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

Sudoku Solver Using Backtracking

📖 Scenario: You have a partially filled Sudoku board. Your task is to complete the board so that every row, column, and 3x3 box contains all digits from 1 to 9 without repetition.Think of it like a puzzle where you fill empty cells step-by-step, checking if your choice fits the rules before moving on.

🎯 Goal: Build a program that uses backtracking to solve the Sudoku puzzle by filling empty cells correctly.

📋 What You'll Learn

Create a 9x9 integer array called board with the given Sudoku puzzle

Create a method IsSafe that checks if placing a number in a cell is valid

Create a method SolveSudoku that uses backtracking to fill the board

Print the solved Sudoku board in a readable format

💡 Why This Matters

🌍 Real World

Sudoku solving algorithms are used in puzzle games and teaching recursion and backtracking techniques.

💼 Career

Understanding backtracking and constraint checking is useful in software development fields like game development, AI, and solving combinatorial problems.

1

Setup the Sudoku board

Create a 9x9 integer array called board with the exact values below, where 0 represents an empty cell:

int[,] board = new int[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} };

DSA C#

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

Hint

Use a two-dimensional array int[,] board and fill it exactly as shown.

2

Create the IsSafe method

Create a method bool IsSafe(int[,] board, int row, int col, int num) that returns true if placing num in board[row, col] does not break Sudoku rules. Check the row, column, and 3x3 box for duplicates.

DSA C#

int[,] board = new int[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} };

// Create IsSafe method here
# Your code here

Hint

Check the row and column by looping from 0 to 8. Then check the 3x3 box by calculating its start row and column.

3

Create the SolveSudoku method

Create a method bool SolveSudoku(int[,] board) that uses backtracking to fill empty cells (cells with 0). It should try numbers 1 to 9 in each empty cell, use IsSafe to check validity, and recursively solve the board. Return true if solved, otherwise false.

DSA C#

int[,] board = new int[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} };

bool IsSafe(int[,] board, int row, int col, int num)
{
    // ... existing code ...
}

// Create SolveSudoku method here
# Your code here

Hint

Look for the first empty cell, try numbers 1 to 9, check with IsSafe, place the number, and recursively call SolveSudoku. If it fails, reset the cell to 0 and try next number.

4

Print the solved Sudoku board

Print the solved Sudoku board row by row. Use nested loops to print each number separated by spaces. Print each row on a new line.

DSA C#

int[,] board = new int[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} };

bool IsSafe(int[,] board, int row, int col, int num)
{
    // ... existing code ...
}

bool SolveSudoku(int[,] board)
{
    // ... existing code ...
}

SolveSudoku(board);

// Print the solved board below
# Your code here

Hint

Use nested loops to print each row and column. Print a space after each number and a new line after each row.

Practice

1. What is the main purpose of using backtracking in a Sudoku solver?

easy

A. To try possible numbers and undo choices if they lead to conflicts

B. To randomly fill the Sudoku grid without checking rules

C. To sort the numbers in each row before solving

D. To count how many empty cells are in the Sudoku grid

Solution

1. Step 1: Understand backtracking role

   Backtracking tries numbers in empty cells and removes them if they cause conflicts.

2. Step 2: Compare other options

   Options A, B, and C do not describe backtracking's trial and error approach.

3. Final Answer:

   To try possible numbers and undo choices if they lead to conflicts -> Option A

4. Quick Check:

   Backtracking = Try and undo choices [OK]

Hint: Backtracking means try and undo wrong choices [OK]

Common Mistakes:

• Thinking backtracking fills randomly without checks
• Confusing backtracking with sorting or counting
• Ignoring the undo step in backtracking

2. Which C# syntax correctly defines a method header for a Sudoku solver using backtracking that returns a boolean?

easy

A. public bool SolveSudoku(int[,] board)

B. bool SolveSudoku(int[][] board)

C. public void SolveSudoku(int[] board)

D. bool SolveSudoku(int[] board);

Solution

1. Step 1: Check method signature correctness

   public bool SolveSudoku(int[,] board) uses correct C# syntax: public access, bool return, 2D array parameter.

2. Step 2: Identify errors in other options

   bool SolveSudoku(int[][] board) uses wrong array syntax for C#, C uses void return instead of bool, D has semicolon ending which is invalid for method definition.

3. Final Answer:

   public bool SolveSudoku(int[,] board) -> Option A

4. Quick Check:

   Correct C# method header = public bool SolveSudoku(int[,] board) [OK]

Hint: Use public bool with int[,] for 2D arrays in C# [OK]

Common Mistakes:

• Using jagged array syntax int[][] instead of int[,]
• Missing public keyword or wrong return type
• Ending method header with semicolon

3. What will be the output of the following code snippet when trying to solve a partially filled Sudoku board?

int[,] board = new int[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}
};
SudokuSolver solver = new SudokuSolver();
bool solved = solver.SolveSudoku(board);
Console.WriteLine(solved);

medium

A. false

B. true

C. Compilation error

D. Runtime exception

Solution

1. Step 1: Understand the input board

   The board is a valid partially filled Sudoku puzzle with zeros as empty cells.

2. Step 2: Analyze SolveSudoku method behavior

   Assuming correct backtracking implementation, the solver will find a solution and return true.

3. Final Answer:

   true -> Option B

4. Quick Check:

   Valid puzzle solved = true [OK]

Hint: Valid puzzles return true after solving [OK]

Common Mistakes:

• Assuming zeros cause errors instead of empty cells
• Thinking solver returns false without trying all options
• Confusing compilation/runtime errors with logic

4. Identify the bug in this backtracking Sudoku solver snippet:

bool IsSafe(int[,] board, 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[startRow + i, startCol + j] == num) return false;
    }
  }
  return true;
}

medium

A. The method does not check if the cell is already filled

B. The row and column checks are incomplete

C. No bug; the method correctly checks safety

D. The 3x3 box check uses wrong start indices calculation

Solution

1. Step 1: Review row and column checks

   The method checks all cells in the row and column for the number, which is correct.

2. Step 2: Review 3x3 box check

   Calculates startRow and startCol correctly using modulo, then checks all 3x3 cells.

3. Step 3: Confirm no missing checks

   Method returns true only if no conflicts found, so it is correct.

4. Final Answer:

   No bug; the method correctly checks safety -> Option C

5. Quick Check:

   Safety check correct = No bug; the method correctly checks safety [OK]

Hint: Check row, column, and 3x3 box carefully [OK]

Common Mistakes:

• Miscomputing start indices for 3x3 box
• Forgetting to check both row and column
• Assuming cell fill check is needed here

5. Given a Sudoku board with multiple empty cells, which strategy improves the backtracking solver's efficiency the most?

hard

A. Fill cells randomly to reduce search space

B. Always try numbers 1 to 9 in order without checks

C. Skip checking 3x3 boxes to save time

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

Solution

1. Step 1: Understand backtracking efficiency

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

2. Step 2: Evaluate other options

   Random filling (A) wastes time, trying numbers blindly (B) is inefficient, skipping box checks (D) breaks rules.

3. Final Answer:

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

4. Quick Check:

   Minimum options first = faster solving [OK]

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

Common Mistakes:

• Trying numbers in fixed order without heuristics
• Ignoring 3x3 box constraints
• Randomly filling cells hoping for quick solve