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 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 

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 <bits/stdc++.h>
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;
}

Java

/*package whatever //do not write package name here */
import java.util.*;
public class GFG {

  // Function that returns the
  // sum of the digits of n
  static int digit_sum(int n)
  {
    int s = 0;
    while (n > 0) {
      s += n % 10;
      n /= 10;
    }
    return s;
  }

  // Function to return the winner of the game
  static String findTheWinner(int arr[], int n)
  {

    int arr1[][] = new int[arr.length][2];

    for(int i=0;i<arr.length;i++){
      arr1[i][0] = arr[i];
      arr1[i][1] = digit_sum(arr[i]);
    }

    // Sort the elements based on
    // the digit sum values
    Arrays.sort(arr1,(a,b)->a[0]-b[0]);

    // Find player A's score
    int scoreA = 0;
    for (int i = n - 1; i >= 0; i -= 2)
      scoreA += arr1[i][0];

    // Find player A's score
    int scoreB = 0;
    for (int i = n - 2; i >= 0; i -= 2)
      scoreB += arr1[i][0];

    // Find the winner
    if (scoreA == scoreB)
      return "Draw";
    else if (scoreA > scoreB)
      return "A";
    return "B";
  }

  public static void main (String[] args) {
    int arr[] = { 12, 43, 25, 23, 30 };
    int n = arr.length;

    System.out.println(findTheWinner(arr, n));

  }
}

// This code is contributed by aadityaburujwale.

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

C#

// C# implementation of the approach
using System;
class GFG
{

  // Function that returns the
  // sum of the digits of n
  static 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
  static 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
  static string findTheWinner(int []arr, int n)
  {

    // Sort the elements based on
    // the digit sum values
    // sort(arr, arr + n, comparator);
    Array.Sort(arr,new Comparison<int>(
      (i1, i2) =>  digit_sum(i2).CompareTo( digit_sum(i1))));
    // 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";
  }
  static void Main() {
    int []arr = { 12, 43, 25, 23, 30 };
    int n = arr.Length;

    Console.Write(findTheWinner(arr, n));
  }
}

// This code is contributed by garg28harsh.

Javascript

<script>

// Javascript implementation of the approach

// Function that returns the
// sum of the digits of n
function digit_sum(n)
{
    var s = 0;
    while (n > 0) {
        s += n % 10;
        n = parseInt(n/10);
    }
    return s;
}

// Compares two integers according
// to their digit sum
function comparator(a, b)
{
    // Sum of digits of a
    var s1 = digit_sum(a);

    // Sum of digits of b
    var 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
function findTheWinner(arr, n)
{

    // Sort the elements based on
    // the digit sum values
    arr.sort(comparator);

    // Find player A's score
    var scoreA = 0;
    for (var i = n - 1; i >= 0; i -= 2)
        scoreA += arr[i];

    // Find player A's score
    var scoreB = 0;
    for (var 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
var arr = [ 12, 43, 25, 23, 30 ];
var n = arr.length;
document.write( findTheWinner(arr, n));

</script>

Output:

A

Time Complexity: O(n*log(n)*d) where n is the size of the array and d is the maximum number of digits in any number present in the array.

Auxiliary Space: O(1)