Problem Description
You are given two arrays nums1 and nums2 consisting of positive integers. You have to replace all the 0's in both arrays with strictly positive integers such that the sum of elements of both arrays becomes equal. Return the minimum equal sum you can obtain, or -1 if it is impossible.
Key Insights
- The sum of the non-zero elements in both arrays can be computed initially.
- The total number of zeros in both arrays directly affects the flexibility of achieving equal sums.
- The difference between the sums of the two arrays can be adjusted by replacing zeros with appropriate values.
- If the number of zeros is insufficient to make the sums equal, it's impossible to achieve the desired outcome.
Space and Time Complexity
Time Complexity: O(n + m), where n and m are the lengths of the two arrays. Space Complexity: O(1), since we are using a constant amount of extra space.
Solution
To solve this problem, we first calculate the sum of the non-zero elements in both arrays. Then, we determine the difference in sums. If the difference can be compensated by the total number of zeros multiplied by the minimum integer value that can replace the zeros, we can calculate the minimum equal sum. If not, we return -1. The approach uses basic arithmetic operations and requires no additional data structures.