Maximize Points by Deleting Values and Their Neighbors

Problem Statement

You are given an integer array nums. In one operation, you can pick any element with value x, add x to your total score, and remove it from the array. However, doing so immediately deletes all occurrences of x - 1 and x + 1 from the array without earning any points for them.

You can repeat this operation until the array is empty.

Return the maximum number of points you can achieve. Note that values in nums can be very large and sparse, so your solution must be efficient with respect to both time and space.

Interface

def max_points(nums: list[int]) -> int:
    pass

Input & Output Format

• Input: nums, a list of non-negative integers.
• Output: An integer representing the maximum possible score.

Constraints

• 1 <= len(nums) <= 10^5
• 1 <= nums[i] <= 10^9

Examples

Example 1

Input: nums = [3, 4, 2]
Output: 6
Explanation:
- Pick 4: score = 4. Deletes 3.
- Remaining elements: [2].
- Pick 2: score = 4 + 2 = 6.
Total score = 6.

Example 2

Input: nums = [2, 2, 3, 3, 3, 4]
Output: 9
Explanation:
- Pick all 3s (total 3 * 3 = 9 points). This deletes all 2s and 4s.
Alternatively, picking all 2s (4 pts) and all 4s (4 pts) gives 8 points.
The maximum possible score is 9.

Edge Cases

• A single element array (e.g., [5] returns 5).
• Arrays where elements are far apart (e.g., [1, 1000000000]), where picking one does not affect the other.
• Arrays with many duplicates of the same number.