Find Subsequence of Length K With the Largest Sum

You are given an integer array nums and an integer k. You want to find a subsequence of nums of length k that has the largest sum.

Return any such subsequence as an integer array of length k.

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 = [2,1,3,3], k = 2
Output: [3,3]
Explanation:
The subsequence has the largest sum of 3 + 3 = 6.

Example 2:

Input: nums = [-1,-2,3,4], k = 3
Output: [-1,3,4]
Explanation: 
The subsequence has the largest sum of -1 + 3 + 4 = 6.

Example 3:

Input: nums = [3,4,3,3], k = 2
Output: [3,4]
Explanation:
The subsequence has the largest sum of 3 + 4 = 7. 
Another possible subsequence is [4, 3].

 

Constraints:

  • 1 <= nums.length <= 1000
  • -105 <= nums[i] <= 105
  • 1 <= k <= nums.length
SOLUTION:
import heapq

class Solution:
    def maxSubsequence(self, nums: List[int], k: int) -> List[int]:
        heap = []
        valIndexes = {}
        for i, num in enumerate(nums):
            if num not in valIndexes:
                heapq.heappush(heap, num)
            valIndexes[num] = valIndexes.get(num, []) + [i]
        op = []
        rest = k
        biggest = heapq.nlargest(k, heap)
        while rest > 0:
            indexes = valIndexes[biggest.pop(0)]
            for index in indexes:
                heapq.heappush(op, index)
                rest -= 1
                if rest == 0:
                    break
        return [nums[i] for i in heapq.nsmallest(k, op)]

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