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

Recall & Review

beginner

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

Backtracking tries to fill the Sudoku grid by placing numbers one by one, and if a number causes a conflict, it goes back (backtracks) to try a different number until the puzzle is solved.

beginner

In Sudoku, what conditions must be checked before placing a number in a cell?

The number must not already appear in the same row, the same column, or the same 3x3 subgrid.

intermediate

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

Because it tries to fill cells deeply by choosing a number and moving forward until it hits a conflict, then it backtracks to try other options, exploring one path fully before moving to another.

beginner

What happens if the backtracking algorithm reaches a cell where no number fits?

It means the previous choices led to a dead end, so the algorithm goes back to the previous cell and tries a different number there.

beginner

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

When all cells are filled with valid numbers without conflicts, meaning the algorithm has successfully placed numbers in every empty cell.

Which of the following is NOT a condition to place a number in a Sudoku cell?

A Number is not in the same row

B Number is not in the same column

C Number is not in the same 3x3 box

D Number is not in the diagonal

Sudoku rules do not restrict numbers on diagonals, only rows, columns, and 3x3 boxes.

What does backtracking do when it finds no valid number for a cell?

A Stops and declares no solution

B Goes back to previous cell to try a different number

C Randomly changes numbers in the grid

D Moves forward to next cell

Backtracking returns to the previous cell to try other options when stuck.

What is the first step in the backtracking Sudoku solver?

A Find the first empty cell

B Fill all cells with 1

C Check if the puzzle is solved

D Remove all numbers from the grid

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

How does the algorithm check if placing a number is valid?

A By checking row, column, and 3x3 box

B By checking the entire grid randomly

C By checking only the row

D By checking only the column

It must check row, column, and 3x3 box to ensure no conflicts.

What type of algorithm is used in Sudoku solving with backtracking?

A Breadth-first search

B Greedy algorithm

C Depth-first search

D Dynamic programming

Backtracking is a form of depth-first search exploring one path fully before backtracking.

Explain how backtracking helps solve a Sudoku puzzle step-by-step.

Think about trying numbers and going back when stuck.

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 using backtracking to solve a Sudoku puzzle?

easy

A. Try placing numbers one by one and backtrack if a conflict occurs

B. Fill all empty cells randomly and check if the puzzle is solved

C. Use a sorting algorithm to arrange numbers in order

D. Replace all zeros with the number 9 directly

Solution

1. Step 1: Understand backtracking approach

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

2. Step 2: Handle conflicts by backtracking

   If a number causes a conflict, the algorithm removes it and tries the next number, going back if needed.

3. Final Answer:

   Try placing numbers one by one and backtrack if a conflict occurs -> Option A

4. Quick Check:

   Backtracking = Try and undo [OK]

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

Common Mistakes:

• Thinking backtracking fills cells randomly
• Assuming sorting solves Sudoku
• Replacing zeros without checks

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

easy

A. if isSafe(board, row, col, num) { placeNumber(); }

B. if isSafe(board, row, col, num) then placeNumber();

C. if (isSafe board, row, col, num) { placeNumber(); }

D. if (isSafe(board, row, col, num)) { placeNumber(); }

Solution

1. Step 1: Understand JavaScript if syntax

   JavaScript requires parentheses around the condition in an if statement.

2. Step 2: Check function call syntax

   Function calls need parentheses with arguments inside, like isSafe(board, row, col, num).

3. Final Answer:

   if (isSafe(board, row, col, num)) { placeNumber(); } -> Option D

4. Quick Check:

   if(condition) with parentheses [OK]

Hint: Use parentheses around conditions in if statements [OK]

Common Mistakes:

• Missing parentheses in if condition
• Using 'then' keyword in JavaScript
• Incorrect function call syntax

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

const 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]
];
solveSudoku(board);
console.log(board);

medium

A. An error because solveSudoku is not defined

B. The original board unchanged with zeros intact

C. A fully solved Sudoku board with no zeros

D. A partially solved board with some zeros replaced

Solution

1. Step 1: Understand solveSudoku function purpose

   solveSudoku uses backtracking to fill all empty cells correctly, solving the puzzle.

2. Step 2: Check console.log output after solving

   After solveSudoku runs, the board is fully solved with no zeros remaining.

3. Final Answer:

   A fully solved Sudoku board with no zeros -> Option C

4. Quick Check:

   Backtracking solves all cells [OK]

Hint: Backtracking fills all empty cells correctly [OK]

Common Mistakes:

• Expecting original board unchanged
• Thinking partial fill is final
• Assuming function is undefined

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

function isSafe(board, row, col, num) {
  for (let x = 0; x < 9; x++) {
    if (board[row][x] === num || board[x][col] === num) {
      return false;
    }
  }
  // Missing 3x3 box check
  return true;
}

What is the main problem here?

medium

A. It returns false too early

B. It does not check the 3x3 subgrid for duplicates

C. It uses wrong loop variable x

D. It modifies the board inside the function

Solution

1. Step 1: Analyze row and column checks

   The code correctly checks if num exists in the same row or column.

2. Step 2: Identify missing 3x3 subgrid check

   Sudoku rules require checking the 3x3 box; this code does not do that, causing errors.

3. Final Answer:

   It does not check the 3x3 subgrid for duplicates -> Option B

4. Quick Check:

   3x3 box check missing = bug [OK]

Hint: Always check row, column, and 3x3 box [OK]

Common Mistakes:

• Ignoring 3x3 box validation
• Thinking loop variable causes error
• Assuming early return is wrong

5. You want to optimize the Sudoku solver by choosing the next empty cell with the fewest possible valid numbers to try. Which technique does this describe?

hard

A. Heuristic with Minimum Remaining Value (MRV) strategy

B. Random guessing of empty cells

C. Depth-first search without pruning

D. Sorting the board rows before solving

Solution

1. Step 1: Understand MRV heuristic

   MRV chooses the empty cell with the fewest valid options to reduce branching and speed up solving.

2. Step 2: Compare with other options

   Random guessing and depth-first search without pruning are less efficient; sorting rows does not help solving.

3. Final Answer:

   Heuristic with Minimum Remaining Value (MRV) strategy -> Option A

4. Quick Check:

   MRV = choose cell with fewest options [OK]

Hint: Pick cell with fewest choices first [OK]

Common Mistakes:

• Confusing random guessing with heuristics
• Ignoring pruning benefits
• Thinking sorting helps solving