Introduction

In this blog post, we will explore how to solve the LeetCode problem "2382" 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 two 0-indexed integer arrays nums and removeQueries, both of length n. For the ith query, the element in nums at the index removeQueries[i] is removed, splitting nums into different segments. A segment is a contiguous sequence of positive integers in nums. A segment sum is the sum of every element in a segment. Return an integer array answer, of length n, where answer[i] is the maximum segment sum after applying the ith removal. Note: The same index will not be removed more than once. Example 1: Input: nums = [1,2,5,6,1], removeQueries = [0,3,2,4,1] Output: [14,7,2,2,0] Explanation: Using 0 to indicate a removed element, the answer is as follows: Query 1: Remove the 0th element, nums becomes [0,2,5,6,1] and the maximum segment sum is 14 for segment [2,5,6,1]. Query 2: Remove the 3rd element, nums becomes [0,2,5,0,1] and the maximum segment sum is 7 for segment [2,5]. Query 3: Remove the 2nd element, nums becomes [0,2,0,0,1] and the maximum segment sum is 2 for segment [2]. Query 4: Remove the 4th element, nums becomes [0,2,0,0,0] and the maximum segment sum is 2 for segment [2]. Query 5: Remove the 1st element, nums becomes [0,0,0,0,0] and the maximum segment sum is 0, since there are no segments. Finally, we return [14,7,2,2,0]. Example 2: Input: nums = [3,2,11,1], removeQueries = [3,2,1,0] Output: [16,5,3,0] Explanation: Using 0 to indicate a removed element, the answer is as follows: Query 1: Remove the 3rd element, nums becomes [3,2,11,0] and the maximum segment sum is 16 for segment [3,2,11]. Query 2: Remove the 2nd element, nums becomes [3,2,0,0] and the maximum segment sum is 5 for segment [3,2]. Query 3: Remove the 1st element, nums becomes [3,0,0,0] and the maximum segment sum is 3 for segment [3]. Query 4: Remove the 0th element, nums becomes [0,0,0,0] and the maximum segment sum is 0, since there are no segments. Finally, we return [16,5,3,0]. Constraints: n == nums.length == removeQueries.length 1 <= n <= 105 1 <= nums[i] <= 109 0 <= removeQueries[i] < n All the values of removeQueries are unique.

Explanation

Here's a breakdown of the solution:

• Disjoint Set Union (DSU): The core idea is to use DSU to efficiently track the segments after each removal. Each index in nums is a node in the DSU. Initially, all nodes are separate. When an element is removed, we union its left and right neighbors, effectively merging the segments.

• Segment Sums: We maintain a sums array where sums[i] stores the sum of the segment represented by the root of node i. When merging segments (union operation), we update the sums accordingly.

• Maximum Segment Sum: After each removal and DSU update, we iterate through all roots (using a set to get unique roots), find their corresponding sums in sums, and determine the maximum segment sum.

• Runtime & Storage Complexity: O(n * alpha(n)) time, where alpha(n) is the inverse Ackermann function (effectively constant in practice), and O(n) space.

Code

    def maximumSegmentSum(nums, removeQueries):
    n = len(nums)
    parent = list(range(n))
    sums = nums[:]
    answer = []
    removed = [False] * n

    def find(i):
        if parent[i] == i:
            return i
        parent[i] = find(parent[i])
        return parent[i]

    def union(i, j):
        root_i = find(i)
        root_j = find(j)
        if root_i != root_j:
            parent[root_i] = root_j
            sums[root_j] += sums[root_i]

    for index in removeQueries:
        removed[index] = True
        left = index - 1
        right = index + 1

        if left >= 0 and not removed[left]:
            union(index, left)
        if right < n and not removed[right]:
            union(index, right)

        max_sum = 0
        roots = set()
        for i in range(n):
            if not removed[i]:
                root = find(i)
                roots.add(root)

        for root in roots:
            max_sum = max(max_sum, sums[root])

        answer.append(max_sum)

    return answer