LeetCode 1048. Longest String Chain

Question

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.

Source: https://leetcode.com/problems/longest-string-chain/

Solution

Bottom-Up DP

For words, the length of longest string chain that ends with word equals $max(pre_0(word),pre_1(word),…,pre_{l-1}(word))+1$

public int longestStrChain(String[] words) {
    // parameter validation
    if (words == null || words.length < 1) {
        return 0;
    }
    // s -> max length of string chain ending with s
    Map<String, Integer> cache = new HashMap<>();
    // sort words by length of each word
    Arrays.sort(words, new Comparator<String>() {
        @Override
        public int compare(String o1, String o2) {
            return o1.length() - o2.length();
        }
    });
    int len = words.length;
    int maxLen = 0;
    for (int i = 0; i < len; i++) {
        int currLen = 1;
        StringBuilder temp = new StringBuilder(words[i]);
        for (int k = 0; k < words[i].length(); k++) {
            char c = temp.charAt(k);
            temp.deleteCharAt(k);
            String predecessor = temp.toString();
            int prevLen = cache.getOrDefault(predecessor, 0);
            currLen = Math.max(currLen, prevLen + 1);
            temp.insert(k, c); // restore the change
        }
        cache.put(words[i], currLen);
        maxLen = Math.max(maxLen, currLen);
    }
    return maxLen;
}