# Find the winner by adding Pairwise difference of elements in the array until Possible in Python

Suppose we have an array A of positive integers, the elements are unique, now, two players P and Q are playing a game. At each move, any one player picks two numbers a and b from the array and if |a – b| is not in the array after that the player adds this number to the array. When a player cannot make the move loses the game. We have to find the winner of the game if player P always starts the game.

So, if the input is like A = [8,9,10], then the output will be P.

To solve this, we will follow these steps −

• n := size of arr

• g := arr, max_val := arr

• for i in range 1 to n, do

• g := gcd(g, arr[i])

• max_val := maximum of max_val, arr[i]

• total :=(max_val / g) - n

• if total is odd, then

• return 'P'

• return 'Q'

## Example

Let us see the following implementation to get better understanding −

Live Demo

from math import gcd
def who_is_the_winner(arr) :
n = len(arr)
g = arr
max_val = arr
for i in range(1, n) :
g = gcd(g, arr[i])
max_val = max(max_val, arr[i])
total = (max_val / g) - n
if (total % 2 == 1) :
return 'P'
return 'Q'

arr = [8,9,10]
print(who_is_the_winner(arr))

## Input

[8,9,10]

## Output

P