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48. Rotate Image

48. Rotate Image

How to rotate a matrix

Nhut Nguyen's photo
Nhut Nguyen
·Jun 5, 2023·

2 min read

Problem statement

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.

Example 1

The matrix of Example 1 and its rotation

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

Example 2

The matrix of Example 2 and its rotation

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

  • n == matrix.length == matrix[i].length.

  • 1 <= n <= 20.

  • -1000 <= matrix[i][j] <= 1000.

Solution: The math behind

For any square matrix, the rotation 90 degrees clockwise can be performed in two steps:

  1. Transpose the matrix.

  2. Mirror the matrix vertically.

Code

#include <iostream>
#include <vector>
using namespace std;
void rotate(vector<vector<int>>& matrix) {
    const int n = matrix.size();
    // transpose
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            swap(matrix[i][j], matrix[j][i]);
        }
    }
    // vertical mirror
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n / 2; j++ ) {
            swap(matrix[i][j], matrix[i][n - 1 - j]);
        }
    }
}
void printMatrix(vector<vector<int>>& matrix) {
    cout << "[";
    for (auto& row: matrix) {
        cout << "[";
        for (auto& a: row) {
            cout << a << ",";
        }
        cout << "],";
    }
    cout << "]\n";
}
int main() {
    vector<vector<int>> matrix{{1,2,3},{4,5,6},{7,8,9}};
    rotate(matrix);
    printMatrix(matrix);
    matrix = {{5,1,9,11},{2,4,8,10},{13,3,6,7},{15,14,12,16}};
    rotate(matrix);
    printMatrix(matrix);
}
Output:
[[7,4,1,],[8,5,2,],[9,6,3,],]
[[15,13,2,5,],[14,3,4,1,],[12,6,8,9,],[16,7,10,11,],]

Complexity

  • Runtime: O(n^2), where n = matrix.length.

  • Extra space: O(1).

Implementation notes

  1. The function std::swap can be used to exchange two values.

  2. When doing the transpose or mirroring, you could visit over one-half of the matrix.


Thanks for reading. Feel free to share your thought about my content and check out my FREE book 10 Classic Coding Challenges.

What is your approach? The problem was picked from leetcode.com. You can submit your solution in any programming language and check the performance.

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