Given a list of words and a sentence find all words that appear in the sentence either in whole or as a substring

Problem

Given a list of string find the strings from the list that appear in the given text.

Example

list = ['red', 'hello', 'how are you', 'hey', 'deployed']
text = 'hello, This is shared right? how are you doing tonight'
result = ['red', 'how are you', 'hello']

'red' because it has 'shared' has 'red' as a substring

This is very similar to this question except that the word we need to look for can be substring as well.
The list is pretty large and increases with increase in the users as opposed to text which is pretty much the same length throughout.
I was thinking of having a solution where the time complexity depends on from the length of the text rather that list of words so that it can be scalable even when lots of users are added.

Solution

I build a trie from the give list of words
Run dfs on the text and check the current word against the trie

Psuedo-Code

def FindWord (trie, text, word_so_far, index):
    index > len(text)
        return
    //Check if the word_so_far is a prefix of a key; if not return
    if trie.has_subtrie(word) == false:
       return 
    //Check if the word_so_far is a key; if ye add to result and look further 
    if trie.has_key(word) == false:
        // Add to result and continue
    //extend the current word we are searching
    FindWord (trie, text, word_so_far + text[index], index + 1)
    //start new from the next index 
    FindWord (trie, text, "", index + 1)

The problem with this is although the runtime now depends on the len(text) it runs with a time complexity O(2^n) after building the trie which is a one time thing for multiple texts so it's fine.

I do not see any overlapping subproblems either to memoize and improve the runtime.

Can you suggest any way I can achieve a runtime that depends on given text as opposed to the list of words which can be per-processed and cached and is also faster that this.

Solution

The theoretically sound version of what you're trying to do is called Aho--Corasick. Implementing the suffix links is somewhat complicated IIRC, so here's an algorithm that just uses the trie.

We consume the text letter by letter. At all times, we maintain a set of nodes in the trie where the traversal can be. Initially this set consists of just the root node. For each letter, we loop through the nodes in the set, descending via the new letter if possible. If the resulting node is a match, great, report it. Regardless, put it in the next set. The next set also contains the root node, since we can start a new match at any time.

Here's my attempt at a quick implementation in Python (untested, no warranty, etc.).

class Trie:
    def __init__(self):
        self.is_needle = False
        self._children = {}

    def find(self, text):
        node = self
        for c in text:
            node = node._children.get(c)
            if node is None:
                break
        return node

    def insert(self, needle):
        node = self
        for c in needle:
            node = node._children.setdefault(c, Trie())
        node.is_needle = True


def count_matches(needles, text):
    root = Trie()
    for needle in needles:
        root.insert(needle)
    nodes = [root]
    count = 0
    for c in text:
        next_nodes = [root]
        for node in nodes:
            next_node = node.find(c)
            if next_node is not None:
                count += next_node.is_needle
                next_nodes.append(next_node)
        nodes = next_nodes
    return count


print(
    count_matches(['red', 'hello', 'how are you', 'hey', 'deployed'],
                  'hello, This is shared right? how are you doing tonight'))