notes/OJ notes/pages/Leetcode Rotate-Image.md

Leetcode Rotate-Image

2022-09-02 15:40

Algorithms:

#algorithm #math

Data structures:

#DS #array

Difficulty:

#coding_problem #difficulty_medium

Additional tags:

#leetcode #CS_list_need_understanding

Revisions:

N/A

Links:

• Link to problem
• Solution and explanation

---

Problem

You are given an n x n 2D matrix representing an image, rotate the image by 90 degrees (clockwise).

You have to rotate the image in-place, which means you have to modify the input 2D matrix directly. DO NOT allocate another 2D matrix and do the rotation.

Examples

Example 1:

**Input:** matrix = [[1,2,3],[4,5,6],[7,8,9]]
**Output:** [[7,4,1],[8,5,2],[9,6,3]]

Example 2:

**Input:** matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
**Output:** [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

Constraints

Thoughts

[!summary] This is a #math problem.

Mainly two ways

Method 1: rotate in rings

#TODO complete in this method.

Method 2: transpose and reflect

transpose reflects the matrix in y = x, reflect changes matrix in axis y

Solution

class Solution {

  void reflect(vector<vector<int>> &mat) {
    // reflect in y axis.
    int n = mat.size();
    for (int i = 0; i < n; i++) {
      for (int j = 0, half = n / 2; j < half; j++) {
        swap(mat[i][j], mat[i][n - j - 1]);
      }
    }
  }

  void transpose(vector<vector<int>> &mat) {
    int n = mat.size();
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < i; j++) {
        swap(mat[i][j], mat[j][i]);
      }
    }
  }

public:
  void rotate(vector<vector<int>> &matrix) {
    // transpose and reflect

    transpose(matrix);
    reflect(matrix);
  }
};