Formatted question description: https://leetcode.ca/all/2099.html

2099. Find Subsequence of Length K With the Largest Sum (Easy)

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

Similar Questions:

Solution 1. Sorting

  • // OJ: https://leetcode.com/problems/find-subsequence-of-length-k-with-the-largest-sum/
    // Time: O(NlogN)
    // Space: O(N)
    class Solution {
    public:
        vector<int> maxSubsequence(vector<int>& A, int k) {
            vector<int> id(A.size());
            iota(begin(id), end(id), 0); // Index array 0, 1, 2, ...
            sort(begin(id), end(id), [&](int a, int b) { return A[a] > A[b]; }); // Sort the indexes in descending order of their corresponding values in `A`
            id.resize(k); // Only keep the first `k` indexes with the greatest `A` values
            sort(begin(id), end(id)); // Sort indexes in ascending order
            vector<int> ans;
            for (int i : id) ans.push_back(A[i]);
            return ans;
        }
    };
    
  • // Todo
    
  • # 2099. Find Subsequence of Length K With the Largest Sum
    # https://leetcode.com/problems/find-subsequence-of-length-k-with-the-largest-sum/
    
    class Solution:
        def maxSubsequence(self, nums: List[int], k: int) -> List[int]:
            res = set(list(range(k)))
            heap = [(x, i) for i, x in enumerate(nums[:k])]
            heapq.heapify(heap) 
    
            for i, x in enumerate(nums[k:], k):
                res.add(i)
                value, index = heapq.heappushpop(heap, (x, i))
                res.remove(index)
                
            
            return [nums[i] for i in sorted(list(res))]
    
    

Solution 2. Quick Select

  • // OJ: https://leetcode.com/problems/find-subsequence-of-length-k-with-the-largest-sum/
    // Time: O(N + KlogK) on average, O(N^2 + KlogK) in the worst case
    // Space: O(N)
    class Solution {
    public:
        vector<int> maxSubsequence(vector<int>& A, int k) {
            vector<int> id(A.size());
            iota(begin(id), end(id), 0);
            nth_element(begin(id), begin(id) + k, end(id), [&](int a, int b) { return A[a] > A[b]; });
            id.resize(k);
            sort(begin(id), end(id));
            vector<int> ans;
            for (int i : id) ans.push_back(A[i]);
            return ans;
        }
    };
    
  • // Todo
    
  • # 2099. Find Subsequence of Length K With the Largest Sum
    # https://leetcode.com/problems/find-subsequence-of-length-k-with-the-largest-sum/
    
    class Solution:
        def maxSubsequence(self, nums: List[int], k: int) -> List[int]:
            res = set(list(range(k)))
            heap = [(x, i) for i, x in enumerate(nums[:k])]
            heapq.heapify(heap) 
    
            for i, x in enumerate(nums[k:], k):
                res.add(i)
                value, index = heapq.heappushpop(heap, (x, i))
                res.remove(index)
                
            
            return [nums[i] for i in sorted(list(res))]
    
    

Solution 3. Quick Select

  • // OJ: https://leetcode.com/problems/find-subsequence-of-length-k-with-the-largest-sum/
    // Time: O(N) on average, O(N^2) in the worst case
    // Space: O(N)
    class Solution {
    public:
        vector<int> maxSubsequence(vector<int>& A, int k) {
            if (k == A.size()) return A;
            vector<int> v(begin(A), end(A)), ans;
            nth_element(begin(v), begin(v) + k - 1, end(v), greater<>());
            int cnt = count(begin(v), begin(v) + k, v[k - 1]);
            for (int i = 0; i < A.size(); ++i) {
                if (A[i] > v[k - 1] || (A[i] == v[k - 1] && --cnt >= 0)) ans.push_back(A[i]);
            }
            return ans;
        }
    };
    
  • // Todo
    
  • # 2099. Find Subsequence of Length K With the Largest Sum
    # https://leetcode.com/problems/find-subsequence-of-length-k-with-the-largest-sum/
    
    class Solution:
        def maxSubsequence(self, nums: List[int], k: int) -> List[int]:
            res = set(list(range(k)))
            heap = [(x, i) for i, x in enumerate(nums[:k])]
            heapq.heapify(heap) 
    
            for i, x in enumerate(nums[k:], k):
                res.add(i)
                value, index = heapq.heappushpop(heap, (x, i))
                res.remove(index)
                
            
            return [nums[i] for i in sorted(list(res))]
    
    

Discuss

https://leetcode.com/problems/find-subsequence-of-length-k-with-the-largest-sum/discuss/1623427/C%2B%2B-Sorting-or-Quick-Select

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