Maximize distinct values after unique ± offsets

Problem Statement

You are given an array of integers nums and a set of distinct integer offsets offsets. You must assign exactly one value from offsets to each element in nums such that the resulting array transformed has the maximum possible number of distinct values.

Specifically, for each index i from 0 to n-1, you choose an offset k from offsets and define transformed[i] = nums[i] + k. Note that you cannot use the same offset index for multiple positions; however, the problem states you have an infinite supply of the values in offsets to choose from for each position. Wait—to clarify: you may pick any k from offsets for each nums[i] independently. The goal is to maximize the number of unique values in the resulting array.

Function Signature

def max_distinct_values(nums: List[int], offsets: List[int]) -> int:

Constraints

• 1 <= len(nums) <= 10^5
• 1 <= len(offsets) <= 100
• -10^9 <= nums[i], offsets[i] <= 10^9

Examples

Example 1: Input: nums = [1, 2, 3], offsets = [0, 10] Output: 3 Explanation: We can choose 1+0=1, 2+10=12, 3+0=3. The set is {1, 12, 3}, size 3.

Example 2: Input: nums = [1, 1, 1], offsets = [0, 1] Output: 2 Explanation: We can choose 1+0=1 and 1+1=2. The set is {1, 2}.