Problem Description

The problem requires you to find the number of unique strings that appear exactly once in each of the two provided string arrays, namely words1 and words2. To solve this, you need to determine the strings that are not repeated within their own arrays and then check how many of these non-repeated strings are common to both arrays.

Intuition

To approach this problem effectively, count the occurrences of each string in both arrays independently. This can be achieved by using data structures that map a string to its frequency (like a dictionary in Python). The standard choice for counting objects in Python is the Counter class from the collections module, which does exactly that: it creates a frequency map where each key is a string from the array and each value is the count of occurrences of that string.

Once each array has been processed into its own counter (frequency map), the solution lies in comparing these two. You iterate through the items in one of the counter objects, checking for strings that have a count of exactly one. If a string with a count of one in the first counter also has a count of one in the second counter, it means that this string is unique in both arrays. The sum of such unique strings gives you the answer.

Solution Approach

The reference solution approach is straightforward and cleverly utilizes Python's Counter class from the collections module to count the frequency of each word in both input arrays words1 and words2.

Here are the steps followed in the implementation:

• Firstly, two Counter objects, cnt1 and cnt2, are created for words1 and words2 respectively. These objects map each word to its frequency in the respective arrays.
• Then, we use a list comprehension combined with the sum function to iterate through the items of cnt1. We only consider the keys k (words) that have a value v (count) of exactly one since we are looking for unique occurrences.
• For each of these keys with a count of one in cnt1, we check if the corresponding count in cnt2 is also exactly one, using the expression cnt2[k] == 1. This filters down to words that are unique in both arrays.
• If both conditions are satisfied (the word appears exactly once in both cnt1 and cnt2), then the condition evaluates to True, which is implicitly interpreted as 1 in the summation.
• The sum function adds up all the 1s, effectively counting the number of strings that meet the specified criteria.
• The result of the sum is the final answer and is returned by the countWords method.

This approach is efficient because it leverages hash maps (via the Counter object in Python) to count the frequency of elements with O(n) complexity, where n is the size of the input array. Consequently, the overall time complexity of the algorithm is O(n + m), where n is the length of words1 and m is the length of words2, since each word in both arrays is processed exactly once.

Example Walkthrough

Let's take an example to illustrate how the solution approach works.

Suppose we have two string arrays:

words1 = ["apple", "banana", "cherry", "date"]
words2 = ["banana", "cherry", "apple", "elderberry", "fig", "cherry"]

Following the steps outlined in the solution approach:

• Step 1: Use the Counter class to map each word to its frequency in both arrays.

from collections import Counter

cnt1 = Counter(words1) # Counter({'apple': 1, 'banana': 1, 'cherry': 1, 'date': 1})
cnt2 = Counter(words2) # Counter({'banana': 1, 'cherry': 2, 'apple': 1, 'elderberry': 1, 'fig': 1})

We observe that in cnt1, every word has a frequency of 1, while in cnt2 "cherry" has a frequency of 2 (which means it's not unique) and all others have a frequency of 1.

• Step 2: Using a list comprehension, we iterate through the items of cnt1 and check if the corresponding count in cnt2 is also 1.

unique_in_both = sum(1 for word in cnt1 if cnt1[word] == 1 and cnt2[word] == 1)

• Step 3: In our example, "apple" and "banana" are the words that have a count of one in both cnt1 and cnt2.

  • For "apple", cnt1["apple"] is 1 and cnt2["apple"] is also 1.
  • For "banana", cnt1["banana"] is 1 and cnt2["banana"] is also 1.
  • "cherry" and "date" do not meet the criteria because "cherry" is not unique in cnt2, and "date" does not exist in cnt2 at all.

• Step 4: So, only "apple" and "banana" are counted, giving us a sum of 2.

Therefore, the countWords method would return 2, which is the number of strings that appear exactly once in each of the arrays words1 and words2.

The example demonstrates the effectiveness of the approach by filtering unique occurrences efficiently through the use of Counter objects and a summation over a conditional check. The final result correctly reflects the number of unique words appearing once in both arrays.

Solution Implementation

Time and Space Complexity

Time Complexity

The time complexity of the code is determined by several factors:

• Creating the first counter cnt1 for words1: This involves iterating over all elements in the words1, so it takes O(n) time where n is the number of elements in words1.
• Creating the second counter cnt2 for words2: Similarly, this takes O(m) time where m is the number of elements in words2.
• Iterating over the cnt1 items and summing: We iterate over the counter cnt1 items once, which takes O(u) time where u is the number of unique words in words1. The conditional check for cnt2[k] == 1 is an O(1) operation because of the hash table lookup in the counter.

Therefore, the total time complexity is O(n + m + u). In the worst case, where all the words are unique, u can be equal to n, simplifying it to O(n + m).

Space Complexity

The space complexity is dominated by the two counters cnt1 and cnt2:

• The counter cnt1 stores each unique word in words1, which takes O(u) space where u is the number of unique words in words1.
• The counter cnt2 stores each unique word in words2, taking O(v) space where v is the number of unique words in words2.

The total space complexity is O(u + v). In the worst case, where all the words are unique, u can be equal to n and v equal to m, which makes the space complexity O(n + m).

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