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:
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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.
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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.
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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.