Maximum money that can be collected by both the players in a game of removal of coins

Given an array arr[] consisting of N positive integers, such that arr[i] represents the value of the coin, the task is to find the maximum amount of money that can be obtained by each player when two players A and B play the game optimally as per the following rules:

• Player A always starts the game.
• In each turn, a player must remove exactly 1 coin from the given array.
• In each turn, player B, it must remove exactly 2 coins from the given array.

Examples:

Input: arr[] = {1, 1, 1, 1}
Output: (A : 2), (B : 2)
Explanation:
Following are the sequences of coins removed for both the players:

• Player A removes arr[0](= 1).
• Player B removes arr[1](= 1) and arr[2](= 1).
• Player A removes arr[3](= 1).

Therefore, the total coins obtained by Player A is 2 and Player B is 2. 

Input: arr[] = {1, 1, 1}
Output: (A : 1), (B : 2)

Approach: The given problem can be solved by using the Greedy Approach. Follow the below steps to solve the problem: 

• Initialize two variables, say amountA and amountB as 0 that stores the total amount of money obtained by the players A and B.
• Sort the given array in descending order.
• If the value of N is 1, then update the value of amountA to arr[0].
• If the value of N is greater than or equal to 2, then update the value of amountA to arr[0] and the value of amountB to arr[1].
• Traverse the array arr[] over the range [2, N] using the variable i, and if the value of i is even then add the value arr[i] to amountB. Otherwise, add the value arr[i] to the amountA.
• After completing the above steps, print the value of amountA and amountB as the result score of both the players A and B respectively.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the maximum score
// obtained by the players A and B
void findAmountPlayers(int arr[], int N)
{
    // Sort the array in descending order
    sort(arr, arr + N, greater<int>());

    // Stores the maximum amount of
    // money obtained by A
    int amountA = 0;

    // Stores the maximum amount of
    // money obtained by B
    int amountB = 0;

    // If the value of N is 1
    if (N == 1) {

        // Update the amountA
        amountA += arr[0];

        // Print the amount of money
        // obtained by both players
        cout << "(A : " << amountA << "), "
             << "(B : " << amountB << ")";
        return;
    }

    // Update the amountA
    amountA = arr[0];

    // Update the amountB
    amountB = arr[1];

    // Traverse the array arr[]
    for (int i = 2; i < N; i++) {

        // If i is an odd number
        if (i % 2 == 0) {

            // Update the amountB
            amountB += arr[i];
        }
        else {

            // Update the amountA
            amountA += arr[i];
        }
    }

    // Print the amount of money
    // obtained by both the players
    cout << "(A : " << amountA << ")\n"
         << "(B : " << amountB << ")";
}

// Driver Code
int main()
{
    int arr[] = { 1, 1, 1 };
    int N = sizeof(arr) / sizeof(arr[0]);
    findAmountPlayers(arr, N);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to find the maximum score
// obtained by the players A and B
static void findAmountPlayers(int[] arr, int N)
{

    // Sort the array in descending order
    Arrays.sort(arr);
    reverse(arr, N);

    // Stores the maximum amount of
    // money obtained by A
    int amountA = 0;

    // Stores the maximum amount of
    // money obtained by B
    int amountB = 0;

    // If the value of N is 1
    if (N == 1)
    {

        // Update the amountA
        amountA += arr[0];

        // Print the amount of money
        // obtained by both players
        System.out.println("(A : " + amountA + "), " +
                           "(B : " + amountB + ")");
        return;
    }

    // Update the amountA
    amountA = arr[0];

    // Update the amountB
    amountB = arr[1];

    // Traverse the array arr[]
    for(int i = 2; i < N; i++)
    {

        // If i is an odd number
        if (i % 2 == 0)
        {

            // Update the amountB
            amountB += arr[i];
        }
        else
        {

            // Update the amountA
            amountA += arr[i];
        }
    }

    // Print the amount of money
    // obtained by both the players
    System.out.println("(A : " + amountA + ")");
    System.out.println("(B : " + amountB + ")");
}

static void reverse(int a[], int n)
{
    int[] b = new int[n];
    int j = n;

    for(int i = 0; i < n; i++)
    {
        b[j - 1] = a[i];
        j = j - 1;
    }
}

// Driver code
public static void main(String []args)
{
    int[] arr = { 1, 1, 1 };
    int N = arr.length;

    findAmountPlayers(arr, N);
}
}

// This code is contributed by sanjoy_62

Python3

# Python3 program for the above approach

# Function to find the maximum score
# obtained by the players A and B
def findAmountPlayers(arr, N):
    # Sort the array in descending order
    arr = sorted(arr)[::-1]

    # Stores the maximum amount of
    # money obtained by A
    amountA = 0

    # Stores the maximum amount of
    # money obtained by B
    amountB = 0

    # If the value of N is 1
    if (N == 1):

        # Update the amountA
        amountA += arr[0]

        # Print the amount of money
        # obtained by both players
        print("(A :",mountA,"), (B :",str(amountB)+")")
        return


    # Update the amountA
    amountA = arr[0]

    # Update the amountB
    amountB = arr[1]

    # Traverse the array arr[]
    for i in range(2, N):

        # If i is an odd number
        if (i % 2 == 0):

            # Update the amountB
            amountB += arr[i]

        else:

            # Update the amountA
            amountA += arr[i]

    # Print amount of money
    # obtained by both the players
    print("(A :",str(amountA)+")\n(B :",str(amountB)+")")

# Driver Code
if __name__ == '__main__':
    arr = [1, 1, 1]
    N = len(arr)
    findAmountPlayers(arr, N)

# This code is contributed by mohit kumar 29.

C#

// C# program for the above approach
using System;
class GFG
{

    // Function to find the maximum score
    // obtained by the players A and B
    static void findAmountPlayers(int[] arr, int N)
    {

        // Sort the array in descending order
        Array.Sort(arr);
        Array.Reverse(arr);

        // Stores the maximum amount of
        // money obtained by A
        int amountA = 0;

        // Stores the maximum amount of
        // money obtained by B
        int amountB = 0;

        // If the value of N is 1
        if (N == 1) {

            // Update the amountA
            amountA += arr[0];

            // Print the amount of money
            // obtained by both players
            Console.WriteLine("(A : " + amountA + "), "
                              + "(B : " + amountB + ")");
            return;
        }

        // Update the amountA
        amountA = arr[0];

        // Update the amountB
        amountB = arr[1];

        // Traverse the array arr[]
        for (int i = 2; i < N; i++) {

            // If i is an odd number
            if (i % 2 == 0) {

                // Update the amountB
                amountB += arr[i];
            }
            else {

                // Update the amountA
                amountA += arr[i];
            }
        }

        // Print the amount of money
        // obtained by both the players
        Console.WriteLine("(A : " + amountA + ")");
        Console.WriteLine("(B : " + amountB + ")");
    }

    // Driver Code
    public static void Main()
    {
        int[] arr = { 1, 1, 1 };
        int N = arr.Length;
        findAmountPlayers(arr, N);
    }
}

// This code is contributed by ukasp.

Javascript

<script>
// Javascript program for the above approach

// Function to find the maximum score
// obtained by the players A and B
function findAmountPlayers(arr, N) {
    // Sort the array in descending order
    arr.sort((a, b) => b - a)

    // Stores the maximum amount of
    // money obtained by A
    let amountA = 0;

    // Stores the maximum amount of
    // money obtained by B
    let amountB = 0;

    // If the value of N is 1
    if (N == 1) {

        // Update the amountA
        amountA += arr[0];

        // Print the amount of money
        // obtained by both players
        document.write("(A : " + amountA + "), "
            + "(B : " + amountB + ")");
        return;
    }

    // Update the amountA
    amountA = arr[0];

    // Update the amountB
    amountB = arr[1];

    // Traverse the array arr[]
    for (let i = 2; i < N; i++) {

        // If i is an odd number
        if (i % 2 == 0) {

            // Update the amountB
            amountB += arr[i];
        }
        else {

            // Update the amountA
            amountA += arr[i];
        }
    }

    // Print the amount of money
    // obtained by both the players
    document.write("(A : " + amountA + ")<br>"
        + "(B : " + amountB + ")");
}

// Driver Code

let arr = [1, 1, 1];
let N = arr.length
findAmountPlayers(arr, N);

// This code is contributed _saurabh_jaiswal
</script>

Output:

(A : 1)
(B : 2)

Time Complexity: O(N*logN) because using sort function
Auxiliary Space: O(1)