Last Stone Weight II — LeetCode 1049 Python Solution

The problem

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.

Example

Input

stones = [2,7,4,1,8,1]

Output

1

Explanation

We can combine 2 and 4 to get 2, so the array converts to [2,7,1,8,1] then,

Python solution

class Solution:
    def lastStoneWeightII(self, stones: List[int]) -> int:
        s = sum(stones)
        m, n = len(stones), s >> 1
        dp = [[0] * (n + 1) for _ in range(m + 1)]
        for i in range(1, m + 1):
            for j in range(n + 1):
                dp[i][j] = dp[i - 1][j]
                if stones[i - 1] <= j:
                    dp[i][j] = max(
                        dp[i][j], dp[i - 1][j - stones[i - 1]] + stones[i - 1]
                    )
        return s - 2 * dp[-1][-1]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1049. Last Stone Weight II is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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