Handling Sum Queries After Update

Problem Description

You are given two 0-indexed arrays nums1 and nums2 and a 2D array queries of queries. There are three types of queries:

1. For a query of type 1, queries[i] = [1, l, r]. Flip the values from 0 to 1 and from 1 to 0 in nums1 from index l to index r. Both l and r are 0-indexed.
2. For a query of type 2, queries[i] = [2, p, 0]. For every index 0 <= i < n, set nums2[i] = nums2[i] + nums1[i] * p.
3. For a query of type 3, queries[i] = [3, 0, 0]. Find the sum of the elements in nums2.

Return an array containing all the answers to the third type queries.

Key Insights

• The problem involves manipulating binary values in nums1 and performing arithmetic operations on nums2 based on these manipulations.
• Efficient handling of the flip operation is crucial since it can be performed multiple times in a potentially large array.
• The cumulative updates to nums2 require a method to efficiently apply changes without direct iteration over potentially large datasets, especially under high query volumes.

Space and Time Complexity

Time Complexity: O(n + q) where n is the length of nums1/nums2 and q is the number of queries. Each type of query can be processed in constant time after the initial setup. Space Complexity: O(n) for storing the updated values in nums2.

Solution

To solve the problem, we can use a straightforward approach that processes each query in order. We handle the flip operation by iterating through the specified range and toggling the values in nums1. For the update operation on nums2, we calculate the contributions based on the current state of nums1. The sum query simply computes the total of nums2 when requested.

1. For type 1 queries, iterate over the range [l, r] in nums1 and flip each value.
2. For type 2 queries, iterate through nums1, multiplying each value by p and adding it to the respective index in nums2.
3. For type 3 queries, compute the sum of all elements in nums2 and store the result for later retrieval.

This approach ensures that we handle each query directly and maintain clarity in how the arrays are manipulated.

Code Solutions