Leetcode #2382: Maximum Segment Sum After Removals
In this guide, we solve Leetcode #2382 Maximum Segment Sum After Removals in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Union Find, Array, Ordered Set, Prefix Sum
Intuition
We need to merge components and check connectivity efficiently.
Union-Find supports near-constant-time merges and finds.
Approach
Initialize each node as its own parent and union pairs as you scan.
Use path compression to keep operations fast.
Steps:
- Initialize parent arrays.
- Union related nodes.
- Use find to check connectivity.
Example
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].
Python Solution
class Solution:
def maximumSegmentSum(self, nums: List[int], removeQueries: List[int]) -> List[int]:
def find(x):
if p[x] != x:
p[x] = find(p[x])
return p[x]
def merge(a, b):
pa, pb = find(a), find(b)
p[pa] = pb
s[pb] += s[pa]
n = len(nums)
p = list(range(n))
s = [0] * n
ans = [0] * n
mx = 0
for j in range(n - 1, 0, -1):
i = removeQueries[j]
s[i] = nums[i]
if i and s[find(i - 1)]:
merge(i, i - 1)
if i < n - 1 and s[find(i + 1)]:
merge(i, i + 1)
mx = max(mx, s[find(i)])
ans[j - 1] = mx
return ans
Complexity
The time complexity is Near O(n) (amortized). The space complexity is O(n).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.