Program to find number of different subsequences GCDs in Python

Suppose we have an array nums with positive values. We have to find the number of different GCDs among all non-empty subsequences of nums. As we know the GCD of a sequence of numbers is the greatest value that divides all the numbers in the sequence evenly.

So, if the input is like nums = [4,6,18], then the output will be 4 because gcd([4]) = 4, gcd([6]) = 6, gcd([18]) = 18 gcd([4,6]) = 2, gcd([4,18]) = 2, gcd([6,18]) = 6, gcd([4,6,18]) = 2 so all numbers are [4,6,18,2], there are 4 numbers.

To solve this, we will follow these steps −

• T := maximum of nums + 1

• nums := a new set containing all distinct numbers of nums

• ans := 0

• for x in range 1 to T - 1, do

  • g := 0

  • for y in range x to T - 1, update in each step by x, do

    • if y is in nums, then

      • g := gcd(g, y)

    • if g is same as x, then

      • come out from loops

  • if g is same as x, then

    • ans := ans + 1

• return ans

Example

Let us see the following implementation to get better understanding

from math import gcd
def solve(nums):
   T = max(nums) + 1
   nums = set(nums)
   ans = 0

   for x in range(1, T):
      g = 0
      for y in range(x, T, x):
         if y in nums:
            g = gcd(g, y)
         if g == x:
            break

      if g == x:
         ans += 1

   return ans

nums = [4,6,18]
print(solve(nums))

Input

[4,6,18]

Output

4