Program to find winner of a rower reducing game in Python

Python Server Side Programming Programming

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

Arnab Chakraborty

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

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