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Matrices
Rotate Image
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Count: 10
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.
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
Python
def rotate_image(matrix):n = len(matrix)# Transpose the matrixfor i in range(n):for j in range(i, n):matrix[i][j], matrix[j][i] = \matrix[j][i], matrix[i][j]# Reverse each rowfor 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
Python
def rotate_image(matrix):n = len(matrix)# Transpose the matrixfor i in range(n):for j in range(i, n):matrix[i][j], matrix[j][i] = \matrix[j][i], matrix[i][j]# Reverse each rowfor 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
Python
def rotate_image(matrix):n = len(matrix)# Transpose the matrixfor i in range(n):for j in range(i, n):matrix[i][j], matrix[j][i] = \matrix[j][i], matrix[i][j]# Reverse each rowfor i in range(n):matrix[i] = matrix[i][::-1]return matrix
rotate image
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Complexity Analysis
Time Complexity: O(n²) where n is the number of rows in the matrix. We need to process each element in the matrix.
Space Complexity: O(1) since we are doing the rotation in-place without using extra space.
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