**π‘ Problem Formulation:** You need to determine whether the smallest number in a given set has a first and last digit that, when combined together, form a prime number. If you’re given an array `[143, 235, 19]`

, the smallest number is `19`

, and the first and last digits `1`

and `9`

form the number `19`

, which is prime. Hence, the desired output, in this case, is `True`

.

## Method 1: Converting to String

This method involves converting the smallest number to a string, extracting the first and last characters, combining them to form a new number, and then checking if this new number is prime. The function `is_prime()`

is used to verify the primeness of the formed number.

Here’s an example:

def is_prime(num): if num < 2: return False for i in range(2, int(num ** 0.5) + 1): if num % i == 0: return False return True def first_last_prime(arr): smallest_num = str(min(arr)) first_last = int(smallest_num[0] + smallest_num[-1]) return is_prime(first_last) # Example Usage print(first_last_prime([143, 235, 19]))

Output:

`True`

This snippet defines a utility function `is_prime()`

that efficiently checks for prime numbers and another function `first_last_prime()`

which finds the smallest number in an array, concatenates its first and last digits, and determines if this new number is prime.

## Method 2: Without String Conversion

In this method, we employ mathematical operations to find the first and last digits of the smallest number without converting it to a string. This avoids overhead caused by type conversions and string manipulations.

Here’s an example:

def is_prime(num): if num < 2: return False for i in range(2, int(num ** 0.5) + 1): if num % i == 0: return False return True def first_last_prime(arr): smallest_num = min(arr) last_digit = smallest_num % 10 while smallest_num >= 10: smallest_num //= 10 first_digit = smallest_num first_last = first_digit * 10 + last_digit return is_prime(first_last) # Example Usage print(first_last_prime([143, 235, 19]))

Output:

`True`

The function `first_last_prime()`

calculates the first and last digits using division and modulus operators and then checks if the new number formed by these digits is prime.

## Method 3: Using List Comprehension and Lambdas

This method takes advantage of the concise syntax provided by list comprehension and lambda functions to achieve the same result in a more compact code.

Here’s an example:

is_prime = lambda num: num > 1 and all(num % i for i in range(2, int(num ** 0.5) + 1)) def first_last_prime(arr): smallest_str = str(min(arr)) return is_prime(int(smallest_str[0] + smallest_str[-1])) # Example Usage print(first_last_prime([143, 235, 19]))

Output:

`True`

The lambda function `is_prime`

succinctly checks for a prime number, and the smallest number’s first and last digits are concatenated and checked for primeness in the `first_last_prime()`

function.

## Method 4: Using Regular Expressions

Regular expressions can be employed to directly extract the first and last digits from the smallest number converted to a string. This approach can make the code more readable for those familiar with regex patterns.

Here’s an example:

import re def is_prime(num): if num < 2: return False for i in range(2, int(num ** 0.5) + 1): if num % i == 0: return False return True def first_last_prime(arr): smallest_str = str(min(arr)) first_last = int(re.search(r'^(.).*(.)$', smallest_str).groups()[0] + re.search(r'^(.).*(.)$', smallest_str).groups()[1]) return is_prime(first_last) # Example Usage print(first_last_prime([143, 235, 19]))

Output:

`True`

A regular expression pattern is used in the `first_last_prime()`

function to capture the first and last digits and check the combined number for primeness via the `is_prime()`

function.

## Bonus One-Liner Method 5: List Comprehension with Math and Lambda

Combining list comprehension with mathematical operations allows us to employ a one-liner Python expression that effectively solves the problem by finding the first and last digits and then checking their combination for primeness.

Here’s an example:

print((lambda x: x > 1 and all(x % i for i in range(2, int(x ** 0.5) + 1))) (int(str(min([143, 235, 19]))[0] + str(min([143, 235, 19]))[-1])))

Output:

`True`

This Python one-liner combines list comprehension and lambda functions to find the first and last digits of the smallest number and checks if their combination is prime using an inline `is_prime()`

check.

## Summary/Discussion

**Method 1:**String Conversion. Easy to follow. Potentially less efficient due to string operations.**Method 2:**No String Conversion. More efficient for large numbers. Slightly more complex due to mathematical operations.**Method 3:**List Comprehension with Lambdas. Compact and elegant. May be less readable for those unfamiliar with lambdas.**Method 4:**Regular Expressions. Good readability for regex-savvy users. Slower due to regex overhead.**Bonus Method 5:**One-Liner. Very concise. Can be difficult to understand and debug.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.