Last Stone Weight

Last Stone Weight

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. The result of this smash is:

• 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.

Examples

Example 1:

Input: stones = [2, 7, 4, 1, 8, 1]
Output: 1
Explanation:
  Smash 8 and 7 -> 1, stones = [2, 4, 1, 1, 1]
  Smash 4 and 2 -> 2, stones = [1, 1, 2, 1]
  Smash 2 and 1 -> 1, stones = [1, 1, 1]
  Smash 1 and 1 -> 0, stones = [1]
  Return 1

Example 2:

Input: stones = [1]
Output: 1

Example 3:

Input: stones = [3, 3]
Output: 0

Constraints

• 1 <= stones.length <= 30
• 1 <= stones[i] <= 1000

Expected Complexity

• Time: O(n log n)
• Space: O(n)