Problem Description
You are given two arrays of integers nums1 and nums2, possibly of different lengths. The values in the arrays are between 1 and 6, inclusive. In one operation, you can change any integer's value in any of the arrays to any value between 1 and 6, inclusive. Return the minimum number of operations required to make the sum of values in nums1 equal to the sum of values in nums2. Return -1 if it is not possible to make the sum of the two arrays equal.
Key Insights
- The problem can be reduced to balancing the difference between the sums of the two arrays.
- If the absolute difference between the sums of the two arrays is greater than the maximum possible adjustments (i.e., the number of elements times the maximum change per element), it's impossible to equalize them.
- We can use a counting approach to track how many elements can be increased or decreased to minimize the number of operations needed.
Space and Time Complexity
Time Complexity: O(n + m), where n is the length of nums1 and m is the length of nums2. This is because we only need to traverse both arrays a couple of times. Space Complexity: O(1), as we are using a fixed amount of extra space for counting.
Solution
To solve the problem, we first calculate the sums of both arrays. We then determine the difference between these sums. Depending on whether nums1 is greater than nums2 or vice versa, we will identify how many operations are needed to adjust the sums. We utilize a counting array to keep track of how many elements can be adjusted upwards or downwards. We then calculate the minimum number of operations required by making the largest possible adjustments first.