48. Rotate Image

📝 Problem Details

• Title: 48. Rotate Image
• Link: https://leetcode.com/problems/rotate-image/
• Difficulty: Medium
• Tags/Categories: Math

input n x n 2D matrix representing an image rotate the image 90 degrees (clockwise) rotation has to be done in-place

💡 Explanation of Solution

1. Transpose the Matrix
	- swap matrix[i][j] with matrix[j][i] for all elements above the diagonal
	- this converts rows into columns

2. Reverse Each Row
	- swap elements symmetrically from left to right in each row 
	- this achieves the 90-degree clockwise rotation

⌛ Complexity Analysis

Time Complexity: O(n^2)
Space Complexity: O(1)

💻 Implementation of Solution

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        int n = matrix.size();
 
        // step 1 : transpose the matrix
        for(int i = 0; i < n; i++) {
            for(int j = i + 1; j < n; j++) {
                swap(matrix[i][j] , matrix[j][i]);
            }
        }
        // step 2 : reverse each row
        for(int i=0; i < n; i++) {
            reverse(matrix[i].begin(), matrix[i].end());
        }
    }
};