2389. Longest Subsequence With Limited Sum

Description

You are given an integer array nums of length n, and an integer array queries of length m.

Return an array answer of length m where answer[i] is the maximum size of a subsequence that you can take from nums such that the sum of its elements is less than or equal to queries[i].

A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

Example 1:

Input: nums = [4,5,2,1], queries = [3,10,21]
Output: [2,3,4]
Explanation: We answer the queries as follows:
- The subsequence [2,1] has a sum less than or equal to 3. It can be proven that 2 is the maximum size of such a subsequence, so answer[0] = 2.
- The subsequence [4,5,1] has a sum less than or equal to 10. It can be proven that 3 is the maximum size of such a subsequence, so answer[1] = 3.
- The subsequence [4,5,2,1] has a sum less than or equal to 21. It can be proven that 4 is the maximum size of such a subsequence, so answer[2] = 4.

Example 2:

Input: nums = [2,3,4,5], queries = [1]
Output: [0]
Explanation: The empty subsequence is the only subsequence that has a sum less than or equal to 1, so answer[0] = 0.

Constraints:

n == nums.length
m == queries.length
1 <= n, m <= 1000
1 <= nums[i], queries[i] <= 10⁶

Solution

longest-subsequence-with-limited-sum.py

class Solution:
    def answerQueries(self, nums: List[int], queries: List[int]) -> List[int]:
        n = len(nums)
        nums.sort()
        res = []
        prefix = list(accumulate(nums, initial = 0))

        for q in queries:
            index = bisect_right(prefix, q) - 1
            res.append(index)

        return res