Problem Description

This problem presents two arrays, word1 and word2, each containing strings. The task is to determine if these two arrays represent the same string when their contents are concatenated together. In other words, if we join all the elements of word1 end-to-end to make a single string and do the same with word2, and those two resulting strings are identical, we should return true. Otherwise, we will return false. It is essential to concatenate the elements in the order they appear in their respective arrays.

Intuition

To solve this problem, we rely on the simple property that strings are equal if they contain the same sequence of characters in the same order. Therefore, the solution approach is straightforward:

• Concatenate all elements in word1 to form a single string.
• Concatenate all elements in word2 to form another single string.
• Compare these two strings for equality.

If both strings are equal, it means the arrays word1 and word2 represent the same string; thus, we return true. If they differ, the arrays represent different strings, so we return false. This is achieved with minimal code by using the join method in Python, which concatenates the elements of a list into a string, separated by the string provided to join (in this case, an empty string as we don't want any characters between the elements).

Solution Approach

The implementation of the solution is straightforward and elegant, thanks to Python's high-level string handling capabilities. The algorithm does not rely on complex data structures or patterns; it primarily uses the built-in string functionality provided by Python.

Here's a step-by-step walk-through of the arrayStringsAreEqual function within the Solution class:

1. The join method is called on an empty string ('') with word1 as the argument. The join method takes all elements in word1, which are strings themselves, and concatenates them in the order they appear in the array. This results in a single string that represents the concatenation of all individual strings in word1.

   joined_word1 = ''.join(word1)

2. The same process is applied to word2:

   joined_word2 = ''.join(word2)

3. Now, we have two strings represented by joined_word1 and joined_word2. All that remains is to check whether these two strings are identical.

   result = joined_word1 == joined_word2

4. The result of this comparison is a boolean (True or False). The function directly returns this result, completing the check with a single line of code:

   return joined_word1 == joined_word2

This approach takes full advantage of Python's ability to handle strings and perform operations on lists. It effectively reduces what could be a more complex algorithm involving manual iteration and concatenation to a simple one-liner that is easy to understand and maintain.

Example Walkthrough

Let's consider an example where word1 = ["ab", "c"] and word2 = ["a", "bc"]. We need to follow the described solution approach to determine if these two arrays represent the same string when concatenated.

1. First, we concatenate the elements of word1 using the join method on an empty string.

   joined_word1 = ''.join(["ab", "c"])  # This evaluates to "abc"

   After applying the join method, we end up with the string "abc".

2. Next, we concatenate the elements of word2.

   joined_word2 = ''.join(["a", "bc"])  # This evaluates to "abc"

   Similarly, the join method results in the string "abc" for word2.

3. Now we have both strings obtained from word1 and word2 respectively. We will now compare these two strings to check if they are identical:

   result = joined_word1 == joined_word2  # This evaluates to True

   In this case, joined_word1 is "abc" and joined_word2 is also "abc". The comparison yields True.

4. Finally, we will directly return the result of the comparison:

   return result  # This returns True

   Since result was True, the function would return True, indicating that word1 and word2 do indeed represent the same string when concatenated.

Therefore, given the inputs word1 = ["ab", "c"] and word2 = ["a", "bc"], the function arrayStringsAreEqual will return True, as the concatenated strings from both arrays are identical.

Solution Implementation

Time and Space Complexity

The time complexity of the code is O(m + n) where m is the total number of characters in word1 and n is the total number of characters in word2. This is because the join operations for word1 and word2 each iterate over their respective arrays to build a single string, which takes linear time relative to the number of characters in each array.

The space complexity of the code is O(m + n) as well, since it needs to allocate space for the new strings generated by ''.join(word1) and ''.join(word2). No additional space is required beyond the strings themselves.

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