花花酱 LeetCode 2099. 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 1: Full sorting + Hashtable

Make a copy of the original array, sort it in whole and put k largest elements in a hashtable.

Scan the original array and append the number to the answer array if it’s in the hashtable.

Time complexity: O(nlogn)
Space complexity: O(n)

Solution 2: k-th element

Use quick select / partial sort to find the k-th largest element of the array. Any number greater than that must be in the sequence. The tricky part is: what about the pivot itself? We couldn’t include ’em all blindly. Need to figure out how many copies of the pivot is there in the k largest and only include as many as of that in the final answer.

Time complexity: O(n+k)
Space complexity: O(n)