Given a matrix, clockwise rotate elements in it.
Examples:
Input 1 2 3 4 5 6 7 8 9 Output: 4 1 2 7 5 3 8 9 6 For 4*4 matrix Input: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Output: 5 1 2 3 9 10 6 4 13 11 7 8 14 15 16 12
The idea is to use loops similar to the program for printing a matrix in spiral form. One by one rotate all rings of elements, starting from the outermost. To rotate a ring, we need to do following.
1) Move elements of top row.
2) Move elements of last column.
3) Move elements of bottom row.
4) Move elements of first column.
Repeat above steps for inner ring while there is an inner ring.
Below is the implementation of above idea. Thanks to Gaurav Ahirwar for suggesting below solution.
Python
# Python program to rotate a matrix# Function to rotate a matrixdef rotateMatrix(mat): if not len(mat): return """ top : starting row index bottom : ending row index left : starting column index right : ending column index """ top = 0 bottom = len(mat)-1 left = 0 right = len(mat[0])-1 while left < right and top < bottom: # Store the first element of next row, # this element will replace first element of # current row prev = mat[top+1][left] # Move elements of top row one step right for i in range(left, right+1): curr = mat[top][i] mat[top][i] = prev prev = curr top += 1 # Move elements of rightmost column one step downwards for i in range(top, bottom+1): curr = mat[i][right] mat[i][right] = prev prev = curr right -= 1 # Move elements of bottom row one step left for i in range(right, left-1, -1): curr = mat[bottom][i] mat[bottom][i] = prev prev = curr bottom -= 1 # Move elements of leftmost column one step upwards for i in range(bottom, top-1, -1): curr = mat[i][left] mat[i][left] = prev prev = curr left += 1 return mat# Utility Functiondef printMatrix(mat): for row in mat: print row# Test case 1matrix =[ [1, 2, 3, 4 ], [5, 6, 7, 8 ], [9, 10, 11, 12 ], [13, 14, 15, 16 ] ]# Test case 2"""matrix =[ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]"""matrix = rotateMatrix(matrix)# Print modified matrixprintMatrix(matrix) |
Output:
5 1 2 3 9 10 6 4 13 11 7 8 14 15 16 12
Time Complexity: O(max(m,n) * max(m,n))
Auxiliary Space: O(m*n)
Please refer complete article on Rotate Matrix Elements for more details!
