Program to find winner of number reducing game in Python

Suppose Amal and Bimal are playing a game. They have a number n and they check whether it is a power of 2 or not. If it is, they divide it by 2. otherwise, they reduce it by the next lower number which is also a power of 2. Whoever reduces the number to 1 will win the game. Amal always starts the game, then we have to find the winner's name.

So, if the input is like n = 19, then the output will be Amal because, 19 is not power of 2, so Amal reduces it to 16, then Bimal divides by 2 to make 8, then again Amal divides by 2 to get 4, then Bimal make it 2 and finally Amal divides to make it 1 and wins the game.

To solve this, we will follow these steps −

• res := 0
• while n > 1, do
  • b := 1
  • while b * 2 < n, do
    • b := b * 2
  • n := n - b
  • res := res + 1
• if res mod 2 is same as 0, then
  • return 'Amal'
• otherwise,
  • return 'Bmal'

Example

Let us see the following implementation to get better understanding −

def solve(n):
   res = 0
   while(n > 1):
      b = 1
      while(b * 2 < n):
         b *= 2
      n -= b
      res += 1
   if res % 2 == 0:
      return 'Amal'
   else:
      return 'Bmal'

n = 19
print(solve(n))

Input

19

Output

Amal