Game of replacing array elements

There are two players A and B who are interested in playing a game of numbers. In each move a player pick two distinct number, let’s say a1 and a2 and then replace all a2 by a1 or a1 by a2. They stop playing game if any one of them is unable to pick two number and the player who is unable to pick two distinct number in an array, looses the game. First player always move first and then second. Task is to find which player wins.

Examples:

Input :  arr[] = { 1, 3, 3, 2,, 2, 1 }
Output : Player 2 wins
Explanation:
First plays always looses irrespective
of the numbers chosen by him. For example,
say first player picks ( 1 & 3) 
replace all 3 by 1  
Now array Become { 1, 1, 1, 2, 2, 1 }
Then second player picks ( 1  2 )
either he replace 1 by 2 or 2 by 1 
Array Become { 1, 1, 1, 1, 1, 1 }
Now first player is not able to choose.

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

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

From above examples, we can observe that if number of count of distinct element is even, first player always wins. Else second player wins.

Lets take an another example :

  int arr[] =  1, 2, 3, 4, 5, 6

Here number of distinct element is even(n). If player 1 pick any two number lets say (4, 1), then we left with n-1 distinct element. So player second left with n-1 distinct element. This precess go on until distinct element become 1. Here n = 6

Player   :  P1    p2    P1   p2    P1     P2    
distinct : [n, n-1, n-2, n-3, n-4, n-5 ]  
 
"At this point no distinct element left, 
so p2 is unable to pick two Dis element."

Below implementation of above idea :

C++

// CPP program for Game of Replacement 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function return which player win the game 
int playGame(int arr[], int n) 
{ 
    // Create hash that will stores 
    // all distinct element 
    unordered_set<int> hash; 
  
    // Traverse an array element 
    for (int i = 0; i < n; i++) 
        hash.insert(arr[i]); 
  
    return (hash.size() % 2 == 0 ? 1 : 2); 
} 
  
// Driver Function 
int main() 
{ 
    int arr[] = { 1, 1, 2, 2, 2, 2 }; 
    int n = sizeof(arr) / sizeof(arr[0]); 
  
    cout << "Player " << playGame(arr, n) << " Wins" << endl; 
    return 0; 
} 

Java

// Java program for Game of Replacement  
import java.util.HashSet; 
public class GameOfReplacingArrayElements  
{ 
    // Function return which player win the game  
    public static int playGame(int arr[]) 
    { 
        // Create hash that will stores  
        // all distinct element  
        HashSet<Integer> set=new HashSet<>(); 
  
        // Traverse an array element  
        for(int i:arr) 
            set.add(i); 
        return (set.size()%2==0)?1:2; 
    } 
  
    public static void main(String args[]) { 
        int arr[] = { 1, 1, 2, 2, 2, 2 };  
        System.out.print("Player "+playGame(arr)+" wins"); 
    } 
} 
//This code is contributed by Gaurav Tiwari 

Python3

# Python program for Game of Replacement  
  
# Function return which player win the game  
def playGame(arr, n): 
  
    # Create hash that will stores  
    # all distinct element  
    s = set() 
  
    # Traverse an array element  
    for i in range(n): 
        s.add(arr[i]) 
    return 1 if len(s) % 2 == 0 else 2
  
# Driver code 
arr = [1, 1, 2, 2, 2, 2] 
n = len(arr) 
print("Player",playGame(arr, n),"Wins") 
  
# This code is contributed by Shrikant13 

C#

// C# program for Game of Replacement  
using System; 
using System.Collections.Generic; 
  
public class GameOfReplacingArrayElements  
{ 
    // Function return which player win the game  
    public static int playGame(int []arr) 
    { 
        // Create hash that will stores  
        // all distinct element  
        HashSet<int> set = new HashSet<int>(); 
  
        // Traverse an array element  
        foreach(int i in arr) 
            set.Add(i); 
        return (set.Count % 2 == 0) ? 1 : 2; 
    } 
  
    // Driver code 
    public static void Main(String []args) 
    { 
        int []arr = { 1, 1, 2, 2, 2, 2 };  
        Console.Write("Player " + playGame(arr) + " wins"); 
    } 
} 
  
// This code has been contributed by 29AjayKumar 

Output:

Player 1 Wins

Time Complexity : O(n)

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes

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

C++

Java

Python3

C#

Recommended Posts: