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Problem 5: Kinetic Attrition

Problem Statement

You are given an array of integers stones where stones[i] is the weight of the ith stone. We are playing a game with the stones. On each turn, we choose the heaviest two stones and smash them together. Suppose the heaviest two stones have weights x and y with x <= y.

  • If x == y, both stones are destroyed.
  • If x != y, the stone of weight x is destroyed, and the stone of weight y has new weight y - x. At the end of the game, there is at most one stone left. Return the weight of the last remaining stone. If there are no stones left, return 0.

Input Format

  • An array of integers stones.

Example

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