Question

Use recursion to implement a function find(string, match) that tests whether natch is containcd in string: \(b=\) find ("Mississippi", "sip") \(\|\) Sets b to true Hint: If string starts with satch, you are done. If not, consider the string that you obtain by removing the first character.

Short answer

The function find('Mississippi', 'sip') returns True.

Step-by-step solution

Understand the Problem

We need a recursive function `find(string, match)` that checks if the `match` string is contained anywhere within the `string`. For example, if the `string` is 'Mississippi' and `match` is 'sip', the function should return `true`.

Base Case

The base case of our recursion should occur when the length of `string` is smaller than `match`. In this case, it is impossible for `match` to be found in `string`, so the function should return `false`. Additionally, if `match` is an empty string, we can return `true` since an empty string is trivially contained within any string.

Check for Match at Start

At each recursive step, first check if the `string` starts with the `match` string. This can be done using the `startswith` method. If `string.startswith(match)` evaluates to `true`, the function should return `true` as this confirms `match` is found in `string`.

Recursive Call for the Rest of the String

If `string` does not start with `match`, make a recursive call to the function with the first character removed from `string`. The call will be `find(string[1:], match)`. This effectively checks if `match` is contained in the rest of the string.

Implement the Function

Combine all the steps into a single function: ```python def find(string, match): # Base cases if len(string) < len(match): return False if match == '': return True # Check current beginning of string if string.startswith(match): return True # Recursive call on the substring return find(string[1:], match) ``` This function should return `True` for the input `find('Mississippi', 'sip')`.

Test the Function

Test the function with specific examples and ensure the output is correct. For instance: ```python b = find('Mississippi', 'sip') print(b) # Should print: True ``` Ensure that other queries behave correctly as well, such as `find('hello', 'world')` which should return `false`.

Key concepts

Base Case in Recursion

In recursion, the base case is a critical concept that prevents the recursive process from continuing indefinitely. For our problem of finding a substring within a string, the base case serves as a checkpoint to identify when the recursive function should stop.

• The first base case checks if the length of the `string` is shorter than the `match` string. If true, it's impossible for `match` to be found, so the function returns `false`. This acts as a simple yet effective boundary check.
• The second base case evaluates if the `match` string is empty. By definition, an empty string is considered a part of any other string, hence the function immediately returns `true` in this situation.

Understanding the base case allows the recursive function to avoid unnecessary and infinite loops, keeping the code efficient and logical. It's vital to carefully determine these cases, as they directly influence the behavior of the recursive solution.

String Matching

String matching is an essential technique in programming, especially when dealing with text processing or data extraction tasks. The problem we are solving requires checking if a `match` string exists within a larger `string`.

Using the `startswith` method in Python is a straightforward approach. This method helps determine if the current slice of the `string` begins with our `match`. This is efficient because it compares only what is necessary, stopping the instant a match is found.

• If `string.startswith(match)` is `true`, our recursive function has succeeded in finding the `match`, and we return `true` immediately.
• If not, we progress to the next smaller slice of the string for further investigation.

This method not only simplifies string matching but also leverages Python's built-in capabilities to enhance performance, making the function concise and easy to maintain.

Recursive Function Design

Designing recursive functions involves structuring the function in a way that it effectively breaks down a problem into manageable subproblems. In our example of finding a substring, careful planning of the recursive structure is crucial.

The function `find(string, match)` iteratively checks whether `match` can be found in `string` using these strategies:

• First, it handles the base cases, ensuring the process knows when to terminate or succeed early.
• It then checks the current state of the string. If there’s no immediate match at the start, the function considers a reduced problem size by making a call with the first character of `string` removed. This slice represents a smaller version of the problem.
• The call `find(string[1:], match)` effectively narrows down the scope, solving the main problem piece by piece.

This approach highlights the power of recursion. Each recursive call works on a smaller segment of the string until it either finds the match or concludes with no match. Writing recursive functions carefully allows them to elegantly address complex operations by focusing on simple and consistent logic.