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1048\. Longest String Chain
Medium
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.
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