Tutorialspoint
Problem
Solution
Submissions
Back

Sudoku Solver

Certification: Advanced Level Accuracy: 100% Submissions: 1 Points: 20

Write a Java program to solve a Sudoku puzzle by filling the empty cells. A sudoku solution must satisfy all of the following rules:

  1. Each of the digits 1-9 must occur exactly once in each row.
  2. Each of the digits 1-9 must occur exactly once in each column.
  3. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

Example 1
    
  
  • Input: 
  
    5 3 . | . 7 . | . . .
  
    6 . . | 1 9 5 | . . .
  
    . 9 8 | . . . | . 6 .
  
    ---------------------
  
    8 . . | . 6 . | . . 3
  
    4 . . | 8 . 3 | . . 1
  
    7 . . | . 2 . | . . 6
  
    ---------------------
  
    . 6 . | . . . | 2 8 .
  
    . . . | 4 1 9 | . . 5
  
    . . . | . 8 . | . 7 9
    • 
  
  • Output: Filled sudoku board
    • 
  
  • Explanation: 
    
    Step 1: Start with the given board with empty cells marked as '.'.
    
    Step 2: Apply backtracking to fill in the empty cells one by one.
    
    Step 3: For each empty cell, try digits 1-9 and validate against sudoku rules.
    
    Step 4: If a valid digit is found, place it and move to the next empty cell.
    
    Step 5: If no valid digit exists for a cell, backtrack and try different digits for previous cells.
    
    Step 6: Continue until all empty cells are filled with valid digits.
  
    •
Example 2
    
  
  • Input: 
  
    . . 9 | 7 4 8 | . . .
  
    7 . . | . . . | . . .
  
    . 2 . | 1 . 9 | . . .
  
    ---------------------
  
    . . 7 | . . . | 2 4 .
  
    . 6 4 | . 1 . | 5 9 .
  
    . 9 8 | . . . | 3 . .
  
    ---------------------
  
    . . . | 8 . 3 | . 2 .
  
    . . . | . . . | . . 6
  
    . . . | 2 7 5 | 9 . .
    • 
  
  • Output: Filled sudoku board
    • 
  
  • Explanation:
    
    Step 1: Start with the given board with empty cells marked as '.'.
    
    Step 2: Apply backtracking to fill in the empty cells one by one.
    
    Step 3: For each empty cell, try digits 1-9 and validate against sudoku rules.
    
    Step 4: If a valid digit is found, place it and move to the next empty cell.
    
    Step 5: If no valid digit exists for a cell, backtrack and try different digits for previous cells.
    
    Step 6: Continue until all empty cells are filled with valid digits.
  
    •
Constraints
    
  
  • The board size is fixed as a 9x9 grid
    • 
  
  • The board will contain only digits 1-9 and the character '.' for empty cells
    • 
  
  • The given board will have at least one solution
    • 
  
  • Time Complexity: O(9^(n*n)) where n is the size of the board (in this case, 9)
    • 
  
  • Space Complexity: O(n*n)
    •
ArraysBacktracking DropboxTutorix
Editorial

Login to view the detailed solution and explanation for this problem.

My Submissions
All Solutions
Refresh
Lang Status Date Code
You do not have any submissions for this problem.
Refresh
User Lang Status Date Code
No submissions found.

Please Login to continue
Solve Problems

 
 
 
Output Window
Clear All Apply Filters

Trending

Others

SIGN IN

Don't have an account? Register

Hint
Solution

Solution Hints

    
  
  • Use backtracking algorithm to solve this problem.
    • 
  
  • Start by finding an empty cell in the board.
    • 
  
  • Try placing each digit 1-9 in the empty cell.
    • 
  
  • For each digit, check if it's valid according to sudoku rules.
    • 
  
  • If valid, place the digit and recursively solve for the next empty cell.
    • 
  
  • If a solution is found, return true. If not, backtrack and try a different digit.
    • 
  
  • If no digits work, reset the cell to empty and return false.
    •

Steps to solve by this approach:

 Step 1: Create a function to find an empty cell in the board.

 Step 2: Create a function to check if placing a digit at a specific position is valid.

 Step 3: Implement the backtracking algorithm that tries digits 1-9 for each empty cell.

 Step 4: For each empty cell, try placing each digit and check if it's valid.

 Step 5: If valid, place the digit and recursively solve the rest of the board.

 Step 6: If the recursive call returns true, a solution has been found.

 Step 7: If the recursive call returns false, backtrack by resetting the cell to empty and try the next digit.

Submitted Code :