Count Pairs Of Similar Strings

The core of this problem is to find out pairs of strings which have the same set of characters. The order of characters and their frequency does not matter.

One way to approach this problem is by using the concept of a set in Python. A set is a collection that is both unordered and unindexed. Sets are unchangeable, meaning we cannot change the items after the set has been created. More importantly, a set cannot have duplicate values. Therefore, when we convert a string to a set, it discards the order and frequency of characters, leaving only the unique characters behind.

Now, if we create a set for each word in the list, the problem boils down to finding pairs of sets that are equal.

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class Solution:
    def similarPairs(self, words: List[str]) -> int:
        # Initialize an empty list to store sets
        words_sets = []

        # Loop through each word in the list
        for word in words:
            # Convert the word to a set and append it to the list
            word_set = set(word)
            words_sets.append(word_set)

        # Initialize a counter for the number of similar pairs
        count = 0

        # Loop through each pair of sets
        for i in range(len(words_sets)):
            for j in range(i+1, len(words_sets)):
                # If the sets are equal, increment the count
                if words_sets[i] == words_sets[j]:
                    count += 1

        return count

This code first converts each word in the words list to a set of characters and stores these sets back in the words list. It then loops through each pair of words (sets) in the list. If a pair of words have the same set of characters (i.e., the sets are equal), it increments the count. The final value of count is the number of similar pairs of words.

This solution has a time complexity of O(n^2), where n is the number of words. This is because for each word, it checks its similarity with every other word in the list. For large inputs, this might lead to performance issues. There are more efficient ways to solve this problem using more complex data structures like hash tables, but this solution provides a good starting point and is easy to understand.

We use the set data structure in this case because of its unique properties:

Uniqueness: A set in Python automatically removes duplicates. Each character will only appear once in a set, no matter how many times it appears in the original string.
Order Invariant: A set doesn’t preserve the order of elements. This means, the set {“a”, “b”} is the same as the set {“b”, “a”}.

These properties make the set data structure ideal for this problem. When we convert each string in ‘words’ to a set, we get a unique representation of the characters that make up the string, regardless of order or frequency. If two strings are made up of the exact same characters, their sets will be identical.

So, by comparing sets instead of the original strings, we can easily determine whether two strings are similar (i.e., consist of the same characters) as required by this problem.

Which line compares that every character is present on the other string?

The line that performs this comparison is the one with the equality check: if set_word1 == set_word2:.

What happens here is that, for each pair of strings in the words list, the code creates a set of characters for each string. These sets, set_word1 and set_word2, contain unique characters from each string, respectively.

The equality check == then compares these two sets. If every character in set_word1 is also present in set_word2, and vice versa (in other words, if the two sets are identical), this condition will be true.

When this condition is true, the code increments the count by 1, indicating that it has found a pair of similar strings according to the problem’s definition (strings that consist of the same characters).

This comparison is done for all pairs of strings in the words list, and the final count is returned as the result.

Does the code use pairwise comparison of strings?

Yes, the code does use pairwise comparison of strings.

This is achieved with the use of two nested loops. The outer loop, for i in range(length):, iterates over each string in the words list. The inner loop, for j in range(i+1, length):, starts from the string after i and iterates over the remaining strings in the list.

Within the loops, for each pair of strings (words[i] and words[j]), the code creates two sets of characters, set_word1 and set_word2, and then compares these sets for equality.

This way, every string is compared with every other string exactly once, effectively implementing pairwise comparison.