LeetCode 2099: Find Subsequence of Length K With the Largest Sum Solution

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2099. Find Subsequence of Length K With the Largest Sum

Easy

Array Hash Table Sorting Heap (Priority Queue)

Problem Explanation

Explanation

To find a subsequence of length k with the largest sum in the given array, we can use a sliding window approach. We can maintain a window of size k and slide it through the array while keeping track of the maximum sum subsequence found so far. At each step, we update the window sum by adding the next element and subtracting the element that falls out of the window. We continue this process until we reach the end of the array, and the window with the largest sum will be our result.

Algorithm:

Initialize variables: sum = 0, maxSum = Integer.MIN_VALUE, maxIdx = 0.
Calculate the initial sum of the first k elements.
Iterate from k to the end of the array:
- Update the sum by adding the current element and subtracting the element that fell out of the window.
- If the current sum is greater than maxSum, update maxSum and the starting index of the subsequence.
Return the subsequence starting from maxIdx to maxIdx + k.

Time Complexity: O(n) where n is the length of the input array nums. Space Complexity: O(1)

Solution Code

class Solution {
    public int[] maxSubsequence(int[] nums, int k) {
        int sum = 0;
        int maxSum = Integer.MIN_VALUE;
        int maxIdx = 0;
        
        for (int i = 0; i < k; i++) {
            sum += nums[i];
        }
        
        for (int i = k; i < nums.length; i++) {
            sum = sum + nums[i] - nums[i - k];
            if (sum > maxSum) {
                maxSum = sum;
                maxIdx = i - k + 1;
            }
        }
        
        int[] result = new int[k];
        for (int i = 0; i < k; i++) {
            result[i] = nums[maxIdx + i];
        }
        
        return result;
    }
}

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