花花酱 LeetCode 2918. Minimum Equal Sum of Two Arrays After Replacing Zeros

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.

Example 1:

Input: nums1 = [3,2,0,1,0], nums2 = [6,5,0]
Output: 12
Explanation: We can replace 0's in the following way:
- Replace the two 0's in nums1 with the values 2 and 4. The resulting array is nums1 = [3,2,2,1,4].
- Replace the 0 in nums2 with the value 1. The resulting array is nums2 = [6,5,1].
Both arrays have an equal sum of 12. It can be shown that it is the minimum sum we can obtain.

Example 2:

Input: nums1 = [2,0,2,0], nums2 = [1,4]
Output: -1
Explanation: It is impossible to make the sum of both arrays equal.

Constraints:

• 1 <= nums1.length, nums2.length <= 105
• 0 <= nums1[i], nums2[i] <= 106

Solution: A few cases

Calculate the sum of number of zeros of each array as (s1, z1), (s2, z2). There are a few cases:

1. z1 == z2 == 0, there is no way to change, just check s1 == s2.
2. z1 == 0, z1 != 0 or z2 == 0, z1 != 0. Need to at least increase the sum by number of zeros, check s1 + z1 <= s2 / s2 + z2 <= s1
3. z1 != 0, z2 != 0, the min sum is max(s1 + z1, s2 + z2)

Time complexity: O(n)
Space complexity: O(1)