36. Valid Sudoku

Author: Shikha-code36

ArraysAndHashing/Medium/36_Valid_Sudoku.py

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+'''
+36. Valid Sudoku
+
+Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:
+1. Each row must contain the digits 1-9 without repetition.
+2. Each column must contain the digits 1-9 without repetition.
+3. Each of the nine 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.
+
+Note:
+A Sudoku board (partially filled) could be valid but is not necessarily solvable.
+Only the filled cells need to be validated according to the mentioned rules.
+
+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: true
+
+Example 2:
+Input: board = 
+[
+  ["8","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: false
+'''
+
+# Approach:
+# Time Complexity: O(N^2) where N is the number of cells in the board (81 cells).
+# Space Complexity: O(N^2) for the sets used to track seen numbers in rows, columns, and boxes.
+'''
+We can use a set to keep track of the numbers we have seen in each row, column, and 3x3 sub-box.
+We will iterate through each cell in the board and check if the number is already in the corresponding row, column, or sub-box set. 
+If it is, we return false. If not, we add the number to the respective sets.
+'''
+
+class Solution:
+    def isValidSudoku(self, board):
+        row_count={}
+        col_count={}
+        box_count={}
+        
+        for r in range(9):
+            for c in range(9):
+                num = board[r][c]
+                
+                if num ==".":
+                    continue
+                bx_in= (r//3)*3+(c//3)
+                if r not in row_count:
+                    row_count[r]=set()
+                if c not in col_count:
+                    col_count[c]=set()
+                if bx_in not in box_count:
+                    box_count[bx_in]=set()
+                
+                if num in row_count[r] or num in col_count[c] or num in box_count[bx_in]:
+                    return False
+                
+                row_count[r].add(num)
+                col_count[c].add(num)
+                box_count[bx_in].add(num)
+                
+        return True
+                
+                    
+
+obj = Solution()
+board =[["1","2",".",".","3",".",".",".","."],
+ ["4",".",".","5",".",".",".",".","."],
+ [".","9","8",".",".",".",".",".","3"],
+ ["5",".",".",".","6",".",".",".","4"],
+ [".",".",".","8",".","3",".",".","5"],
+ ["7",".",".",".","2",".",".",".","6"],
+ [".",".",".",".",".",".","2",".","."],
+ [".",".",".","4","1","9",".",".","8"],
+ [".",".",".",".","8",".",".","7","9"]]
+
+print(obj.isValidSudoku(board))
+
+