Problem
Solution
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Valid Sudoku Puzzles
Certification: Advanced Level
Accuracy: 0%
Submissions: 0
Points: 20
Write a C++ program to count the number of valid Sudoku puzzle configurations possible for a given partially filled 9x9 grid.
Example 1
- Input:
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 - Output: 1
- Explanation:
- The given partial puzzle has exactly one valid completion.
Example 2
- Input:
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 - Output: 6670903752021072936960
- Explanation:
- An empty grid has this many valid Sudoku configurations.
Constraints
- Grid size = 9x9
- Each cell contains 0 (empty) or 1-9
- At least one valid solution guaranteed
- Time Complexity: O(9^n) where n = number of empty cells
- Space Complexity: O(n)
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Solution Hints
- Use backtracking to explore all possibilities
- Check row, column, and box validity for each move
- Use pruning and bit manipulation to improve speed
- Consider using bit manipulation for checking valid numbers.
- For large counts, use appropriate data types to handle big integers.