Compute Score Difference in Reversing Array Game

Problem Statement

You are playing a game with an array of integers nums. You and an opponent take turns removing elements from the front of the array. The game proceeds as follows:

1. You go first. You remove the first element of the current array and add its value to your total score.
2. After each turn, if the element removed was even, the remaining elements in the array are reversed.
3. The game continues until the array is empty. The opponent removes the next element on their turn and adds it to their score.

Write a function calculate_score_difference(nums) that returns the difference between your total score and your opponent's total score (i.e., your_score - opponent_score).

Function Signature

def calculate_score_difference(nums: List[int]) -> int:

Constraints

• 0 <= len(nums) <= 10^4
• 0 <= nums[i] <= 10^6

Examples

Example 1: Input: nums = [1, 2, 3]

• Turn 1 (You): Remove 1. Score: 1. Array: [2, 3] (Odd, no reverse).
• Turn 2 (Opponent): Remove 2. Score: 2. Array: [3] (Even, reverse [3] -> [3]).
• Turn 3 (You): Remove 3. Score: 1+3=4. Array: []. Result: 4 - 2 = 2.

Example 2: Input: nums = [2, 4, 6]

• Turn 1 (You): Remove 2. Score: 2. Array: [4, 6] -> reversed [6, 4] (Even, reverse).
• Turn 2 (Opponent): Remove 6. Score: 6. Array: [4] (Even, reverse [4] -> [4]).
• Turn 3 (You): Remove 4. Score: 2+4=6. Array: []. Result: 6 - 6 = 0.