Program to check n can be shown as sum of k or not in Python

Suppose we have a number n, and another number k. We have to check whether n can be represented as a sum of k prime numbers or not.

So, if the input is like n = 30 k = 3, then the output will be True because 30 can be represented like 2 + 11 + 17.

To solve this, we will follow these steps −

• if n < k*2, then
  • return False
• if k > 2, then
  • return True
• if k is same as 2, then
  • if n is even, then
    • return True
  • if (n-2) is prime, then
    • return True
  • return False
• if n is prime, then
  • return True
• return False

Example

Let us see the following implementation to get better understanding −

def isPrime(num):
   if num > 1:
      for i in range(2, num):
         if num % i == 0:
            return False
      return True
   return False

def solve(n, k):
   if n < k*2:
      return False
  
   if k > 2:
      return True

   if k == 2:
      if n%2 == 0:
         return True

      if isPrime(n-2):
         return True
      return False

   if isPrime(n):
      return True
   return False

n = 30
k = 3
print(solve(n, k))

Input

30, 3

Output

True