Number Of Matching Subsequences Problem

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Input: s = "abcde", words = ["a","bb","acd","ace"]
Output: 3
Explanation: There are three strings in words that are a subsequence of s: "a", "acd", "ace".

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Input: s = "dsahjpjauf", words = ["ahjpjau","ja","ahbwzgqnuk","tnmlanowax"]
Output: 2

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class Solution {
public:
    // Brute force checking will time out, we need efficent way to look up words
    // Create an vector that stores indices for each character a-z in S
    // Then for each word, do a binary search for next index for current character in word 
    // that is greater than the index we last found for the last character
    // If it doesn't exist, word doesn't exist, otherwise continue to search for word
    int numMatchingSubseq (string S, vector<string>& words) {
        vector<vector<int>> alpha (26);
        for (int i = 0; i < S.size (); ++i) 
            alpha[S[i] - 'a'].push_back (i);
        int res = 0;

        for (const auto& word : words) {
            int x = -1;
            bool found = true;

            for (char c : word) {
                auto it = upper_bound (alpha[c - 'a'].begin (), alpha[c - 'a'].end (), x);
                if (it == alpha[c - 'a'].end ()) 
                    found = false;
                else 
                    x = *it;
            }

            if (found) res++;
        }

        return res;
    }
};