# Program to check person 1 can win the candy game by taking maximum score or not in Python

PythonServer Side ProgrammingProgramming

Suppose two players are playing a game. Where several candies placed on a line, and person 1 is given a list of numbers called nums that is representing the point value of each candy. On each person's turn, they can pick 1, 2, or 3 candies from the front of the line, then delete them from list, and get the sum of their points added to their score. This game will end when all the candies are deleted and the person with the higher score will be the winner. We have to check person 1 can win this game or not.

So, if the input is like nums = [1, 1, 2, 3, 50], then the output will be True, as person 1 can take 1 candy, then the other player has to take 1, 2 or 3 candies. In any case, person 1 can take the candy with the value of 50.

To solve this, we will follow these steps −

• n := size of nums

• table := an array with three 0s.

• for i in range n − 1 to 0, decrease by 1, do

• profit := −inf

• sum_val := 0

• for j in range i to minimum of i + 3 and n, do

• sum_val := sum_val + nums[j]

• profit := maximum of profit and (sum_val − table[j − i])

• set table := a list with three values [profit, table[0], table[1]]

• return true when table[0] > 0, otherwise false

Let us see the following implementation to get better understanding −

## Example

Live Demo

import math
class Solution:
def solve(self, nums):
n = len(nums)
table = [0, 0, 0]
for i in range(n − 1, −1, −1):
profit = −math.inf
sum_val = 0
for j in range(i, min(i + 3, n)):
sum_val += nums[j]
profit = max(profit, sum_val − table[j − i])
table[:] = [profit, table[0], table[1]]
return table[0] > 0
ob = Solution()
nums = [1, 1, 2, 3, 50]
print(ob.solve(nums))

## Input

[1, 1, 2, 3, 50]

## Output

True
Updated on 26-Dec-2020 10:44:27