Maximum Segment Sum After Removals

arrayunion-findprefix sum

Problem Statement

You are given two 0-indexed integer arrays nums and removeQueries , both of length n . For the i ^th 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 i ^th removal.

Note: The same index will not be removed more than once.

Examples

Example 1

Input: nums = [1,2,5,6,1], removeQueries = [0,3,2,4,1]
Output: [14,7,2,2,0]
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]
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 <= 10 ^5

1 <= nums[i] <= 10 ^9

0 <= removeQueries[i] < n

All the values of removeQueries are unique .

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicUnion-Find