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

Recall & Review

beginner

What is the main idea behind the backtracking algorithm used in Sudoku solving?

Backtracking tries to fill empty cells one by one with numbers 1 to 9. If a number breaks Sudoku rules, it goes back (backtracks) and tries a different number until the puzzle is solved.

beginner

In Sudoku, what are the three main rules that must be checked before placing a number in a cell?

1. The number must not appear in the same row.
2. The number must not appear in the same column.
3. The number must not appear in the same 3x3 box.

beginner

What does the function to find an empty cell return if the Sudoku board is completely filled?

It returns None (or equivalent) indicating there are no empty cells left, meaning the puzzle is solved.

intermediate

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

Because it tries to fill one cell completely before moving to the next, going deep into one possible solution path and backtracking if it hits a dead end.

beginner

How does the Sudoku solver know when to stop the recursion?

When there are no empty cells left to fill, the recursion stops and the board is solved.

What is the first step in the backtracking Sudoku solver?

A Remove numbers from the board

B Find an empty cell to fill

C Check if the board is solved

D Fill all cells with 1

The solver first finds an empty cell to try filling with numbers.

Which of these is NOT a rule to check before placing a number in Sudoku?

A Number must be greater than 5

B Number must not be in the same row

C Number must not be in the same column

D Number must not be in the same 3x3 box

Sudoku numbers range from 1 to 9; no rule requires numbers to be greater than 5.

What happens if no number fits in an empty cell during backtracking?

A The solver backtracks to previous cell

B The solver fills the cell with zero

C The solver stops and returns failure

D The solver skips the cell

Backtracking means going back to the previous cell to try a different number.

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

A Only even numbers

B Only 5

C 1 to 9

D Only prime numbers

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

When does the Sudoku solver declare the puzzle solved?

A When the first empty cell is filled

B When half the cells are filled

C When no numbers are left to try

D When all cells are filled correctly

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 to find the right solution.

Describe the three main checks needed before placing a number in a Sudoku cell.

Sudoku rules prevent repeating numbers in these areas.

Practice

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

easy

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

B. To fill the Sudoku grid randomly without checking rules

C. To sort the numbers in each row before placing them

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

Solution

1. Step 1: Understand backtracking role

   Backtracking tries placing numbers and removes them if they cause conflicts.

2. Step 2: Compare options

   Only To try possible numbers and undo choices if they lead to conflicts describes this trial and undo process correctly.

3. Final Answer:

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

4. Quick Check:

   Backtracking = Try and undo [OK]

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

Common Mistakes:

• Thinking backtracking fills randomly
• Confusing backtracking with sorting
• Ignoring the undo step in backtracking

2. Which Rust syntax correctly defines a function to check if a number can be placed in a Sudoku cell?

easy

A. fn can_place(board: &[[u8; 9]; 9], row: usize, col: usize, num: u8) -> bool { /* code */ }

B. function can_place(board, row, col, num) { /* code */ }

C. def can_place(board, row, col, num): return True

D. let can_place = (board, row, col, num) => { /* code */ }

Solution

1. Step 1: Identify Rust function syntax

   Rust functions start with fn, specify parameter types and return type.

2. Step 2: Match options to Rust syntax

   Only fn can_place(board: &[[u8; 9]; 9], row: usize, col: usize, num: u8) -> bool { /* code */ } uses fn and types correctly.

3. Final Answer:

   fn can_place(board: &[[u8; 9]; 9], row: usize, col: usize, num: u8) -> bool { /* code */ } -> Option A

4. Quick Check:

   Rust fn syntax = fn can_place(board: &[[u8; 9]; 9], row: usize, col: usize, num: u8) -> bool { /* code */ } [OK]

Hint: Rust functions start with fn and specify types [OK]

Common Mistakes:

• Using JavaScript or Python syntax in Rust
• Omitting parameter types
• Not specifying return type

3. Given this partial Rust code snippet for Sudoku backtracking, what will be printed?

let mut board = [[0u8; 9]; 9];
board[0][0] = 5;
println!("{}", board[0][0]);

medium

A. 0

B. 5

C. Error

D. None

Solution

1. Step 1: Understand board initialization

   The board is a 9x9 grid initialized with zeros.

2. Step 2: Check assignment and print

   board[0][0] is set to 5, so printing it outputs 5.

3. Final Answer:

   5 -> Option B

4. Quick Check:

   board[0][0] = 5 prints 5 [OK]

Hint: Assigned value prints, not initial zero [OK]

Common Mistakes:

• Assuming default zero prints after assignment
• Confusing index order
• Expecting error due to mutability

4. Identify the bug in this Rust function snippet for Sudoku backtracking:

fn solve(board: &mut [[u8; 9]; 9]) -> bool {
  for row in 0..9 {
    for col in 0..9 {
      if board[row][col] == 0 {
        for num in 1..9 {
          if can_place(board, row, col, num) {
            board[row][col] = num;
            if solve(board) {
              return true;
            }
            board[row][col] = 0;
          }
        }
        return false;
      }
    }
  }
  true
}

medium

A. The function never returns true when the board is full

B. The board parameter should not be mutable

C. The range 1..9 excludes 9, should be 1..10

D. The nested loops should be swapped

Solution

1. Step 1: Check number range in loop

   Rust range 1..9 iterates from 1 to 8 (exclusive end), missing 9 which is required for Sudoku.

2. Step 2: Compare options

   Only The range 1..9 excludes 9, should be 1..10 correctly identifies the range bug and suggests 1..10 (1 through 9).

3. Step 3: Verify other options

   A: Incorrect; returns true after loops if no empty cells. C: Wrong; mutable needed for changes. D: Unnecessary; order is fine.

4. Final Answer:

   The range 1..9 excludes 9, should be 1..10 -> Option C

5. Quick Check:

   Rust 1..9 = 1-8, use 1..10 for 1-9 [OK]

Hint: Remember Rust 1..10 excludes 10, includes 9 [OK]

Common Mistakes:

• Thinking 1..10 includes 10
• Not marking board mutable
• Swapping loops unnecessarily

5. How does the backtracking algorithm ensure that the Sudoku solution is valid and complete?

hard

A. By placing numbers only if they don't violate Sudoku rules and backtracking on conflicts until the board is full

B. By filling all cells with random numbers and checking at the end

C. By sorting each row and column before placing numbers

D. By using a queue to store all possible numbers for each cell

Solution

1. Step 1: Understand backtracking validation

   The algorithm tries numbers only if they don't break Sudoku rules (row, column, box).

2. Step 2: Understand backtracking completeness

   If a number leads to conflict later, it removes it (backtracks) and tries another number until the board is full.

3. Step 3: Eliminate wrong options

   Options B, C, and D describe incorrect or unrelated methods.

4. Final Answer:

   By placing numbers only if they don't violate Sudoku rules and backtracking on conflicts until the board is full -> Option A

5. Quick Check:

   Backtracking = Try-valid-undo until complete [OK]

Hint: Backtracking tries valid numbers, undoes on conflict [OK]

Common Mistakes:

• Thinking random fill works
• Confusing sorting with validation
• Using queues instead of recursion