Check if a Number Can Be Written as a Sum of Distinct Factorial Numbers in Python

Suppose we have a positive number n, we have to check whether n can be written as the sum of unique positive factorial numbers or not.

So, if the input is like n = 144, then the output will be True, as 4! + 5! = 24 + 120 = 144

To solve this, we will follow these steps −

• fact := 1

• res := a new list

• x := 2

• while fact <= n, do

  • insert fact at the end of res

  • fact := fact * x

  • x := x + 1

• for i in range size of res -1 to 0, decrease by 1, do

  • if n >= res[i], then

    • n := n - res[i]

• return true when n is same as 0

Let us see the following implementation to get better understanding −

Example

 Live Demo

class Solution:
def solve(self, n):
   fact = 1
   res = []
   x = 2
   while fact <= n:
      res.append(fact)
      fact = fact * x
      x += 1
   for i in range(len(res)-1,-1,-1):
      if n>=res[i]:
         n-=res[i]
   return n==0
ob = Solution()
print(ob.solve(144))

Input

144

Output

True