# Leetcode 1049 - 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 = [2,7,4,1,8,1] |

`Note:`

- This is a
`01 knapsack`

problem.- The capacity of our bag is
`half`

of the total weight.

- The capacity of our bag is
- The DP formula is
`DP[j] = max(DP[j], DP[j - stones[i]] + stones[i])`

. - Iterate stones first, then the bag.
- The inner loop must be in
`descending`

order.

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