# 1048 Longest String Chain

You are given an array of `words` where each word consists of lowercase English letters.

`wordA` is a predecessor of `wordB` if and only if we can insert exactly one letter anywhere in `wordA` without changing the order of the other characters to make it equal to `wordB`.

• For example, `"abc"` is a predecessor of `"abac"`, while `"cba"` is not a predecessor of `"bcad"`.

A word chain is a sequence of words `[word1, word2, ..., wordk]` with `k >= 1`, where `word1` is a predecessor of `word2`, `word2` is a predecessor of `word3`, and so on. A single word is trivially a word chain with `k == 1`.

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

Example 1:

``````Input: words = ["a","b","ba","bca","bda","bdca"]
Output: 4
Explanation: One of the longest word chains is ["a","ba","bda","bdca"].
``````

Example 2:

``````Input: words = ["xbc","pcxbcf","xb","cxbc","pcxbc"]
Output: 5
Explanation: All the words can be put in a word chain
["xb", "xbc", "cxbc", "pcxbc", "pcxbcf"].
``````

Example 3:

``````Input: words = ["abcd","dbqca"]
Output: 1
Explanation: The trivial word chain ["abcd"] is one of the longest word chains.
["abcd","dbqca"] is not a valid word chain because the ordering of the letters is changed.
``````

Constraints:

• `1 <= words.length <= 1000`
• `1 <= words[i].length <= 16`
• `words[i]` only consists of lowercase English letters.
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 `````` ``````class Solution: def longestStrChain(self, words: List[str]) -> int: count = defaultdict(set) dp = {} min_len = math.inf max_len = -math.inf for w in words: word_len = len(w) count[word_len].add(w) min_len = min(min_len, word_len) max_len = max(max_len, word_len) for w in count[min_len]: dp[w] = 1 for l in range(min_len+1, max_len+1): for w in count[l]: chain_len = 1 for i in range(len(w)): pw = w[:i] + w[i+1:] if pw in dp and dp[pw] + 1 > chain_len: chain_len = dp[pw] + 1 dp[w] = chain_len return max(dp.values()) ''' Shorter ''' class Solution: def longestStrChain(self, words: List[str]) -> int: dp = {} for w in sorted(words, key=len): dp[w] = max( dp.get(w[:i] + w[i + 1:], 0) + 1 for i in range(len(w)) ) return max(dp.values())``````