# 5 Best Ways to Check if a Number is a Strong Number in Python

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π‘ Problem Formulation: In number theory, a Strong number (or factorial number) is a number whose sum of the factorial of digits is equal to the original number. For example, if the input number is 145, the output should indicate it’s a Strong number because 1! + 4! + 5! = 145.

## Method 1: Using Iteration

This method checks the strength of a number by iterating through each digit, computing its factorial, and summing them up to compare with the original number. It’s a straightforward brute-force approach.

Here’s an example:

```def factorial(n):
return 1 if n == 0 else n * factorial(n - 1)

def is_strong_number(num):
return num == sum(factorial(int(d)) for d in str(num))

# Test the function
print(is_strong_number(145))```

Output: `True`

This code defines a factorial function and a function to check if a number is strong. It converts the number into a string, iterates through each character, converts it back to an integer, computes the factorial, and sums these factorials. The outcome is compared with the original number.

## Method 2: Using Memoization

This technique leverages memoization to store previously calculated factorials which reduces the computational time for repeated digits.

Here’s an example:

```factorials = {0: 1}

def factorial(n):
if n not in factorials:
factorials[n] = n * factorial(n - 1)
return factorials[n]

def is_strong_number(num):
return num == sum(factorial(int(d)) for d in str(num))

# Test the function
print(is_strong_number(145))```

Output: `True`

In this improved solution, a dictionary called ‘factorials’ caches the factorial results. This optimization is particularly helpful if you’re testing multiple numbers repeatedly.

## Method 3: Using an Iterative Factorial Function

This method relies on an iterative factorial function instead of a recursive one. It’s an optimized approach, which is generally faster and avoids the recursion limit in Python.

Here’s an example:

```def factorial(n):
result = 1
for i in range(2, n + 1):
result *= i
return result

def is_strong_number(num):
return num == sum(factorial(int(d)) for d in str(num))

# Test the function
print(is_strong_number(145))```

Output: `True`

This code defines an iterative factorial function which multiplies numbers up to the given integer. The main advantage is efficiency, as it doesn’t involve the overhead of recursive function calls.

## Method 4: Using Library Functions

This method makes use of Python’s standard library functions to calculate factorials, which is typically optimized and compiled in C for efficiency.

Here’s an example:

```from math import factorial

def is_strong_number(num):
return num == sum(factorial(int(d)) for d in str(num))

# Test the function
print(is_strong_number(145))```

Output: `True`

Using the `factorial` function from Python’s `math` module provides a clean and efficient way to perform factorial calculations without implementing the logic from scratch.

## Bonus One-Liner Method 5: Functional Programming Approach

This one-liner method employs a functional programming style, utilizing map, sum, and the factorial function from the math module in a single expression.

Here’s an example:

```from math import factorial

def is_strong_number(num):
return num == sum(map(factorial, map(int, str(num))))

# Test the function
print(is_strong_number(145))```

Output: `True`

The example uses `map` to apply the `factorial` function to each digit of the number after converting it to an integer. It’s a concise approach but may sacrifice some readability for brevity.

## Summary/Discussion

• Method 1: Iterative Brute-Force. Simple to understand. May be inefficient for large numbers due to repeated calculations.
• Method 2: Memoized Factorial. More efficient for numbers with repeated digits thanks to caching. Slightly more complex due to memoization logic.
• Method 3: Iterative Factorial Function. More memory-efficient than recursion and avoids maximum recursion depth issues. Faster for large numbers but less pythonic.
• Method 4: Standard Library Utilization. Highly efficient and clean code using optimized library functions. Relies on Python’s standard library.
• Method 5: Functional Programming One-Liner. Extremely concise, showcasing the power of Python’s functional programming capabilities. Can decrease readability.