Problem Description

In this problem, we are given an array of string words. Our task is to find all the strings in the array that are a substring of another string within the same array. In other words, we are looking for any string w1 from the words array that can be found within another string w2 in the same array, where w1 and w2 are not the same string. A substring, by definition, is a contiguous sequence of characters within a string; it could be as short as one character or as long as the string itself minus one character. Our final output is an array that includes these substrings, and the order of the substrings in the output doesn't matter.

Intuition

The intuition behind the solution is straightforward: we need to find if any word is part of another word in the array. We can achieve this by comparing each word with every other word in the array. This can be done through a nested loop where for every word w1, we look through the whole array to check if there's another word w2 that contains w1 as a substring. If such a w2 is found, we can conclude that w1 is a substring of another word in the array.

We use an inner loop and an outer loop to iterate through the array of words. For each word in the outer loop (w1), we iterate through all other words in the array in the inner loop (w2). If we find that w1 is contained within w2 (w1 is a substring of w2) and w1 is not the same as w2 (to avoid comparing a word with itself), we can add w1 to the answer list. Once w1 has been found as a substring, we don't need to check the rest of the words for w1, so we use a break statement to move on to the next word in the outer loop.

This approach ensures that we check all pairs of words to determine which ones are substrings of another. Once all checks are completed, we return the list of substrings we found.

Note that we may have duplicate words in the input array, and our approach avoids adding a word multiple times to the answer list by breaking the inner loop as soon as we find the first match.

Solution Approach

The solution approach takes advantage of a simple brute force method to solve the problem, utilizing two nested for loops to compare every pair of words.

Algorithms and Patterns

Brute Force Comparison

1. We iterate through the words array using an outer loop. Each word encountered in this loop will be referred to as w1.
2. For each w1, we use another inner loop to iterate through all other words in the array, which we refer to as w2.
3. We compare w1 to every w2, ensuring not to compare a word with itself by checking that the indices i and j are not equal (i != j). If w1 is the same as w2, it doesn't count as a substring, so we only want to find instances where w1 is contained in a different w2.

Substring Check

1. The check w1 in w2 is used to determine if w1 is a substring of w2. This is a built-in operation in Python that checks for the presence of a sequence of characters within another sequence.
2. If the condition is met, we append w1 to our answer list ans.
3. After appending w1 to the answer list, we don't need to check it against the remaining w2 words in the loop, as we have already confirmed it is a substring. This is where we break the inner loop.

Data Structures

• A list ans is used to store the words that satisfy the condition of being a substring of another word.

Code Representation

The solution in Python looks like this:

1class Solution:
2    def stringMatching(self, words: List[str]) -> List[str]:
3        ans = []
4        for i, w1 in enumerate(words):
5            for j, w2 in enumerate(words):
6                if i != j and w1 in w2:
7                    ans.append(w1)
8                    break
9        return ans

In this code snippet, enumerate is a handy function that provides a counter (i and j) to the loop which we use to ensure we are not comparing the same word with itself. When we find a match, we immediately break out of the inner loop to avoid unnecessary checks, which is a minor optimization within the brute force approach.

The idea of breaking out of the loop as soon as we find a word is a substring ensures that the algorithm doesn't do excessive work. However, it's worth noting that the algorithm's time complexity is O(n^2 * m), where n is the number of words and m is the average length of a word. This is because, in the worst case, for each outer loop word, we potentially check all other words and each character within those words for being a substring.

By returning the ans list after the loops have completed, we have solved the problem by collecting all strings in the input array that are substrings of another word.

Example Walkthrough

Let's consider a small example to illustrate the solution approach. Suppose we have the following array of strings:

1words = ["mass", "as", "hero", "superhero", "cape"]

We want to find all strings that are a substring of another string in this list. Using the brute force method, we follow these steps:

1. We start with the outer loop, taking w1 = "mass".

2. We enter the inner loop and compare w1 with every w2.

   • When j = 0, we compare w1 with "mass"; since they are the same, we continue.
   • When j = 1, we compare w1 with "as"; the word "mass" does not contain "as" as a substring, we continue.
   • When j = 2, we compare w1 with "hero", we continue since there's no match.
   • The same goes for "superhero" and "cape", no matches are found.

3. We move on to w1 = "as".

   • When j = 0, comparing "as" to "mass", we find that w1 is a substring of w2. We add "as" to the answer list and break the loop.

4. Next is w1 = "hero".

   • No matches for "mass", "as", but when we reach "superhero", we find that w1 is a substring of w2. We add "hero" to the answer list and break the loop.

5. For w1 = "superhero" and w1 = "cape", we find no substrings, as they are not contained in any other word in the list.

Now that we have gone through each word, our answer list ans contains ["as", "hero"]. These two words were identified as substrings of "mass" and "superhero" respectively.

By looping through the entire list of words and comparing each pair, we have effectively applied the brute force solution to determine our answer.

Solution Implementation

Time and Space Complexity

Time Complexity

The time complexity of the given code can be analyzed by looking at the two nested loops where it iterates over all possible pairs of strings in the list, except when they are the same string (i.e., where i != j). For each pair, the code checks if one string is a substring of another by using in operation.

If we assume n is the number of words and m the maximum length of a word, the check w1 in w2 has a worst-case complexity of O(m^2) because in the worst case, every character in w1 might be checked against every character in w2 before a match is found or the end of w2 is reached.

Given that we have two nested loops each going through n elements, and assuming the worst-case scenario for the substring check, the overall time complexity of this algorithm would be O(n^2 * m^2).

Space Complexity

The space complexity of the code is determined by the additional memory we use, aside from the input. Here, the only extra space that we use is the ans list, which in the worst case may contain all the original strings, if all strings are substrings of at least one other string.

Thus the space required for the ans list is O(n * m), as it can store at most n strings, with each string having a length at most m.

The final space complexity for the algorithm is O(n * m) since this is the most significant additional space the algorithm uses.

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