题目链接

思路

数学推导

代码实现

• dp

class Solution:
    def cuttingRope(self, n: int) -> int:
        dp = [0 for _ in range(n+1)]
        dp[2] = 1
        for i in range(3, n+1):
            for j in range(1, i):
                dp[i] = max(dp[i], max((i-j)*j, j*dp[i-j]))
        return dp[-1]

• dp优化

class Solution:
    def cuttingRope(self, n: int) -> int:
        dp = [0, 1, 1]
        for i in range(3, n+1):
            dp[i % 3] = max(max(dp[(i-1)%3], i-1),
                            2 * max(dp[(i-2)%3], i-2),
                            3 * max(dp[(i-3)%3], i-3),
                        )
        return dp[n%3]