Maximum Sum Queries

Problem Description

You are given two 0-indexed integer arrays nums1 and nums2, each of length n, and a 1-indexed 2D array queries where queries[i] = [x_i, y_i]. For the i-th query, find the maximum value of nums1[j] + nums2[j] among all indices j (0 <= j < n), where nums1[j] >= x_i and nums2[j] >= y_i, or -1 if there is no j satisfying the constraints. Return an array answer where answer[i] is the answer to the i-th query.

Key Insights

• We need to efficiently find the maximum sum of nums1[j] + nums2[j] that meets the conditions specified in each query.
• Sorting the combined values of nums1 and nums2 can facilitate quicker searching for valid indices.
• The problem can be approached using binary search to efficiently handle the constraints of each query.

Space and Time Complexity

Time Complexity: O(n log n + q log n), where n is the length of nums1/nums2 and q is the number of queries. The sorting takes O(n log n) and each query can be processed in O(log n) using binary search. Space Complexity: O(n), for storing the combined values and sorted indices.

Solution

To solve the problem, we can follow these steps:

1. Create a combined array of tuples containing values from nums1 and nums2 along with their indices.
2. Sort this combined array based on the values of nums1 and nums2.
3. For each query, use binary search to find the starting point where nums1 and nums2 meet the conditions x_i and y_i.
4. Track the maximum sum of nums1[j] + nums2[j] while iterating through valid indices.

Code Solutions