Sudoku Solver Using Backtracking in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the backtracking approach in solving Sudoku?

Backtracking tries to fill empty cells one by one with numbers 1 to 9. If a number fits without breaking Sudoku rules, it moves to the next cell. If stuck, it goes back (backtracks) to change previous numbers.

beginner

Which three conditions must be checked before placing a number in a Sudoku cell?

1. The number is not already in the same row.
2. The number is not already in the same column.
3. The number is not already in the 3x3 subgrid containing the cell.

intermediate

Why is backtracking considered a depth-first search method in Sudoku solving?

Because it tries to fill one cell completely before moving to the next, going deep into possible solutions. If a dead end is reached, it returns to previous cells to try different numbers.

beginner

What happens if the backtracking algorithm cannot find a valid number for a cell?

It backtracks by returning to the previous cell and tries the next possible number there. This process repeats until a valid number is found or all options are exhausted.

beginner

How does the algorithm know when the Sudoku puzzle is solved?

When all cells are filled with valid numbers following Sudoku rules, meaning no empty cells remain and all constraints are satisfied.

What is the first step in the backtracking Sudoku solver?

A Fill all cells with 1

B Check if the puzzle is already solved

C Find the first empty cell

D Randomly place numbers

The algorithm starts by finding the first empty cell to try possible numbers.

Which of these is NOT a condition to place a number in Sudoku?

A Number not in the same row

B Number not in the same diagonal

C Number not in the same column

D Number not in the same 3x3 box

Sudoku rules do not restrict numbers on diagonals.

What does the algorithm do if no number fits in the current empty cell?

A Skips the cell

B Stops and returns failure

C Fills with zero

D Backtracks to previous cell

Backtracking means going back to previous cells to try different numbers.

How many numbers does the algorithm try for each empty cell?

A 1 to 9

B Only 5

C Only even numbers

D Only prime numbers

It tries all numbers from 1 to 9 to find a valid fit.

When is the Sudoku puzzle considered solved by the algorithm?

A When all cells are filled correctly

B When half the cells are filled

C When no numbers are repeated in rows only

D When the first row is filled

The puzzle is solved only when all cells are filled following Sudoku rules.

Explain how backtracking helps solve Sudoku puzzles step-by-step.

Think about trying and undoing moves like exploring paths.

Describe the conditions that must be checked before placing a number in a Sudoku cell.

Remember Sudoku rules for rows, columns, and boxes.

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