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Sudoku Solver

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to solve a Sudoku puzzle using backtracking. A Sudoku puzzle is a 9×9 grid where some cells are filled with digits 1-9, and the goal is to fill the remaining empty cells. The rules are: each row, column, and 3×3 sub-box must contain all digits from 1 to 9 exactly once.

Example 1
    
  
  • Input: 9x9 Sudoku grid with some filled cells and empty cells (represented by 0)
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  • Output: Solved Sudoku
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  • Explanation: 
    • Fill empty cells (represented by 0) following Sudoku rules. 
    • Each row, column, and 3×3 box must contain digits 1-9 exactly once. 
    • Use backtracking to try different possibilities and find the solution.
    •
Example 2
    
  
  • Input: Invalid Sudoku (no solution)
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  • Output: "No solution exists"
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  • Explanation: 
    • Some Sudoku puzzles may not have a valid solution. 
    • The algorithm will try all possibilities and determine no solution exists. 
    • Return appropriate message indicating unsolvable puzzle.
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Constraints
    
  
  • The Sudoku grid is always 9×9
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  • Empty cells are represented by 0
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  • Given digits are between 1-9
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  • There is at most one unique solution
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  • Time Complexity: O(9^(n*n)) in worst case where n=9
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  • Space Complexity: O(n*n) for recursion stack
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Backtracking Goldman SachsTutorix
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Hint
Solution

Solution Hints

    
  
  • Use backtracking algorithm to try filling each empty cell with digits 1-9
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  • For each empty cell, check if placing a digit is valid according to Sudoku rules
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  • A digit is valid if it doesn't appear in the same row, column, or 3×3 sub-box
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  • If a digit placement leads to a solution, continue; otherwise backtrack and try next digit
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  • Use helper functions to check row, column, and box validity separately
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  • Find empty cells systematically and fill them one by one
    •

Steps to solve by this approach:

 Step 1: Find the first empty cell (containing 0) in the Sudoku grid
 Step 2: Try placing digits 1 through 9 in the empty cell
 Step 3: For each digit, check if placement is valid by verifying row, column, and 3×3 box constraints
 Step 4: If placement is valid, place the digit and recursively solve the remaining puzzle
 Step 5: If recursive call returns true, the puzzle is solved; if false, backtrack by removing the digit
 Step 6: If no digit (1-9) works for current cell, return false to trigger backtracking
 Step 7: If no empty cells remain, the puzzle is completely solved and return true

Submitted Code :