Program to find winner of a rower reducing game in Python

PythonServer Side ProgrammingProgramming

Suppose we have an array height. There are n different towers with different height. Amal and Bimal are playing a game. The game rules are like below

  • Amal always plays first

  • During each move, the current player selects a tower of height X and reduce the height to Y [1 <= Y < X; Y evenly divides X]

  • Whoever has no move will lose the game

We have to find the winner’s name.

So, if the input is like height = [3,1,2], then the output will be Bimal, because the initial heights are {3,1,2}. If Amal reduces the height of tower 2 to 1, Bimal can reduce 3 by 1, but Amal has no move so Bimal wins.

To solve this, we will follow these steps −

  • Define a function util() . This will take a,n
  • ans := 0
  • for i in range 0 to n - 1, do
    • ans := ans XOR a[i]
  • return ans
  • From the main method do the following
  • n := size of height
  • b := an array of size n and fill with 0
  • for i in range 0 to n - 1, do
    • if height[i] is same as 1, then
      • b[i] := 0
    • otherwise
      • b[i] := 0
      • j := 2
      • root := floor of square root of height[i]
      • while height[i] is not same as 1 and j<=root, do
        • if height[i] mod j is same as 0, then
          • while height[i] mod j is same as 0, do
            • b[i] := b[i] + 1
            • height[i] := floor of height[i]/j
        • j := j + 1
      • if height[i] is not same as 1, then
        • b[i] := b[i] + 1
  • ans := util(b, n)
  • if ans is not same as 0, then
    • return "Amal"
  • otherwise,
    • return "Bimal"

Example

Let us see the following implementation to get better understanding −

def util(a,n):
   ans = 0
   for i in range(n):
      ans = ans^a[i]

   return ans

def solve(height):
   n = len(height)
   b = [0 for i in range(n)]

   for i in range(n):
      if(height[i] == 1):
         b[i] = 0
      else:
         b[i] = 0
         j = 2

         root = int(pow(height[i],0.5))
         while(height[i] != 1 and j<=root):
            if(height[i]%j == 0):
               while(height[i]%j == 0):
                  b[i] += 1
                  height[i] = height[i]//j

            j += 1

         if(height[i] != 1):
            b[i] += 1

   ans = util(b, n)

   if(ans != 0):
      return "Amal"
   else:
      return "Bimal"

height = [3,1,2]
print(solve(height))

Input

[3,1,2]

Output

Bimal
raja
Updated on 23-Oct-2021 07:40:31

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