Minimum Range Update Operations

You are given two integer arrays source and target of equal length n. In a single operation you may perform either of the following on source:

1. Pick a prefix source[0..i] and add 1 to every element in it.
2. Pick a suffix source[i..n-1] and add 1 to every element in it.

Return the minimum number of operations required to transform source into target. If it is impossible, return -1.

Examples:

source = [1, 1, 1, 1, 1] target = [3, 4, 5, 4, 3] result = 4 -> +1 on prefix[0..4] -> [2,2,2,2,2] -> +1 on prefix[0..2] -> [3,3,3,2,2] -> +1 on prefix[0..1]+suffix[3..4] requires 2 ops, etc.

Key observation: the cost is the sum of positive differences in the derivative d[i] = target[i] - source[i] - (target[i-1] - source[i-1]). If any target[i] < source[i], the answer is -1 because the operations can only add.

Follow-up Questions:

• What if you were allowed to subtract from prefixes/suffixes as well?
• What if the operation could be applied to any contiguous range, not just prefixes/suffixes?