Introduction

In this blog post, we will explore how to solve the LeetCode problem "2386" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an integer array nums and a positive integer k. You can choose any subsequence of the array and sum all of its elements together. We define the K-Sum of the array as the kth largest subsequence sum that can be obtained (not necessarily distinct). Return the K-Sum of the array. 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. Note that the empty subsequence is considered to have a sum of 0. Example 1: Input: nums = [2,4,-2], k = 5 Output: 2 Explanation: All the possible subsequence sums that we can obtain are the following sorted in decreasing order: - 6, 4, 4, 2, 2, 0, 0, -2. The 5-Sum of the array is 2. Example 2: Input: nums = [1,-2,3,4,-10,12], k = 16 Output: 10 Explanation: The 16-Sum of the array is 10. Constraints: n == nums.length 1 <= n <= 105 -109 <= nums[i] <= 109 1 <= k <= min(2000, 2n)

Explanation

Here's the solution to find the K-Sum of an array:

• Separate Positive and Negative Numbers: Split the input array into positive and negative numbers. The sum of all positive numbers represents the maximum possible subsequence sum. Transform negative numbers to their absolute values.
• Min-Heap for K-th Largest: Use a min-heap to maintain the k largest subsequence sums. Initialize the heap with 0 (empty subsequence sum). Iteratively, for each absolute value of the negative numbers, add two new potential sums to the heap: one by adding the number to the current smallest sum and another by keeping the current smallest sum. Keep the heap size at most k.

• Final Result: After processing all absolute values of the negative numbers, the maximum subsequence sum minus the smallest value in the heap gives us the K-Sum.

• Runtime Complexity: O(n + m log m + k log k), where n is the length of the input array and m is number of negative numbers (after absolute transformation). Storage Complexity: O(k)

Code

    import heapq

def kSum(nums, k):
    """
    Calculates the K-Sum of an array, which is the kth largest subsequence sum.

    Args:
        nums: An integer array.
        k: A positive integer representing the kth largest subsequence sum.

    Returns:
        The K-Sum of the array.
    """

    positive_sum = 0
    negatives = []

    for num in nums:
        if num > 0:
            positive_sum += num
        else:
            negatives.append(abs(num))

    negatives.sort()  # Sorting is crucial for efficiency with heapq

    heap = [0]
    heapq.heapify(heap)

    for neg in negatives:
        new_heap = []
        for val in heap:
            heapq.heappush(new_heap, val)
            heapq.heappush(new_heap, val + neg)

        heap = heapq.nsmallest(k, new_heap)
        heapq.heapify(heap)  # Maintain heap property

    return positive_sum - heap[k - 1]