Compute the Final Robot Score

Problem Statement

You are evaluating a fleet of autonomous robots undergoing combat stress testing. You are given an array of positive integers scores, where scores[i] represents the initial performance score of the i-th robot.

In each round of the simulation, the two robots with the highest scores are chosen to compete:

• Let the two highest scores be x and y, where x <= y.
• If x == y, both robots exhaust their energy and are permanently deactivated (removed from the fleet).
• If x < y, the weaker robot x is deactivated, and the stronger robot y has its score reduced to y - x before returning to the fleet.

This process repeats until at most one active robot remains. Return the score of the final remaining robot, or 0 if all robots have been deactivated.

Function Signature

def compute_final_robot_score(scores: list[int]) -> int:
    pass

Input & Output Format

• Input: A list of integers scores (1 <= len(scores) <= 10^5, 1 <= scores[i] <= 10^9).
• Output: An integer representing the final robot score, or 0 if no robots remain.

Examples

Example 1

Input: scores = [2, 7, 4, 1, 8, 1]
Output: 1

Explanation:

1. The two highest scores are 7 and 8. They clash, and a robot with score 8 - 7 = 1 remains. Pool: [2, 4, 1, 1, 1].
2. The two highest scores are 2 and 4. They clash, resulting in 4 - 2 = 2. Pool: [2, 1, 1, 1].
3. The two highest scores are 2 and 1. They clash, resulting in 2 - 1 = 1. Pool: [1, 1, 1].
4. The two highest scores are 1 and 1. Both are deactivated. Pool: [1].
5. Only one robot remains with score 1.

Example 2

Input: scores = [5, 5]
Output: 0

Explanation: Both robots have score 5. They destroy each other, leaving 0 robots.

Constraints & Edge Cases

• 1 <= len(scores) <= 10^5
• 1 <= scores[i] <= 10^9
• Edge cases to consider:
  • Single element array (len(scores) == 1): return the element immediately.
  • All scores are equal and len(scores) is even: all robots cancel out, returning 0.
  • Large values up to 10^9: ensure integer comparisons do not overflow in fixed-width languages.