2586. Count the Number of Vowel Strings in Range

Problem Description

In this problem, you're given an array of strings named words, and two integers left and right that represent the indices within the array. The task is to count how many strings from the sub-array starting at index left and ending at index right (both inclusive) are "vowel strings." A vowel string is defined as a string that both starts and ends with a vowel character. The vowels in this case are the characters 'a', 'e', 'i', 'o', and 'u'. The answer you need to provide is the total number of such vowel strings that exist within the specified range of indices in the words array.

Intuition

The solution approach is fairly straightforward and relies on a direct check of each string within the specified bounds (left to right inclusive). For each string, you need to perform two checks: (1) whether the first character is a vowel, and (2) whether the last character is a vowel. If both conditions are true, then that string qualifies as a vowel string.

To arrive at this solution, it's clear that you must visit each string within the given index range; hence, a loop or iterator is necessary. Within the loop, you need to examine the specific characters of the string - only the first and last characters since these are the ones that determine if a string is a vowel string according to the problem definition.

The use of the Python slicing notation words[left:right+1] simplifies accessing the sub-array we're interested in. The sum function is a concise way to count the number of True evaluations, thereby providing us the total count of vowel strings. By using a generator expression, it performs the check and counts in a single line without the need for an explicit loop or additional variables for counting.

Thus, the approach is to execute the steps as a single inline operation that efficiently traverses the relevant subset of strings and tallies those that meet the vowel string criteria.

Solution Approach

The implementation of the Reference Solution Approach leans on a simple but effective strategy. It is a simulation of the conditions directly stated in the problem description with a healthy usage of Python's expressive syntax and built-in functions.

Here's a step-by-step description of how the solution works:

1. Slicing: The first operation is to slice the words array to obtain the relevant sub-array. This is done using the Python slicing syntax words[left:right+1]. The left:right+1 slice notation selects all the elements from index left up to and including the index right.

2. Generator Expression: Next, a generator expression is used to iterate over each word in the sliced sub-array of words. Generator expressions are a compact and memory-efficient way to work with sequences in Python. They allow for iterating over data without creating an intermediate list in memory, which would be the case if a list comprehension was used.

3. Conditional Check: During the iteration, the condition that each word w starts with a vowel (w[0] in 'aeiou') and ends with a vowel (w[-1] in 'aeiou') is checked. The w[0] and w[-1] syntax accesses the first and last characters of the string w, respectively. The in 'aeiou' part checks if a given character is among the characters 'a', 'e', 'i', 'o', 'u'.

4. Summation: Finally, the sum() function wraps the generator expression. sum adds up the True (which count as 1) evaluations of the conditional checks for every word in the sliced array. Since False is equivalent to 0, only the True cases contribute to the sum. The result is the count of all strings that are vowel strings within the given index range.

No additional data structures are used as this approach operates directly on the input data and produces the sum immediately, following an efficient memory and time usage pattern.

Here's a bit of code from the solution which encapsulates the process:

1return sum(
2    w[0] in 'aeiou' and w[-1] in 'aeiou' for w in words[left : right + 1]
3)

Each w represents a string within the specified range. The in keyword is used twice to perform the vowel checks, and the and keyword connects the two conditions. Only when both conditions are satisfied does the expression evaluate to True, subsequently increasing the sum total. This neat inline loop-and-check code effectively solves the problem in an idiomatic and Pythonic way.

Example Walkthrough

Let's consider an example to illustrate the solution approach described above. Suppose we have an array of strings and we want to count the number of vowel strings within a specified range of indices:

words = ["apple", "banana", "anaconda", "eagle", "kiwi", "onion", "ubi", "orange"]

Let's say left = 2 and right = 5. The sub-array we need to evaluate is from index 2 to index 5, which includes the words: ["anaconda", "eagle", "kiwi", "onion"]. Now, let's apply the solution step by step:

1. Slicing: We slice the words array using words[left:right+1], which results in ["anaconda", "eagle", "kiwi", "onion"].

2. Generator Expression: Using the generator expression, we iterate over each word in this sliced sub-array.

3. Conditional Check:

   • "anaconda": Starts with 'a' and ends with 'a', both of which are vowels. Hence, this word satisfies the condition.
   • "eagle": Starts with 'e' and ends with 'e', both vowels. This word satisfies the condition.
   • "kiwi": Starts with 'k' and ends with 'i'. Since 'k' is not a vowel, this word does not satisfy the condition.
   • "onion": Starts with 'o' and ends with 'n', and 'n' is not a vowel. This word also does not satisfy the condition.

4. Summation: The expression will evaluate to True for "anaconda" and "eagle", resulting in a count of 2. For "kiwi" and "onion", the expression evaluates to False.

Therefore, according to our generator expression, we have:

1sum(
2    w[0] in 'aeiou' and w[-1] in 'aeiou' for w in ["anaconda", "eagle", "kiwi", "onion"]
3)

The sum would be calculated as 1 + 1 + 0 + 0 = 2. Hence, there are 2 vowel strings in the array within the range of indices 2 to 5.

The inline code for this example simply counts the occurrences where both conditions are met and provides us with the final answer. In this case, the function call would look like this:

1count_vowel_strings(words, 2, 5)

And it would return 2, which is exactly the number of strings that start and end with a vowel in the specified range.

Solution Implementation

Time and Space Complexity

The time complexity of the provided function vowelStrings is O(m), where m is the number of elements processed by the sum operation, calculated by the given range right - left + 1. The function iterates through each element in the slice words[left : right + 1] once to compute the sum, resulting in a linear relationship between the number of elements and the time taken, hence O(m).

The space complexity of the code is O(1) as there are no additional data structures used that grow with the size of the input. The variables used in the list comprehension within the sum function do not require extra space that depends on the size of the input list, thus it remains constant regardless of the input size.

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