109 lines
2 KiB
Markdown
109 lines
2 KiB
Markdown
# Leetcode Rotate-Image
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2022-09-02 15:40
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> ##### Algorithms:
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>
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> #algorithm #math
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>
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> ##### Data structures:
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>
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> #DS #array
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>
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> ##### Difficulty:
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>
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> #coding_problem #difficulty-medium
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>
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> ##### Additional tags:
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>
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> #leetcode #CS_list_need_understanding
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>
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> ##### Revisions:
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>
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> N/A
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##### Links:
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- [Link to problem](https://leetcode.com/problems/rotate-image/)
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- [Solution and explanation](https://leetcode.com/problems/rotate-image/solution/)
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---
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### Problem
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You are given an `n x n` 2D `matrix` representing an image, rotate the image by **90** degrees (clockwise).
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You have to rotate the image [**in-place**](https://en.wikipedia.org/wiki/In-place_algorithm), which means you have to modify the input 2D matrix directly. **DO NOT** allocate another 2D matrix and do the rotation.
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#### Examples
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**Example 1:**
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```
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**Input:** matrix = [[1,2,3],[4,5,6],[7,8,9]]
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**Output:** [[7,4,1],[8,5,2],[9,6,3]]
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```
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**Example 2:**
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```
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**Input:** matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
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**Output:** [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]
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```
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#### Constraints
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### Thoughts
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> [!summary]
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> This is a #math problem.
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Mainly two ways
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#### Method 1: rotate in rings
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#TODO complete in this method.
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#### Method 2: transpose and reflect
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transpose reflects the matrix in `y = x`,
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reflect changes matrix in axis y
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### Solution
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```cpp
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class Solution {
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void reflect(vector<vector<int>> &mat) {
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// reflect in y axis.
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int n = mat.size();
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for (int i = 0; i < n; i++) {
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for (int j = 0, half = n / 2; j < half; j++) {
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swap(mat[i][j], mat[i][n - j - 1]);
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}
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}
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}
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void transpose(vector<vector<int>> &mat) {
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int n = mat.size();
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < i; j++) {
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swap(mat[i][j], mat[j][i]);
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}
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}
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}
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public:
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void rotate(vector<vector<int>> &matrix) {
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// transpose and reflect
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transpose(matrix);
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reflect(matrix);
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}
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};
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```
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