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

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:

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// 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;
}
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Output:
A



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