Word containing other words

There exists solution using string matching algorithm KMP and graphs.

Algorithm:

1) Iterate over words. Set each word for «main word», the word you want to build. Execute following steps for each such word.

2) You fixed one word, lets call it W. Now iterate over all words again and run KPM comparing them to W. Now you can build a graph on letters of word W. Lets explain on example:

W = "abacdeeee"
Other_word = ["aba", "cde", "eee"]

Word "aba" would connect letter 1 in word W to letter 4.
Word "cde" would connect 4 to 7.
Word "eee" would connect 7 to 9.

Each letter in W is node and other words will make edges. 
If there exists a path between first and last letter, which you can 
check using BFS/DFS, you can build word W out of other words.

3) Repeat the process for each word and choose the longest that can be built from others.

Time complexity:

Lets say N is number of words and L is average length.

For a single word you run KMP with each other word, which would take O(N * (L + L)). Building graph takes O(N^2) in worst case, same for BFS. For each word W you spend O(NL + N^2) worst case, but number of edges will most likely be proportional to N, so average is O(NL).

As you need to the above for each N, you get result:

Worst complexity: O(N^2*L + N^3)

Average complexity: O(N^2*L)