# Number Of Matching Subsequences Problem

## Description

LeetCode Problem 792.

Given a string s and an array of strings words, return the number of words[i] that is a subsequence of s.

A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.

• For example, “ace” is a subsequence of “abcde”.

Example 1:

``````1
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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".
``````

Example 2:

``````1
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Input: s = "dsahjpjauf", words = ["ahjpjau","ja","ahbwzgqnuk","tnmlanowax"]
Output: 2
``````

Constraints:

• 1 <= s.length <= 5 * 10^4
• 1 <= words.length <= 5000
• 1 <= words[i].length <= 50
• s and words[i] consist of only lowercase English letters.

## Sample C++ Code

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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;
}
};
``````