Time: 2831 ms (23.84%), Space: 17.8 MB (95.13%) - LeetHub

Author: hogan-tech

0037-sudoku-solver/0037-sudoku-solver.py

@@ -0,0 +1,72 @@
+# time complexity: O(9!^9)
+# space complexity: O(1)
+from collections import defaultdict
+from typing import List
+
+
+class Solution:
+    def solveSudoku(self, board: List[List[str]]) -> None:
+        n = len(board)
+
+        rows, cols, boxes = defaultdict(
+            set), defaultdict(set), defaultdict(set)
+
+        for r in range(n):
+            for c in range(n):
+                if board[r][c] == '.':
+                    continue
+
+                digit = int(board[r][c])
+                rows[r].add(digit)
+                cols[c].add(digit)
+                boxes[(r // 3) * 3 + c // 3].add(digit)
+
+        def isValid(r: int, c: int, digit: int):
+            boxId = (r // 3) * 3 + c // 3
+            return digit not in rows[r] and digit not in cols[c] and digit not in boxes[boxId]
+
+        def backtrack(r: int, c: int):
+            if r == n - 1 and c == n:
+                return True
+            elif c == n:
+                c = 0
+                r += 1
+
+            if board[r][c] != '.':
+                return backtrack(r, c + 1)
+
+            boxId = (r // 3) * 3 + c // 3
+            for digit in range(1, n + 1):
+                if not isValid(r, c, digit):
+                    continue
+
+                board[r][c] = str(digit)
+                rows[r].add(digit)
+                cols[c].add(digit)
+                boxes[boxId].add(digit)
+
+                if backtrack(r, c + 1):
+                    return True
+
+                board[r][c] = '.'
+                rows[r].remove(digit)
+                cols[c].remove(digit)
+                boxes[boxId].remove(digit)
+
+            return False
+
+        backtrack(0, 0)
+
+
+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"]
+]
+print(Solution().solveSudoku(board))