maximum subsequence score leetcode 2542 python

certainly! the "maximum subsequence score" problem is a well-known problem on leetcode (problem 2542). in this problem, you are given two lists of integers, `nums1` and `nums2`, both of the same length `n`. the goal is to select a subsequence from these lists that maximizes the score defined as the sum of the selected elements from `nums1` multiplied by the minimum of the selected elements from `nums2`.

problem statement

you need to maximize the score defined as:
\[ \text{score} = \text{sum of selected elements from } nums1 \times \text{min of selected elements from } nums2 \]

example

for example, given:

the maximum score can be obtained by selecting the elements from `nums1` corresponding to the largest values in `nums2`.

steps to solve the problem

1. **pair the arrays**: create pairs of values from `nums1` and `nums2`.
2. **sort by the second array**: sort these pairs based on the values from `nums2` in descending order. this will allow us to consider the largest possible minimums first.
3. **use a max heap**: as we iterate through the sorted pairs, we can use a max heap (or a priority queue) to keep track of the elements from `nums1` that we can select. this helps in maintaining the sum of the selected elements efficiently.
4. **calculate the score**: for each element from `nums2`, calculate the score based on the current minimum and the sum of the selected elements.

implementation

here is how you can implement this in python:

explanation of the code

1. **pairing and sorting**: we create pairs of `nums1[i]` and `nums2[i]` and sort them based on the values in `nums2` in descending order.
2. **using a heap**: we maintain a heap to keep track of the largest `k` elements from `nums1`.
3. **calculating scores**: we check if we have exactly `k` elements in our heap, and if so, we compute the score and keep track of the maximum score found.

complexity analysis

- **time complexity**: the sorting step takes \(o(n \log n)\), and maintaining the heap ta ...

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maximum subsequence score
LeetCode 2542
Python
dynamic programming
array manipulation
two pointers
sliding window
greedy algorithm
optimal substructure
subsequence
score calculation
algorithm efficiency
problem solving
coding interview
complexity analysis