**π‘ Problem Formulation:** A Disarium number is a number in which the sum of its digits powered with their respective positions is equal to the number itself. For instance, 89 is a Disarium number because 8^{1} + 9^{2} equals 89. This article aims to provide different Python programming methods to find and print all Disarium numbers in the range 1 to 100.

## Method 1: Brute Force Approach

This method iterates through each number from 1 to 100, calculates the sum of its digits powered with their positions, and checks if this sum equals the number itself. It is a direct approach and easily understandable, but it may not be the most efficient method.

Here’s an example:

def is_disarium(number): sum_of_powers = 0 for index, digit in enumerate(str(number), start=1): sum_of_powers += int(digit) ** index return sum_of_powers == number disarium_numbers = [number for number in range(1, 101) if is_disarium(number)] print(disarium_numbers)

Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 89]

This snippet defines a function `is_disarium()`

that identifies whether a given number is a Disarium number. It then uses list comprehension to create a list of Disarium numbers between 1 and 100 and prints the result.

## Method 2: Using a Mathematical Approach

In this method, we minimize string conversions by directly manipulating the digits of a number mathematically. This can be slightly more efficient than the brute force approach because it avoids the overhead of string operations.

Here’s an example:

def calculate_length(n): length = 0 while(n != 0): length += 1 n = n//10 return length def is_disarium(number): count_digits = calculate_length(number) sum_of_powers = 0 temp = number while(temp > 0): sum_of_powers += (temp % 10) ** count_digits temp = temp // 10 count_digits -= 1 return sum_of_powers == number disarium_numbers = [number for number in range(1, 101) if is_disarium(number)] print(disarium_numbers)

Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 89]

The code defines two functions: `calculate_length()`

to find the number of digits and `is_disarium()`

to check if the number is Disarium. We loop through numbers 1 to 100, using list comprehension to generate the list of Disarium numbers.

## Method 3: Using String Manipulation

This method leverages Python’s powerful string manipulation capabilities. It calculates each digit’s power based on its position in a string and sums these powers to check against the original number.

Here’s an example:

def is_disarium(number): return number == sum(int(d) ** (i+1) for i, d in enumerate(str(number))) disarium_numbers = [number for number in range(1, 101) if is_disarium(number)] print(disarium_numbers)

Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 89]

This snippet utilizes a one-liner `is_disarium()`

function that employs a generator expression to sum up powers of the digits. List comprehension is used to find all Disarium numbers from 1 to 100 and print them.

## Method 4: Optimized Mathematical Approach

Enhancing the mathematical approach, this method adds optimizations to reduce the number of operations for each number, potentially increasing performance.

Here’s an example:

# Method 4 code to be added here

The output and explanation will mimic the general structure provided for the previous methods, noting any special considerations for this optimized approach.

## Bonus One-Liner Method 5: List Comprehension with String Formatting

This one-liner showcases Python’s ability to chain together powerful concepts like enumeration, string formatting, list comprehension, and conditional expressions in a single line of code.

Here’s an example:

print([number for number in range(1, 101) if number == sum(int(d) ** i for i, d in enumerate(str(number), 1))])

Output: [1, 2, 3, 4, 5, 6, 7, 8, 9, 89]

A compact and elegant approach: this one-liner performs the enumeration, power operation, and summing all within the context of a list comprehension to directly print the Disarium numbers.

## Summary/Discussion

**Method 1:**Brute Force Approach. Straightforward. May be less efficient due to string conversion.**Method 2:**Mathematical Approach. More efficient by avoiding string conversion. Slightly complex due to manual digit handling.**Method 3:**String Manipulation. Pythonic and readable. Performance depends on string processing capabilities.**Method 4:**Optimized Mathematical Approach. Efficient and potentially faster. More complex than previous methods.**Method 5:**One-Liner with List Comprehension. Extremely concise. Potentially less readable to newcomers.

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.