💡 Problem Formulation: A Strong Number is a number in which the sum of the factorial of its digits is equal to the original number itself. For instance, 145 is a strong number because 1! + 4! + 5! = 145. The aim is to write a Python program that determines whether a given number is a strong number or not.
Method 1: Using Loop and Factorial Function
This method involves creating a function to calculate the factorial of each digit and then summing these factorials to check if it equals the original number. The function accepts an integer and returns a boolean indicating whether it is a strong number.
Here’s an example:
def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n-1)
def is_strong_number(num):
temp = num
sum_of_factorials = 0
while(temp):
digit = temp % 10
sum_of_factorials += factorial(digit)
temp //= 10
return sum_of_factorials == num
print(is_strong_number(145))
Output: True
This code snippet defines a recursive function factorial() to compute the factorial of a number and a function is_strong_number() to determine if the original number is strong. We deconstruct the number digit by digit, sum the factorial of each digit, and compare the resultant sum to the initial number.
Method 2: Using Iterative Factorial Computation
An iterative approach to computing factorials can be more efficient than recursive methods. In this method, we calculate the factorial of each digit without using recursion and determine if the sum equals the number itself.
Here’s an example:
def factorial(n):
result = 1
for i in range(1, n+1):
result *= i
return result
def is_strong_number(num):
sum_of_factorials = sum(factorial(int(digit)) for digit in str(num))
return sum_of_factorials == num
print(is_strong_number(145))
Output: True
In this snippet, the factorial() function uses a for loop for calculation, thus avoiding the overhead of recursive calls. The is_strong_number() function computes the sum of the factorials in a more Pythonic way by using a generator expression, making the code concise and readable.
Method 3: Using Memoization to Cache Factorials
For larger numbers, repeatedly computing factorials can be wasteful. By using a memoization technique, we can cache previously calculated factorial values to avoid redundant computations.
Here’s an example:
factorial_cache = {}
def factorial(n):
if n in factorial_cache:
return factorial_cache[n]
factorial_cache[n] = 1 if n == 0 else n * factorial(n-1)
return factorial_cache[n]
def is_strong_number(num):
temp, sum_of_factorials = num, 0
while temp:
digit = temp % 10
sum_of_factorials += factorial(digit)
temp //= 10
return sum_of_factorials == num
print(is_strong_number(145))
Output: True
The code defines a factorial_cache dictionary to store computed factorials. The factorial() function then works recursively but looks up in the cache before computing a new factorial. The result is an efficient calculation of strong numbers, especially beneficial when checking larger numbers.
Method 4: Using a Precomputed Factorial Lookup Table
This method relies on the fact that digits only range from 0 to 9, so we can precompute the factorial for each digit and store them in a list, serving as a lookup table for our factorial sums.
Here’s an example:
factorial_table = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
def is_strong_number(num):
return sum(factorial_table[int(digit)] for digit in str(num)) == num
print(is_strong_number(145))
Output: True
This approach is extremely efficient because it removes the need for factorial calculations at runtime. The is_strong_number() function simply iterates through each digit of the number, looks up the precomputed factorial, and adds it to the sum.
Bonus One-Liner Method 5: The Functional Approach
Leverage Python’s functional programming features like map() and sum() with lambda functions to create an ultra-compact one-liner that checks for a strong number.
Here’s an example:
is_strong_number = lambda num: num == sum((1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880)[int(digit)] for digit in str(num)) print(is_strong_number(145))
Output: True
This one-liner defines is_strong_number as a lambda function that directly computes and compares the sum of factorial values (from a precalculated list as in Method 4) with the original number. It’s a concise and readable solution but may be cryptic to those unfamiliar with Python’s functional programming constructs.
Summary/Discussion
- Method 1: Loop with Recursive Factorial. Simple and clear. It may be inefficient for large numbers due to recursive overhead.
- Method 2: Iterative Factorial Computation. More efficient than recursion. Pythonic and elegant, but slightly longer code.
- Method 3: Memoization of Factorials. Most efficient for repeated checks or large numbers. Complexity added with caching.
- Method 4: Precomputed Factorial Lookup. Extremely efficient and fast. Limited to the scope of digits 0-9.
- Method 5: One-liner Functional. Compact and slick. Could be hard to understand for beginners or less readable.