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ROTATE 90 DEGREES CLOCKWISE HOW TO
ROTATE 90 DEGREES CLOCKWISE CODE
ROTATE 90 DEGREES CLOCKWISE SERIES

Count zeros in a row-wise and column-wise sorted matrix.

Nested loops (In-place): Time = O(n²), Space = O(1).

Matrix Transpose: Time = O(n²), Space = O(1).

Extra Space: Time = O(n²), Space = O(n²).

Can we design a general algorithm for rotating matrix by multiple of 90 degrees?Ĭomparisons of Time and Space Complexities.

ROTATE 90 DEGREES CLOCKWISE HOW TO

How to generalize the solution for the m x n rectangular matrix?.Can we find transpose in-place using some different approach?.How can we rotate the matrix in a clockwise direction?.

ROTATE 90 DEGREES CLOCKWISE CODE

Can we solve the problem by first reversing each row and then doing transpose of the matrix? If yes, then write code for it.Possible questions by the Interviewer: Ideas to Think! Space Complexity = O(1), as no extra memory is needed. If this triangle is rotated 90° counterclockwise.

ROTATE 90 DEGREES CLOCKWISE SERIES

Then in the next column of the transposed table, type a series of numbers as. Select the table and press Ctrl + C keys to copy the table data, select a blank cell and right click to display the context menu, and then click Paste Special > Transpose. (-y, x) Example 1 : Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. To rotate a table anticlockwise in 90 degrees, you can do as below steps: 1. We are traversing each element of the matrix only once using nested loop and fixing its correct position. When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure. The last row of the input matrix = The last column of the output matrix in the reverse order.Īlgorithm Pseudo Code int rotateMatrix(int X, int n) Time and Space Complexity Analysis.The second row of the input matrix = The second column of the output matrix in the reverse order and so.

The first row of the input matrix = The first column of the output matrix in the reverse order.

So one basic idea would be simple - use an extra matrix of the same size and directly copy elements from the original matrix according to the above observation.

First column in the output matrix: 4, 3, 2, 1.

First row in the input matrix: 1, 2, 3, 4,.

Similarly, second, third, …rows have turned into their respective column in reverse order. The origin is the rotation’s fixed point unless stated otherwise. In a 90 degree clockwise rotation, the point of a given figure’s points is turned in a clockwise direction with respect to the fixed point. If we observe input and output matrices, then the following pattern would be visible: The first row has turned into the first column in reverse order. The 90-degree clockwise rotation represents the movement of a point or a figure with respect to the origin, (0, 0). Think and Enjoy :) Brute force approach using extra space Algorithm Idea and Steps Otherwise, no problem, this is an opportunity to learn a new pattern in problem-solving. If solved, then well done! We would like to hear your ideas in the comment. Important Note: Before moving to the solutions, we recommend learners solve this problem.