Delete Greatest Value in Each Row

Problem Description

You are given an m x n matrix grid consisting of positive integers. Perform the following operation until grid becomes empty: Delete the element with the greatest value from each row. If multiple such elements exist, delete any of them. Add the maximum of deleted elements to the answer. Return the answer after performing the operations described above.

Key Insights

• Each operation reduces the number of columns in the matrix by one.
• The maximum value from each row needs to be identified and deleted in each operation.
• The total maximum values collected from each operation contribute to the final result.

Space and Time Complexity

Time Complexity: O(m * n) - where m is the number of rows and n is the number of columns. Space Complexity: O(1) - since we are only using a few extra variables for calculations.

Solution

To solve the problem, we can use a simple approach:

1. Iterate through the matrix while it still has columns.
2. For each row, find the maximum value and store it in a list.
3. After collecting the maximum values from all rows, find the maximum of these values and add it to the answer.
4. Remove the maximum values from their respective rows.
5. Repeat until all columns are processed.

The algorithm primarily uses a list to track the maximum values deleted in each iteration and a loop to process each row.

Code Solutions