How to Solve Number of Matching Subsequences

To solve the 'Number of Matching Subsequences' problem, the key idea is to use array scanning combined with hash lookups to efficiently count matching subsequences. This method reduces the time complexity compared to brute force solutions. By mapping characters in the string s and efficiently checking subsequences in words, we can determine the count of valid subsequences in linear time.

Problem Statement

You are given a string s and a list of strings words. Your task is to return the number of strings from words that are subsequences of the string s.

A subsequence of a string is a sequence that can be derived by deleting some or no characters of the string without changing the relative order of the remaining characters.

Examples

Example 1

Input: s = "abcde", words = ["a","bb","acd","ace"]

Output: 3

There are three strings in words that are a subsequence of s: "a", "acd", "ace".

Example 2

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

Output: 2

Example details omitted.

Constraints

• 1 <= s.length <= 5 * 104
• 1 <= words.length <= 5000
• 1 <= words[i].length <= 50
• s and words[i] consist of only lowercase English letters.

Solution Approach

Efficient Array Scanning with Hash Lookup

To solve this problem efficiently, you can map the characters of string s into a hash table. Then, scan each word in the words list, checking if the characters can be matched in order within s using this hash table.

Using Binary Search for Optimized Search

A more optimized approach uses binary search to find the next character of the word within s. This can be combined with the previously mentioned hash lookup to efficiently check for subsequences.

Trie-based Approach for Faster Matching

Alternatively, a trie can be built using all words, allowing for faster subsequence matching by scanning through s and checking if a word in the trie can be matched as a subsequence.

Complexity Analysis

The time complexity depends on the approach: using hash lookup, it's O(N + M), where N is the length of s and M is the total length of all words. If using binary search, it may improve to O(N log M). The space complexity is O(M) for storing the words in the hash table or trie.

What Interviewers Usually Probe

• The candidate demonstrates an understanding of subsequence matching and optimizes using hash maps or binary search.
• The candidate is able to apply different data structures, such as hash maps, binary search, or tries, to optimize subsequence search.
• The candidate is able to reduce time complexity efficiently and handle large input sizes within constraints.

Common Pitfalls or Variants

Common pitfalls

• Brute force checking of each word as a subsequence could lead to time complexity that exceeds the problem's limits.
• Not using an efficient data structure like a hash table or trie might result in slow performance for larger inputs.
• Overlooking edge cases where words might not match the sequence order in s or contain extra characters.

Follow-up variants

• Use dynamic programming to store partial subsequences for more complex scenarios.
• Instead of checking each word individually, preprocess the input string s to speed up subsequence checks.
• Modify the approach to handle multiple strings where each has different character sets or sequences.

How GhostInterview Helps

• GhostInterview helps by guiding you through optimal approaches like array scanning and hash lookup for matching subsequences.
• The platform offers practice with common pitfalls like brute-forcing and provides solutions to improve time and space efficiency.
• GhostInterview suggests various strategies, including binary search and trie-based solutions, to help tackle this problem effectively.

Topic Pages

• Array
• Hash Table
• String
• Binary Search
• Dynamic Programming
• Trie
• Sorting

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FAQ

What is the primary approach for solving the Number of Matching Subsequences problem?

The primary approach is to combine array scanning with hash lookup, allowing for efficient subsequence matching in string s.

How do you avoid brute-force solutions in this problem?

You avoid brute force by using a hash table or binary search, significantly reducing the time complexity when checking if a word is a subsequence.

Can this problem be solved with a trie?

Yes, a trie-based approach can be used to store the words and scan string s, offering faster subsequence matching.

What are the time and space complexities for this problem?

The time complexity is O(N + M) with hash lookup, where N is the length of s and M is the total length of all words. The space complexity is O(M).

What is the key pattern in solving this problem?

The key pattern is using efficient array scanning combined with hash lookup to determine subsequences in a time-efficient manner.