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Find the winner of the Game of removing odd or replacing even array elements
  • Last Updated : 12 Nov, 2020

Given an array arr[] consisting of N integers. Two players, Player 1 and Player 2, play turn-by-turn in which one player can may either of the following two moves:

  • Convert even array element to any other integer.
  • Remove odd array element.

The player who is not able to make any move loses the game. The task is to print the winner of the game. Print -1 if the game may go on forever.

Examples:

Input: arr[] = {3, 1, 9, 7}
Output: Player 2
Explanation: Since all array elements are odd, no conversion is possible.
Turn 1: Player 1 deletes 3.
Turn 2: Player 2 deletes 1.
Turn 3: Player 1 deletes 9.
Turn 4: Player 2 deletes 7. Now, Player 1 has no moves left. Therefore, Player 2 wins the game.

Input: arr[]={4, 8}
Output: -1



Approach: Follow the steps below to solve the problem:

  • Traverse the array.
  • Count the number of even and odd elements present in the array.
  • If the number of even elements is zero, perform the following operations: 
    • If the count of odd is even, then Player 2 will win the game.
    • Otherwise, Player 1 will win the game.
  • If the count of odd is odd and only one even element is present in the array, then Player 1 will win the game.
  • Otherwise, there will be a draw every time.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to evaluate the
// winner of the game
void findWinner(int arr[], int N)
{
    // Stores count of odd
    // array elements
    int odd = 0;
 
    // Stores count of even
    // array elements
    int even = 0;
 
    // Traverse the array
    for (int i = 0; i < N; i++) {
 
        // If arraay element is odd
        if (arr[i] % 2 == 1) {
 
            odd++;
        }
        // Otherwise
        else {
 
            even++;
        }
    }
 
    // If count of even is zero
    if (even == 0) {
 
        // If count of odd is even
        if (odd % 2 == 0) {
 
            cout << "Player 2" << endl;
        }
 
        // If count of odd is odd
        else if (odd % 2 == 1) {
 
            cout << "Player 1" << endl;
        }
    }
 
    // If count of odd is odd and
    // count of even is one
    else if (even == 1 && odd % 2 == 1) {
 
        cout << "Player 1" << endl;
    }
 
    // Otherwise
    else {
 
        cout << -1 << endl;
    }
}
 
// Driver Code
int main()
{
    int arr[] = { 3, 1, 9, 7 };
    int N = sizeof(arr)
            / sizeof(arr[0]);
 
    findWinner(arr, N);
 
    return 0;
}

Java




// Java program for the above approach
import java.util.*;
 
class GFG{
    
// Function to evaluate the
// winner of the game
static void findWinner(int arr[], int N)
{
     
    // Stores count of odd
    // array elements
    int odd = 0;
 
    // Stores count of even
    // array elements
    int even = 0;
 
    // Traverse the array
    for(int i = 0; i < N; i++)
    {
         
        // If arraay element is odd
        if (arr[i] % 2 == 1)
        {
            odd++;
        }
         
        // Otherwise
        else
        {
            even++;
        }
    }
 
    // If count of even is zero
    if (even == 0)
    {
         
        // If count of odd is even
        if (odd % 2 == 0)
        {
            System.out.println("Player 2");
        }
 
        // If count of odd is odd
        else if (odd % 2 == 1)
        {
            System.out.println("Player 1");
        }
    }
 
    // If count of odd is odd and
    // count of even is one
    else if (even == 1 && odd % 2 == 1)
    {
        System.out.println("Player 1");
    }
 
    // Otherwise
    else
    {
        System.out.println(-1);
    }
}
 
// Driver Code
public static void main(String args[])
{
    int arr[] = { 3, 1, 9, 7 };
    int N = arr.length;
     
    findWinner(arr, N);
}
}
 
// This code is contributed by ipg2016107

Python3




# Python3 program for the above approach
 
# Function to evaluate the
# winner of the game
def findWinner(arr, N):
     
    # Stores count of odd
    # array elements
    odd = 0
 
    # Stores count of even
    # array elements
    even = 0
 
    # Traverse the array
    for i in range(N):
         
        # If arraay element is odd
        if (arr[i] % 2 == 1):
            odd += 1
 
        # Otherwise
        else:
            even += 1
 
    # If count of even is zero
    if (even == 0):
         
        # If count of odd is even
        if (odd % 2 == 0):
            print("Player 2")
 
        # If count of odd is odd
        elif (odd % 2 == 1):
            print("Player 1")
 
    # If count of odd is odd and
    # count of even is one
    elif (even == 1 and odd % 2 == 1):
        print("Player 1")
 
    # Otherwise
    else:
        print(-1)
 
# Driver code
if __name__ == '__main__':
 
    arr = [ 3, 1, 9, 7 ]
    N = len(arr)
 
    findWinner(arr, N)
 
# This code is contributed by Shivam Singh

C#




// C# program for the above approach
using System;
 
class GFG{
    
// Function to evaluate the
// winner of the game
static void findWinner(int []arr, int N)
{
     
    // Stores count of odd
    // array elements
    int odd = 0;
 
    // Stores count of even
    // array elements
    int even = 0;
 
    // Traverse the array
    for(int i = 0; i < N; i++)
    {
         
        // If arraay element is odd
        if (arr[i] % 2 == 1)
        {
            odd++;
        }
         
        // Otherwise
        else
        {
            even++;
        }
    }
 
    // If count of even is zero
    if (even == 0)
    {
         
        // If count of odd is even
        if (odd % 2 == 0)
        {
            Console.WriteLine("Player 2");
        }
 
        // If count of odd is odd
        else if (odd % 2 == 1)
        {
            Console.WriteLine("Player 1");
        }
    }
 
    // If count of odd is odd and
    // count of even is one
    else if (even == 1 && odd % 2 == 1)
    {
        Console.WriteLine("Player 1");
    }
 
    // Otherwise
    else
    {
        Console.WriteLine(-1);
    }
}
 
// Driver Code
public static void Main()
{
    int []arr = { 3, 1, 9, 7 };
    int N = arr.Length;
     
    findWinner(arr, N);
}
}
 
// This code is contributed by bgangwar59
Output: 
Player 2










 

Time Complexity: O(N)  
Auxiliary Space: O(1)

 

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