LeetCode 1048. Longest String Chain

最长单词链算法解析

最新推荐文章于 2022-07-05 04:26:29 发布

原创最新推荐文章于 2022-07-05 04:26:29 发布 · 334 阅读

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本文深入探讨了在给定单词列表中寻找最长单词链的问题，通过两种不同算法的对比，详细解析了基于长度的动态规划解决方案，附带Python实现代码。

Given a list of words, each word consists of English lowercase letters.

Let's say word1 is a predecessor of word2 if and only if we can add exactly one letter anywhere in word1 to make it equal to word2. For example, "abc" is a predecessor of "abac".

A word chain is a sequence of words [word_1, word_2, ..., word_k] with k >= 1, where word_1 is a predecessor of word_2, word_2 is a predecessor of word_3, and so on.

Return the longest possible length of a word chain with words chosen from the given list of words.

Example 1:

Input: ["a","b","ba","bca","bda","bdca"]
Output: 4
Explanation: one of the longest word chain is "a","ba","bda","bdca".

Note:

1 <= words.length <= 1000
1 <= words[i].length <= 16
words[i] only consists of English lowercase letters.

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非常好的一道题目，直接想到的是DFS，假设存在n个单词，每个单词平均长度是l，那么没两个单词判断是不是前驱需要的复杂度是O(l)，总体加上记忆化搜索的复杂度是O(n^2*l)，当然n^2可以优化，但是优化到多少不好说，而且优化剪枝写起来非常烦躁，得根据长度进行预处理，又浪费了不少空间。

另外一种思路是从长度入手，每个词可能的前驱规模是O(l)，如果某个前驱的个数知道，那么可以直接递推求最大值就好。求某个词所有前驱的复杂度是O(l^2)，所以整体的复杂度是O(n*l^2)，当然需要预先排序，在n>>l的情况下，显然这种思路更好，以下是代码：

class Solution:
    def longestStrChain(self, words):
        words.sort(key=lambda x:len(x))
        dp = {}
        for word in words:
            dp[word] = max(dp[word[:i]+word[i+1:]]+1 if word[:i]+word[i+1:] in dp else 0 for i in range(len(word)))
        return max(dp.values())
s = Solution()
print(s.longestStrChain(["a","b","ba","bca","bda","bdca"]))