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Last Stone Weight

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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, and
  • 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

Smash 8 and 7 to get 1. Then 4 and 2 to get 2. Then 2 and 1 to get 1. Then 1 and 1 to get 0. Last stone is 1.

Example 2
Input
stones = [1]
Output
1

There is only one stone, so it is the last remaining stone.

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

Both stones have equal weight. Smashing them destroys both, leaving no stones. Return 0.

Constraints

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

Optimal complexity

Time

O(n log n)

Space

O(n)

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