Program to check whether first player can take more candies than other or not in Python

Suppose we have a list of numbers called candies and two persons are racing to collect the most number of candies. Here the race is turn based, person 1 is starting first, and in each turn he can pick up candies from the front or from the back. We have to check whether person 1 can collect more candies than other or not.

So, if the input is like candies = [1, 4, 3, 8], then the output will be True, as person 1 can take 8 candies in the first round and regardless of whether second person picks 1 or 3, person 1 can win by taking any remaining candy.

To solve this, we will follow these steps −

• N := size of candies

• Define a function difference() . This will take left, right

• if left is same as right, then

  • return candies[left]

• return maximum of (candies[left] − difference(left + 1, right)) and (candies[right] − difference(left, right − 1))

• from the main method do the following −

• return true when difference(0, N − 1) > 0, otherwise false

Let us see the following implementation to get better understanding −

Example

 Live Demo

class Solution:
   def solve(self, candies):
      N = len(candies)
      def difference(left, right):
         nonlocal candies
         if left == right:
            return candies[left]
         return max(candies[left] − difference(left + 1, right), candies[right] − difference(left, right − 1))
      return difference(0, N − 1) > 0
ob = Solution()
candies = [1, 4, 3, 8]
print(ob.solve(candies))

Input

[1, 4, 3, 8]

Output

True