Matrices

Rotate Image

medium

DESCRIPTION (inspired by Leetcode.com)

Write a function to rotate an n x n 2D matrix representing an image by 90 degrees clockwise. The rotation must be done in-place, meaning you should modify the input matrix directly without using an additional matrix for the operation.

Input:

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

Output:

[
    [3,2,1],
    [6,5,4],
    [9,8,7]
]

Explanation: The matrix is rotated by 90 degrees clockwise, transforming its columns into rows in reverse order.

Code Editor

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Explanation

This problem can be done in two steps. We first transpose the matrix, then reverse the elements in each row.

Step 1:

Transpose the matrix by swapping the elements across the diagonal. This can be done in-place by using a nested for loop to swap the elements.

Visualization


def rotate_image(matrix):
    n = len(matrix)
    # Transpose the matrix
    for i in range(n):
        for j in range(i, n):
            matrix[i][j], matrix[j][i] = \
                matrix[j][i], matrix[i][j]
    # Reverse each row
    for i in range(n):
        matrix[i] = matrix[i][::-1]
    return matrix

n = 3

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Step 2:

Reverse the elements in each row of the matrix.

Visualization


def rotate_image(matrix):
    n = len(matrix)
    # Transpose the matrix
    for i in range(n):
        for j in range(i, n):
            matrix[i][j], matrix[j][i] = \
                matrix[j][i], matrix[i][j]
    # Reverse each row
    for i in range(n):
        matrix[i] = matrix[i][::-1]
    return matrix

swap matrix[2][2] and matrix[2][2]

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Solution

Try these examples:

Visualization


def rotate_image(matrix):
    n = len(matrix)
    # Transpose the matrix
    for i in range(n):
        for j in range(i, n):
            matrix[i][j], matrix[j][i] = \
                matrix[j][i], matrix[i][j]
    # Reverse each row
    for i in range(n):
        matrix[i] = matrix[i][::-1]
    return matrix

rotate image

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What is the time complexity of this solution?

O(2ⁿ)

O(4ⁿ)

O(n²)

O(n log n)

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