vault backup: 2026-06-05 18:15:42

leetcode/note/medium/36_valid_sudoku.md

@@ -6,8 +6,115 @@ tags:
   - array
   - hash-table
   - matrix
-status: unsolve
-date_solved: 2026-05-26
+status: Solved
+date_solved: 2026-06-05
 leetcode_url: https://leetcode.com/problems/valid-sudoku/
 review_needed: false
 ---
+
+# 36. Valid Sudoku
+
+> [!info] **Problem Link**: [LeetCode - Valid Sudoku](https://leetcode.com/problems/valid-sudoku/)
+
+## 📝 Problem Description
+
+Determine if a **9 x 9 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 `3 x 3` 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:**
+```python
+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:**
+```python
+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`
+**Explanation:** Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top-left 3x3 sub-box, it is invalid.
+
+---
+
+## 💡 Approaches & Explanations
+
+### Approach 1: Hash Sets for Rows, Columns, and Boxes — *Optimal*
+We use three collections of sets to track the numbers we've seen:
+1. `rows`: 9 sets, one for each row.
+2. `cols`: 9 sets, one for each column.
+3. `boxes`: 9 sets, one for each 3x3 sub-grid.
+
+We iterate through every cell `(r, c)` in the 9x9 board. If the cell is not empty (i.e., not `.`):
+- Calculate the box index: `box_idx = (r // 3) * 3 + (c // 3)`.
+- Check if the digit already exists in `rows[r]`, `cols[c]`, or `boxes[box_idx]`.
+- If it exists, the board is invalid.
+- If not, add the digit to all three sets and continue.
+
+#### 📊 Complexity Analysis
+- **Time Complexity:** $\mathcal{O}(1)$ or $\mathcal{O}(N^2)$ where $N=9$. Since the board size is fixed at 9x9, we always perform 81 operations.
+- **Space Complexity:** $\mathcal{O}(1)$ or $\mathcal{O}(N^2)$ to store the sets for rows, columns, and boxes. In the worst case, we store 81 entries.
+
+---
+
+## 💻 Code Implementations
+
+### Python3
+```python
+class Solution:
+    def isValidSudoku(self, board: List[List[str]]) -> bool:
+        cols = collections.defaultdict(set)
+        rows = collections.defaultdict(set)
+        squares = collections.defaultdict(set)  # key = (r // 3, c // 3)
+
+        for r in range(9):
+            for c in range(9):
+                if board[r][c] == ".":
+                    continue
+                if (
+                    board[r][c] in rows[r]
+                    or board[r][c] in cols[c]
+                    or board[r][c] in squares[(r // 3, c // 3)]
+                ):
+                    return False
+                cols[c].add(board[r][c])
+                rows[r].add(board[r][c])
+                squares[(r // 3, c // 3)].add(board[r][c])
+
+        return True
+```
+
+---
+
+## 🧠 Key Takeaways & Lessons
+- **Coordinate Mapping:** Mapping a 2D coordinate `(r, c)` to a 1D sub-grid index or a tuple key `(r // 3, c // 3)` is a crucial technique for matrix problems.
+- **Trade-off:** Using hash sets provides $\mathcal{O}(1)$ lookup time, making the validation process very efficient.
+- **Constraints Matter:** Since the board size is fixed (9x9), "optimal" here refers to the single-pass nature and clean logic rather than asymptotic growth beyond the constant size.