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Problem: Last Stone Weight

Explore how to solve the Last Stone Weight problem by implementing a max heap using Java's PriorityQueue with a reverse order comparator. Understand how to repeatedly smash the two heaviest stones and manage heap operations effectively, gaining insights into heap-based problem-solving and algorithmic efficiency.

Statement

You are given an integer array stones, where each element stones[i] represents the weight of the ithi^{th} stone.

A game is played with these stones. In each turn, the two heaviest stones are selected and smashed together. Let the weights of these two stones be x and y, where x \leq y. The outcome of the smash is as follows:

  • If x == y, both stones are completely destroyed.

  • If x \neq y, the stone of weight x is destroyed, and the stone of weight y is reduced to a new weight of y ...