Prerequisites: Matrix, Loops, Map/Priority Queue.
Problem: Given an N x M matrix, sort its elements diagonally.
Solution Approach:
The core of the solution is the fact that, elements on the same diagonal have the same row-column index difference.
Steps:
- Initialize Data Structures: Create a map where the key represents the difference between row and column indices, and the value is a priority queue to store elements on each diagonal.
- Populate Diagonals: Traverse the matrix and insert each element into the appropriate diagonal in the map based on its row-column index difference.
- Sort Diagonals: Traverse the matrix again and replace each element with the top element of the corresponding diagonal’s priority queue, effectively sorting each diagonal.
- Output: print the sorted matrix.
Time Complexity:
- Let N be the number of rows and M be the number of columns.
- Populating Diagonals: O(N * M) to traverse all elements of the matrix.
- Sorting Diagonals: O(N * M * log(min(N, M))) to sort each diagonal using priority queues.
- Overall time complexity: O(N * M * log(min(N, M)))
Space Complexity:
- Additional space is used to store the map and priority queues.
- Space complexity: O(N * M) for the map and priority queues, and additional constant space for variables used in the program.