SOLVEMORE - Editorial

Problem Link - Problem link

Problem Statement:

Chef came across a new online judge that has N problems, and decided that he wants to solve them.

Chef takes A_i consecutive minutes to solve the i-th problem, and will take a break of B_i minutes immediately after solving it.
That is, Chef will solve a problem, then take a break. Solve another problem, then take another break, and so on.

Chef has K minutes of free time. If he chooses the problems and their order optimally, what is the maximum number of problems he can solve in this time?

Note that a problem is considered solved if Chef finishes solving it by the K-th minute, even if the break time of the last problem extends past minute K. See the sample tests below for an example.

Approach:

The code solves the problem by calculating the total time Chef needs to solve and take breaks for each problem. Each problem has two components: solving time A[i] and break time B[i] . The goal is to pick problems such that the total time spent doesn’t exceed Chef’s available free time K.

Key Points of Approach:

  1. Sorting the Problems: The problems are sorted by their total time (solving time + break time) in ascending order, prioritizing problems that take the least time.

  2. Tracking the Total Time: The algorithm iterates through the sorted problems, keeping a running total of the time. If the total time exceeds K, it adjusts by skipping a problem or part of it to fit within the available time.

  3. Final Result: The algorithm calculates the maximum number of problems Chef can solve within K minutes.

This approach ensures Chef solves as many problems as possible within the available time.

Time Complexity

The time complexity is O(NlogN), where N is the number of problems, due to sorting the problems.

Space Complexity:

The space complexity is O(N), where N is the number of problems, due to storing the problems and their times.