Smallest Value After Replacing With Sum of Prime Factors

Ah, the classic problem of finding the smallest value after replacing a number with the sum of its prime factors. It’s like trying to find the smallest piece of cake at a party where everyone is fighting over the biggest slice. You know, the one that looks delicious but is actually just a bunch of crumbs?

Imagine you have a number, let’s say 12. You think, “Wow, I’m so lucky to have this number!” But then you realize it’s just a facade, hiding its true self. When you break it down into its prime factors (which are 2 and 3), you find out that it’s really just 2 + 2 + 3 = 7. So, 12 is just a big, fat liar!

In this problem, we keep replacing the number with the sum of its prime factors until we can’t anymore. It’s like a never-ending cycle of disappointment, but hey, at least we get to the truth eventually!

Python Code Solution

Copy Code

class Solution:
    def smallestValue(self, n: int) -> int:
        def getPrimeSum(n: int) -> int:
            primeSum = 0
            for i in range(2, n + 1):
                while n % i == 0:
                    n //= i
                    primeSum += i
            return primeSum

        primeSum = getPrimeSum(n)
        while n != primeSum:
            n = primeSum
            primeSum = getPrimeSum(n)
        return n

Approach Explanation

The code defines a function smallestValue that takes an integer n as input. It uses a helper function getPrimeSum to calculate the sum of the prime factors of n. The main function keeps replacing n with its prime sum until n equals the prime sum. It’s a simple yet effective way to peel back the layers of a number to reveal its true essence.

Time and Space Complexity

Complexity Type	Complexity
Time Complexity	O(n log n)
Space Complexity	O(1)

Real-World Example

Let’s say you’re at a buffet, and you keep piling your plate with food. But every time you take a bite, you realize you can only eat so much. Eventually, you have to put some food back, and you end up with a smaller portion than you started with. This is similar to our problem: we keep reducing the number until we reach the smallest possible value.

Similar Problems

If you enjoyed this problem, you might also like these:

• 2-Sum Solution in Python
• 3-Sum Solution in Python
• 4-Sum Solution in Python