problem: 0048 rotate image

Author: cychiu8

0048 Rotate Image/0048 Rotate Image.md

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+# 0048. Rotate Image
+
+- Difficulty: medium
+- Link: https://leetcode.com/problems/rotate-image/
+- Topics: Array-String, Matrix
+
+# Clarification
+
+1. Check the inputs and outputs
+    - INPUT: List[List[int]]
+    - OUTPUT: List[List[int]]
+2. Check the main goal
+    - You have to rotate the image **[in-place](https://en.wikipedia.org/wiki/In-place_algorithm)**
+
+# Naive Solution
+
+### Thought Process
+
+1. 定義 matrix 邊界，設定上下左右邊界
+2. 由左上開始 rotate
+    
+    ![Untitled](./Untitled.png)
+    
+- Rotate 的方式
+    
+    ![Untitled](./Untitled%201.png)
+    
+- Implement
+    
+    ```python
+    class Solution:
+        def rotate(self, matrix: List[List[int]]) -> None:
+            """
+            Do not return anything, modify matrix in-place instead.
+            """
+            left = 0
+            right = len(matrix[0]) - 1
+            
+            while left < right:
+                for i in range(0, right - left):
+                    top, bottom = left, right
+                    left_top = matrix[top][left + i]
+                    matrix[top][left + i] = matrix[bottom - i][left]
+                    matrix[bottom - i][left] = matrix[bottom][right - i]
+                    matrix[bottom][right - i] = matrix[top + i][right]
+                    matrix[top + i][right] = left_top
+                left += 1
+                right -= 1
+    ```
+    
+
+### Complexity
+
+- Time complexity: $O(n^2)$
+- Space complexity: $O(1)$
+
+### Problems & Improvement
+
+- 多個位置轉換，需抓出好的基準點 (例如 boundary )，較不易混淆
+
+# Improvement
+
+### Thought Process
+
+1. 轉置矩陣
+2. reverse column
+
+![Untitled](./Untitled%202.png)
+
+- 交換的方式
+    
+    ![Untitled](./Untitled%203.png)
+    
+- Implement
+    
+    ```python
+    class Solution:
+        def rotate(self, matrix: List[List[int]]) -> None:
+            """
+            Do not return anything, modify matrix in-place instead.
+            """
+            lenCol = len(matrix)
+            for i in range(0, lenCol):
+                for j in range(i + 1, lenCol):
+                    matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
+                    
+            for i in range(0, lenCol):
+                for j in range(0, lenCol // 2):
+                    matrix[i][j], matrix[i][lenCol - 1 -j] = matrix[i][lenCol - 1 -j], matrix[i][j]
+    ```
+    
+
+### Complexity
+
+- Time complexity: $O(n^2)$
+- Space complexity: $O(1)$
+
+# Check special cases, check error
+
+- 
+
+# Note
+
+- [Rotate Image - Matrix - Leetcode 48](https://www.youtube.com/watch?v=fMSJSS7eO1w)