Problem Description

The problem gives us an array of strings called patterns and a single string called word. Our task is to count and return the number of strings from the patterns array that are also substrings of the word. A substring is defined as a sequence of characters that appear in unbroken succession within another string. For example, "cat" is a substring of "concatenate".

To solve this problem, we must check each pattern in the patterns array and determine whether it can be found within the word. Every time we find a pattern that is a substring of word, we increment our count by one. Once we have checked all the patterns, we return the total count.

Intuition

The solution leverages a simple yet efficient approach:

• Iterate through each string in the patterns array.
• Check if the current string pattern is a substring in word.
• Count the number of occurrences where a pattern is a substring of word.

In Python, this solution is very concise due to the language's concise syntax for string containment (in keyword) and list comprehensions (or generator expressions). The expression p in word returns True if pattern p is a substring of word and False otherwise.

A generator expression is used to iterate through all patterns, yielding a True (equivalent to 1) or False (equivalent to 0) for each check. The sum function is then used to add up these values, resulting in the total count of patterns that are substrings of word.

The efficiency of this approach lies in its simplicity—there are no explicit loops or complex logic required; the solution is a straightforward application of built-in Python features to match patterns in a string.

Solution Approach

The solution to this problem is a straightforward application of string manipulation and searching. No complex algorithms or additional data structures are necessary. This is because Python's inherent abilities to handle string operations make it an ideal language for such tasks.

Here's a step-by-step walkthrough of the implementation:

• The solution defines a class Solution with a method numOfStrings that takes in two arguments: a list of strings patterns and a single string word.

• The method numOfStrings returns the result of a sum function which is applied to a generator expression. The generator expression is the key part of this solution:

  sum(p in word for p in patterns)

  This line uses the in keyword, which in Python, checks for the existence of a substring within another string.

• The generator expression (p in word for p in patterns) goes through each pattern p in the patterns list, checks whether p is a substring of word, and yields True or False accordingly.

• Each True or False is implicitly converted to 1 or 0 as the sum function evaluates the expression.

• The sum function then adds up these 1s and 0s. The result is the total number of times a pattern from patterns is found as a substring in word.

• The complexity of the solution is O(n * m) where n is the number of patterns and m is the length of the string word, assuming the in keyword takes O(m) in the worst case (when the pattern is similar to the end part of word and has to be checked for each character).

No additional data structures are utilized, and the Python-specific in keyword optimizes the string searching, making the code concise and easy to understand.

Example Walkthrough

Let's say we have a list of patterns ["a", "abc", "bc", "d"] and the word "abc". To determine how many strings from the patterns array are substrings of the word, we proceed as follows:

1. We start with the pattern "a". Is "a" a substring of "abc"? Yes, it is. The string "abc" does contain the substring "a". So we can count that. Now our count is 1.

2. Next, we check the pattern "abc". Is "abc" a substring of "abc"? Yes, the whole word is a match. We increment our count again. Now the count is 2.

3. Then, we check "bc". Is "bc" a substring of "abc"? Yes, "bc" appears at the end of "abc" so it's a match. We update the count again. The count is now 3.

4. Finally, we check "d". Is "d" a substring of "abc"? No, "abc" does not contain the substring "d". The count remains the same.

At the end of this process, we have found that 3 of our patterns are also substrings of the word "abc". Therefore, the method numOfStrings would return 3 for this example using the generator expression as described above.

Using the solution approach:

class Solution:
    def numOfStrings(self, patterns, word):
        return sum(p in word for p in patterns)

# Our example patterns and word
patterns = ["a", "abc", "bc", "d"]
word = "abc"

# Create an instance of Solution
solution_instance = Solution()
# Call numOfStrings method and print the result
print(solution_instance.numOfStrings(patterns, word))  # Output: 3

This code snippet shows how to use the Solution class to solve our example. The output 3 matches our manual count from the walkthrough.

Solution Implementation

Time and Space Complexity

Time Complexity

The time complexity of the given function primarily depends on two factors: the number of strings in the patterns list and the length of the word string. For each pattern, the function checks whether that pattern exists within the word, which is an O(n) operation where n is the length of the word. Assuming the average length of the patterns is k, and there are m patterns in total, the overall time complexity would be O(m * n).

Therefore, if m is the number of patterns and n is the length of the word, the time complexity is:

O(m * n)

Space Complexity

The space complexity of this function is O(1) because it uses only a constant amount of additional memory outside of the inputs. The sum operation with a generator expression does not create a new list in memory; it simply iterates over the patterns and accumulates the count. No additional data structures are used that would scale with the input size.

Hence, the space complexity is:

O(1)

Learn more about how to find time and space complexity quickly using problem constraints.