Program to find number of ways we can get a number which is sum of nth power of unique numbers in Python

Suppose we have a number x and another number n. We have to find number of ways we can get x as sum of nth power of some unique numbers.

So, if the input is like x = 100 n = 2, then the output will be 3 because possible solutions are 6^2 + 8^2, 10^2 and 1^2 + 3^2 + 4^2 + 5^2 + 7^2.

To solve this, we will follow these steps −

• ans := 0
• Define a method called solve() this will take four parameters x, n, cn and cs, the initial
• values for cs = 0, cn = 1
• p := cn^n
• while p + cs < x, do
  • ans := ans + solve(x, n, cn + 1, p + cs)
  • cn := cn + 1
  • p := cn^n
• if p + cs is same as x, then
  • ans := ans + 1
• return ans

Example

Let us see the following implementation to get better understanding −

from math import pow

def solve(x, n, cn = 1, cs = 0):
   ans = 0
   p = pow(cn, n)
   while p + cs < x:
      ans += solve(x, n, cn + 1, p + cs)
      cn = cn + 1
      p = pow(cn, n)

   if p + cs == x:
      ans = ans + 1
   return ans

x = 100
n = 2
print(solve(x, n))

Input

100, 2

Output

3