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1048. 最长字符串链

English Version

题目描述

给出一个单词数组 words ，其中每个单词都由小写英文字母组成。

如果我们可以 不改变其他字符的顺序 ，在 wordA 的任何地方添加 恰好一个 字母使其变成 wordB ，那么我们认为 wordA 是 wordB 的 前身 。

  • 例如，"abc" 是 "abac" 的 前身 ，而 "cba" 不是 "bcad" 的 前身

词链是单词 [word_1, word_2, ..., word_k] 组成的序列，k >= 1，其中 word1 是 word2 的前身，word2 是 word3 的前身，依此类推。一个单词通常是 k == 1 的 单词链 。

从给定单词列表 words 中选择单词组成词链，返回 词链的 最长可能长度 。
 

示例 1：

输入：words = ["a","b","ba","bca","bda","bdca"]
输出：4
解释：最长单词链之一为 ["a","ba","bda","bdca"]

示例 2:

输入：words = ["xbc","pcxbcf","xb","cxbc","pcxbc"]
输出：5
解释：所有的单词都可以放入单词链 ["xb", "xbc", "cxbc", "pcxbc", "pcxbcf"].

示例 3:

输入：words = ["abcd","dbqca"]
输出：1
解释：字链["abcd"]是最长的字链之一。
["abcd"，"dbqca"]不是一个有效的单词链，因为字母的顺序被改变了。

 

提示：

  • 1 <= words.length <= 1000
  • 1 <= words[i].length <= 16
  • words[i] 仅由小写英文字母组成。

解法

先按字符串长度升序排列，再利用动态规划或者哈希表求解。

Python3

动态规划：

class Solution:
    def longestStrChain(self, words: List[str]) -> int:
        def check(w1, w2):
            if len(w2) - len(w1) != 1:
                return False
            i = j = cnt = 0
            while i < len(w1) and j < len(w2):
                if w1[i] != w2[j]:
                    cnt += 1
                else:
                    i += 1
                j += 1
            return cnt < 2 and i == len(w1)

        n = len(words)
        dp = [1] * (n + 1)
        words.sort(key= lambda x: len(x))
        res = 1
        for i in range(1, n):
            for j in range(i):
                if check(words[j], words[i]):
                    dp[i] = max(dp[i], dp[j] + 1)
            res = max(res, dp[i])
        return res

哈希表：

class Solution:
    def longestStrChain(self, words: List[str]) -> int:
        words.sort(key= lambda x: len(x))
        res = 0
        mp = {}
        for word in words:
            x = 1
            for i in range(len(word)):
                pre = word[:i] + word[i + 1:]
                x = max(x, mp.get(pre, 0) + 1)
            mp[word] = x
            res = max(res, x)
        return res

Java

哈希表：

class Solution {
    public int longestStrChain(String[] words) {
        Arrays.sort(words, Comparator.comparingInt(String::length));
        int res = 0;
        Map<String, Integer> map = new HashMap<>();
        for (String word : words) {
            int x = 1;
            for (int i = 0; i < word.length(); ++i) {
                String pre = word.substring(0, i) + word.substring(i + 1);
                x = Math.max(x, map.getOrDefault(pre, 0) + 1);
            }
            map.put(word, x);
            res = Math.max(res, x);
        }
        return res;
    }
}

TypeScript

function longestStrChain(words: string[]): number {
    words.sort((a, b) => a.length - b.length);
    let ans = 0;
    let hashTable = new Map();
    for (let word of words) {
        let c = 1;
        for (let i = 0; i < word.length; i++) {
            let pre = word.substring(0, i) + word.substring(i + 1);
            c = Math.max(c, (hashTable.get(pre) || 0) + 1);
        }
        hashTable.set(word, c);
        ans = Math.max(ans, c);
    }
    return ans;
}

C++

哈希表：

class Solution {
public:
    int longestStrChain(vector<string> &words) {
        sort(words.begin(), words.end(), [&](string a, string b)
             { return a.size() < b.size(); });
        int res = 0;
        unordered_map<string, int> map;
        for (auto word : words)
        {
            int x = 1;
            for (int i = 0; i < word.size(); ++i)
            {
                string pre = word.substr(0, i) + word.substr(i + 1);
                x = max(x, map[pre] + 1);
            }
            map[word] = x;
            res = max(res, x);
        }
        return res;
    }
};

Go

哈希表：

func longestStrChain(words []string) int {
	sort.Slice(words, func(i, j int) bool { return len(words[i]) < len(words[j]) })
	res := 0
	mp := make(map[string]int)
	for _, word := range words {
		x := 1
		for i := 0; i < len(word); i++ {
			pre := word[0:i] + word[i+1:len(word)]
			x = max(x, mp[pre]+1)
		}
		mp[word] = x
		res = max(res, x)
	}
	return res
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

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