, 0, 0, 0, 3},
    {4, 0, 0, 8, 0, 3, 0, 0, 1},
    {7, 0, 0, 0, 2, 0, 0, 0, 6},
    {0, 6, 0, 0, 0, 0, 2, 8, 0},
    {0, 0, 0, 4, 1, 9, 0, 0, 5},
    {0, 0, 0, 0, 8, 0, 0, 7, 9}
};

bool isSafe(int row, int col, int num) {
    for (int x = 0; x < 9; x++) {
        if (board[row][x] == num) return false;
        if (board[x][col] == num) return false;
    }
    int startRow = row - row % 3;
    int startCol = col - col % 3;
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            if (board[startRow + i][startCol + j] == num) return false;
        }
    }
    return true;
}

bool solveSudoku() {
    for (int row = 0; row < 9; row++) {
        for (int col = 0; col < 9; col++) {
            if (board[row][col] == 0) {
                for (int num = 1; num <= 9; num++) {
                    if (isSafe(row, col, num)) {
                        board[row][col] = num;
                        if (solveSudoku()) {
                            return true;
                        } else {
                            board[row][col] = 0;
                        }
                    }
                }
                return false;
            }
        }
    }
    return true;
}

// Call solveSudoku and print the board
// Your code here

Hint

Call solveSudoku() and then print each row of board with spaces between numbers.

Practice

1. What is the main idea behind the backtracking technique used in a Sudoku solver?

easy

A. Use a fixed pattern to fill the board

B. Fill the board randomly without checking rules

C. Try placing numbers and undo if they lead to conflicts

D. Only fill cells with a single possible number

Solution

1. Step 1: Understand backtracking in Sudoku

   Backtracking tries numbers in empty cells and checks if they fit the Sudoku rules.

2. Step 2: Undo if conflict arises

   If a number causes a conflict later, it is removed (backtracked) and another number is tried.

3. Final Answer:

   Try placing numbers and undo if they lead to conflicts -> Option C

4. Quick Check:

   Backtracking = Try and undo [OK]

Hint: Backtracking means try, check, and undo if needed [OK]

Common Mistakes:

• Thinking backtracking fills randomly
• Assuming backtracking fills only once without undo
• Believing backtracking uses fixed patterns

2. Which of the following is the correct way to check if a number can be placed in a Sudoku cell in C++?

easy

A. if (isSafe(board, row, col, num)) { board[row][col] = num; }

B. if (board[row][col] == num) { placeNumber(); }

C. if (num > 9) { board[row][col] = num; }

D. if (board[row][col] != 0) { board[row][col] = num; }

Solution

1. Step 1: Understand the safety check function

   The function isSafe checks if placing num at board[row][col] follows Sudoku rules.

2. Step 2: Place number only if safe

   Only if isSafe returns true, the number is placed in the cell.

3. Final Answer:

   if (isSafe(board, row, col, num)) { board[row][col] = num; } -> Option A

4. Quick Check:

   Use isSafe before placing number [OK]

Hint: Always check safety before placing number [OK]

Common Mistakes:

• Placing number without checking rules
• Checking if cell already has the number incorrectly
• Using invalid conditions for placement

3. What will be the output of the following code snippet when solving a Sudoku board?

int board[9][9] = {
  {5,3,0,0,7,0,0,0,0},
  {6,0,0,1,9,5,0,0,0},
  {0,9,8,0,0,0,0,6,0},
  {8,0,0,0,6,0,0,0,3},
  {4,0,0,8,0,3,0,0,1},
  {7,0,0,0,2,0,0,0,6},
  {0,6,0,0,0,0,2,8,0},
  {0,0,0,4,1,9,0,0,5},
  {0,0,0,0,8,0,0,7,9}
};
solveSudoku(board);

Assuming solveSudoku correctly solves the puzzle, what will be the value at board[0][2] after solving?

medium

A. 9

B. 4

C. 7

D. 1

Solution

1. Step 1: Identify the empty cell at (0,2)

   The cell at row 0, column 2 is initially 0 (empty).

2. Step 2: Solve Sudoku and find correct number

   After solving, the number 4 fits at (0,2) without conflicts in row, column, or box.

3. Final Answer:

   4 -> Option B

4. Quick Check:

   board[0][2] = 4 after solve [OK]

Hint: Check solved board cell for correct number [OK]

Common Mistakes:

• Guessing without checking Sudoku rules
• Confusing row and column indices
• Assuming initial zeros remain zeros

4. Consider this buggy code snippet for checking if a number can be placed in a Sudoku cell:

bool isSafe(int board[9][9], int row, int col, int num) {
  for (int x = 0; x < 9; x++) {
    if (board[row][x] == num || board[x][col] == num)
      return false;
  }
  int startRow = row - row % 3;
  int startCol = col - col % 3;
  for (int i = 0; i < 3; i++) {
    for (int j = 0; j < 3; j++) {
      if (board[i][j] == num)
        return false;
    }
  }
  return true;
}

What is the bug in this code?

medium

A. The 3x3 box check uses wrong indices; should use startRow + i and startCol + j

B. The row and column checks are missing

C. The function does not return false when number is found

D. The modulo operation is incorrect

Solution

1. Step 1: Analyze 3x3 box checking loop

   The inner loop checks board[i][j] instead of board[startRow + i][startCol + j], so it checks wrong cells.

2. Step 2: Correct indices for box check

   To check the correct 3x3 box, add startRow and startCol offsets to i and j.

3. Final Answer:

   The 3x3 box check uses wrong indices; should use startRow + i and startCol + j -> Option A

4. Quick Check:

   Box check indices must include startRow/startCol [OK]

Hint: Add startRow/startCol offsets when checking 3x3 box [OK]

Common Mistakes:

• Checking wrong cells in 3x3 box
• Ignoring row or column checks
• Incorrect modulo usage

5. You want to optimize a Sudoku solver using backtracking by adding a heuristic. Which of the following strategies best reduces the search space?

hard

A. Fill cells row-wise ignoring constraints until stuck

B. Try numbers in random order for each empty cell

C. Always fill the first empty cell found without checking possibilities

D. Choose the empty cell with the fewest possible valid numbers first

Solution

1. Step 1: Understand heuristic to reduce search space

   Choosing the cell with the fewest valid options first reduces branching and speeds up solving.

2. Step 2: Compare other strategies

   Filling first empty cell or random tries increase backtracking steps; ignoring constraints causes errors.

3. Final Answer:

   Choose the empty cell with the fewest possible valid numbers first -> Option D

4. Quick Check:

   Minimum remaining values heuristic = choose cell with fewest options [OK]

Hint: Pick cell with least options first to speed solving [OK]

Common Mistakes:

• Filling cells without checking possibilities
• Trying numbers randomly wastes time
• Ignoring constraints leads to wrong solutions