查看“Matrix chain multiplication”的源代码

[[Category:刷题]]
[[Category:动态规划]]
矩阵链乘法，找出进行操作最少的加括号方式。使用动态规划求解，利用分治的思想。

对于乘法 ''ABCD''，取 ''A''(''BCD''), (''AB'')(''CD''), (''ABC'')''D'' 三种情况的最小值，子问题递归求解。

<ref>https://www.geeksforgeeks.org/matrix-chain-multiplication-dp-8/</ref>

== 相关题目 ==

=== [https://leetcode.com/problems/burst-balloons/description/ LeetCode 312. Burst Balloons] ===

等价于一个矩阵链乘问题。<ref>https://leetcode.com/problems/burst-balloons/discuss/1450284/Classic-Matrix-Chain-Multiplication-with-a-minor-tweak.-Very-easy!!-(C%2B%2B)</ref>

<syntaxhighlight lang=python>
from functools import cache


def maxCoins(self, nums: List[int]) -> int:
    nums.insert(0, 1)
    nums.append(1)

    @cache
    def rec(left, right):
        if left >= right:
            return 0
        return max((rec(left, i) + rec(i + 1, right) + nums[left - 1] * nums[i] * nums[right])
                   for i in range(left, right))
    return rec(1, len(nums) - 1)
</syntaxhighlight>

== 参考资料 ==

<references />