Pinpointing questions based solely on the problem description can be difficult. Therefore, it is important to delve deeper into the characteristics of the problem. When using the two heaps approach to solve a problem, it is important to carefully consider the problem's characteristics. Typically, if we need to extract two sets of values from the data to obtain the answer, we will use two heaps—a min heap and a max heap to extract the smallest and largest elements. It is worth noting that new values may be added to the data randomly. Let's explore a few questions to build our intuition.
- PRO - Promotion
- This problem involves finding the minimum and maximum values in a set of numbers. In the context of the problem, every day of a promotion brings in new sales, and at the end of each day, the receipts with the largest and smallest sums are chosen from a ballot box. They are only used once and need to be discarded once used.
- IPO | Solution
- The problem is to find the k most valuable projects that maximize profit while minimizing capital investment before an IPO. At each stage, we want to choose the project that costs the least but yields the most profit. To achieve this, we start by creating a min heap with all the capital values. This brings the least capital-intensive projects to the top. We need to ensure that, at each iteration of k, the projects we choose meet the available capital. We add all the items that meet our capital requirements to a max-heap—called the profit heap, where we use the profit to determine the order. At each iteration of k, the profit heap will contain feasible projects given the capital constraints, and we will select the most profitable one using a max heap. We add that project to our available capital. If, at any time, we have projects that exceed our available capital requirement, we break the loop.
- Sliding window median | Solution
- Similar to Median of a data Stream, instead using lazy delete method to delete the items form the heap when moving the window.
- It is better to use tree sets or ordered sets, but this problem can also be solved with the two heaps solution to clear the idea for similar questions.
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