Problem Description

The task is to count how many strings from the given array words have the string pref as their prefix. A prefix is defined as a substring that appears at the start of another string. For example, if pref is "ab", and you have a string "abcd" in words, it counts because "abcd" starts with "ab".

Intuition

The intuitive solution to this problem is straightforward. You simply iterate through each string in the array words and check if it starts with the string pref. The method startswith() in Python is perfect for this task as it does exactly what's needed—it returns True if the string object it's called on starts with the specified prefix, which in this case, is pref.

By using a list comprehension, we effectively generate a list of boolean values, True for strings that start with pref and False otherwise. Wrapping this list comprehension with Python's sum() function cleverly counts the number of True values in that list, because True is equivalent to 1 and False is equivalent to 0 when it comes to addition. Hence, we get the total count of strings with the given prefix in one elegant line of code.

Solution Approach

The solution is implemented in Python and makes use of a list comprehension and the built-in startswith() method for strings. The elegance of the solution lies in its simplicity and efficient use of the language's features.

Here are the steps taken in the algorithm:

1. Loop through each string w in the array words using a list comprehension. For each string, check if it starts with the prefix pref. This is done using the startswith() method, which is called on each w.

2. The startswith() method returns a boolean value True or False. This list comprehension creates a list of boolean values corresponding to each string in words.

3. The sum() function is then used to add up all the boolean values in the list. In Python, True is treated as 1 and False as 0 when summed. So, sum() essentially counts all the True values, which represent the strings that start with pref.

4. The result of the sum() function gives us the total number of strings in words that contain pref as a prefix.

The code for this solution is concise and can be written as:

class Solution:
    def prefixCount(self, words: List[str], pref: str) -> int:
        return sum(w.startswith(pref) for w in words)

This code fragment is the complete implementation of the solution. It defines a class Solution with a method prefixCount, which takes an array of strings words and a string pref as arguments and returns an integer. The prefixCount method only contains the above-mentioned list comprehension wrapped in the sum() function, which calculates and returns the count directly.

The solution does not require additional data structures and is a good example of Python's expressive capability to solve problems in a very readable and succinct manner.

Example Walkthrough

Let's illustrate the solution with a small example. Suppose we have an array of strings words that contains ["apple", "appreciate", "appetite", "banana", "application"] and our prefix pref is "app".

As we iterate through words:

• The first word "apple" starts with "app". startswith() returns True.
• The second word "appreciate" also starts with "app". startswith() returns True.
• The third word "appetite" starts with "app" as well. startswith() returns True.
• The fourth word "banana" does not start with "app". startswith() returns False.
• The fifth word "application" starts with "app". startswith() returns True.

Using the list comprehension [w.startswith(pref) for w in words], we get a list of boolean values: [True, True, True, False, True].

Passing this list to the sum() function adds up the True values (with each True being equivalent to 1): sum([True, True, True, False, True]) which equals 1 + 1 + 1 + 0 + 1, giving us a total of 4.

So, the total count of strings with the prefix "app" in the words array is 4. This demonstrates the simplicity and elegance of the solution using Python's built-in functions.

Solution Implementation

Time and Space Complexity

The given Python function prefixCount iterates over each word in the list words and checks if it starts with the prefix pref using the startswith method. The computation complexity analysis is as follows:

Time Complexity

The time complexity of the function is O(n * k), where n is the number of words in the list and k is the length of the prefix pref. This is because for each of the n words, the startswith method checks up to k characters to determine if the word starts with the prefix.

Space Complexity

The space complexity of the function is O(1). The function uses a generator expression within the sum function, which calculates the result on-the-fly and does not require additional space proportional to the input size. The only additional memory used is for the counter in the sum function, which is a constant space requirement.

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