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Sudoku Solver

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

Write a C# program to implement the SolveSudoku(char[][] board) function that solves a 9x9 Sudoku puzzle. The Sudoku board is represented as a 9x9 char array where empty cells are filled with '.' and cells with digits are filled with '1' to '9'. Your program should modify the input board directly.

Example 1
    
  
  • Input: board = [
    
    ['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: [
    
    ['5','3','4','6','7','8','9','1','2'],
    
    ['6','7','2','1','9','5','3','4','8'],
    
    ['1','9','8','3','4','2','5','6','7'],
    
    ['8','5','9','7','6','1','4','2','3'],
    
    ['4','2','6','8','5','3','7','9','1'],
    
    ['7','1','3','9','2','4','8','5','6'],
    
    ['9','6','1','5','3','7','2','8','4'],
    
    ['2','8','7','4','1','9','6','3','5'],
    
    ['3','4','5','2','8','6','1','7','9']
    
  ]
    •
Example 2
    
  
  • Input: board = [
    
    ['.','.','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: [
    
    ['5','1','9','7','4','8','6','3','2'],
    
    ['7','8','3','6','5','2','4','1','9'],
    
    ['4','2','6','1','3','9','8','7','5'],
    
    ['3','5','7','9','8','6','2','4','1'],
    
    ['2','6','4','3','1','7','5','9','8'],
    
    ['1','9','8','5','2','4','3','6','7'],
    
    ['9','7','5','8','6','3','1','2','4'],
    
    ['8','3','2','4','9','1','7','5','6'],
    
    ['6','4','1','2','7','5','9','8','3']
    
  ]
    •
Constraints
    
  
  • board.length == 9
    • 
  
  • board[i].length == 9
    • 
  
  • board[i][j] is a digit '1'-'9' or '.'
    • 
  
  • It is guaranteed that the input board has only one solution
    • 
  
  • Time Complexity: O(9^(n*n)) where n is the board size (worst case)
    • 
  
  • Space Complexity: O(n*n)
    •
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Hint
Solution

Solution Hints

    
  
  • Use backtracking to solve the Sudoku puzzle
    • 
  
  • For each empty cell, try placing digits 1-9
    • 
  
  • Check if the digit is valid in the current position (row, column, and 3x3 box)
    • 
  
  • If valid, place the digit and recursively try to solve the rest of the board
    • 
  
  • If the recursive call is successful, the puzzle is solved. Otherwise, backtrack
    •

Steps to solve by this approach:

 Step 1: Create a recursive function to solve the Sudoku board.
 Step 2: Iterate through each cell of the 9x9 grid.
 Step 3: When an empty cell is found (marked with '.'), try placing each digit from '1' to '9'.
 Step 4: For each digit, check if it's valid in the current position by examining the row, column, and 3x3 box.
 Step 5: If the digit is valid, place it in the cell and recursively try to solve the rest of the board.
 Step 6: If the recursive call is successful, the puzzle is solved.
 Step 7: If the recursive call is not successful, backtrack by resetting the cell to '.' and try the next digit.

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