Last Stone Weight II

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 any two stones and smash them together. Suppose the 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 smallest possible weight of the left stone. If there are no stones left, return 0.

Example 1:

Input: stones = [2,4,1,5,6,3]

Output: 1

Explanation:

1. We smash 2 and 1 which makes the array [1,4,5,6,3]
2. We smash 4 and 3 which makes the array [1,1,5,6]
3. We smash 5 and 6 which makes the array [1,1,1]
4. We smash 1 and 1 which makes the array [1]

Example 2:

Input: stones = [4,4,1,7,10]

Output: 2

Constraints:

• 1 <= stones.length <= 30
• 1 <= stones[i] <= 100

Topics

Array Dynamic Programming

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