# Find the winner of the Game

Given an array arr[] of N integers and two players A and B are playing a game where the players pick the element with the maximum digit sum in their turns. In the end, the player with the maximum sum of the picked elements wins the game. Assuming that the player A always starts the game first and both the players play optimally, the task is to find the winner of the game.

Examples:

Input: arr[] = {12, 43, 25, 23, 30}
Output: B
A choses 43
B chooses 25
A chooses 23
B chooses 30
A chooses 12
A’s score = 43 + 23 + 12 = 78
B’s score = 25 + 30 = 55

Input: arr[] = {2, 1, 1, 2}
Output: Draw

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Sort the array based on the digit sum values of the integers, if the digit sum of two integers is same then they will be compared based on their values, this is because the value will maximize the sum in the end. After the array has been sorted based on the custom comparator, player A will try to pick the elements starting from the greatest (greedily).

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function that returns the ` `// sum of the digits of n ` `int` `digit_sum(``int` `n) ` `{ ` `    ``int` `s = 0; ` `    ``while` `(n > 0) { ` `        ``s += n % 10; ` `        ``n /= 10; ` `    ``} ` `    ``return` `s; ` `} ` ` `  `// Compares two integers according ` `// to their digit sum ` `bool` `comparator(``int` `a, ``int` `b) ` `{ ` ` `  `    ``// Sum of digits of a ` `    ``int` `s1 = digit_sum(a); ` ` `  `    ``// Sum of digits of b ` `    ``int` `s2 = digit_sum(b); ` ` `  `    ``// If the digit sum of a is equal ` `    ``// to the digit sum of b ` `    ``if` `(s1 == s2) ` `        ``return` `(a < b); ` `    ``return` `(s1 < s2); ` `} ` ` `  `// Function to return the winner of the game ` `string findTheWinner(``int` `arr[], ``int` `n) ` `{ ` ` `  `    ``// Sort the elements based on ` `    ``// the digit sum values ` `    ``sort(arr, arr + n, comparator); ` ` `  `    ``// Find player A's score ` `    ``int` `scoreA = 0; ` `    ``for` `(``int` `i = n - 1; i >= 0; i -= 2) ` `        ``scoreA += arr[i]; ` ` `  `    ``// Find player A's score ` `    ``int` `scoreB = 0; ` `    ``for` `(``int` `i = n - 2; i >= 0; i -= 2) ` `        ``scoreB += arr[i]; ` ` `  `    ``// Find the winner ` `    ``if` `(scoreA == scoreB) ` `        ``return` `"Draw"``; ` `    ``else` `if` `(scoreA > scoreB) ` `        ``return` `"A"``; ` `    ``return` `"B"``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 12, 43, 25, 23, 30 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` ` `  `    ``cout << findTheWinner(arr, n); ` ` `  `    ``return` `0; ` `} `

## Python3

 `# Python3 implementation of the above approach  ` ` `  `# Function that returns the  ` `# sum of the digits of n  ` `def` `digit_sum(n):  ` `     `  `    ``s ``=` `0``;  ` `    ``while` `n > ``0``:  ` `        ``s ``+``=` `n ``%` `10` `        ``n ``/``=` `10` `         `  `    ``return` `s ` ` `  `# Function to return the winner  ` `# of the game  ` `def` `findTheWinner(arr, n): ` ` `  `    ``# Sort the elements based on  ` `    ``# the digit sum values  ` `    ``arr.sort(key ``=` `digit_sum) ` ` `  `    ``# Find player A's score  ` `    ``scoreA ``=` `0` `    ``i ``=` `n ``-` `1` `    ``while` `i >``=` `0``: ` `        ``scoreA ``+``=` `arr[i] ` `        ``i ``-``=` `2` ` `  `    ``# Find player A's score  ` `    ``scoreB ``=` `0` `    ``i ``=` `n ``-` `2` `    ``while` `i >``=` `0``: ` `        ``scoreA ``+``=` `arr[i] ` `        ``i ``-``=` `2` ` `  `    ``# Find the winner  ` `    ``if` `scoreA ``=``=` `scoreB:  ` `        ``return` `"Draw"` `    ``elif` `(scoreA > scoreB):  ` `        ``return` `"A"` `         `  `    ``return` `"B"` ` `  `# Driver code  ` `if` `__name__``=``=``"__main__"``: ` `     `  `    ``arr ``=` `[ ``12``, ``43``, ``25``, ``23``, ``30` `] ` `    ``n ``=` `len``(arr);  ` ` `  `    ``print``(findTheWinner(arr, n))  ` `     `  `# This code is contributed by Yash_R `

Output:

```A
```

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