Using Line by Line Diagonal Traversal - O(n*m) time and O(n*m) space
The idea is to traverse the matrix diagonally from bottom-left to top-right, one diagonal at a time. Since a matrix with R rows and C columns has exactly R+C-1 diagonals, we iterate through each diagonal line and identify the starting position, number of elements, and the indices of elements belonging to that diagonal, collecting them in sequence to produce the desired diagonal ordering.
Step by step approach:
Identify total number of diagonals (rows + columns - 1) and iterate through each one.
For each diagonal, calculate its starting column position based on the diagonal number.
Determine how many elements exist in the current diagonal.
Extract each element from the current diagonal by calculating its exact row and column indices.
Collect all elements in a result container to return the diagonal ordering.
Using Starting Point Traversal - O(n*m) time and O(n*m) space
The idea is to traverse the matrix diagonally from bottom-left to top-right by identifying each diagonal's starting point and following it up. Since every diagonal moves in the same direction (up and right), the approach divides the matrix into two parts: first processing all diagonals that start from the first column (from top to bottom), then processing the remaining diagonals that start from the bottom row (from left to right, excluding the already processed bottom-left corner).
