Three players P1, P2 and P3 are playing a game. But at a time only two players can play the game, so they decided, at a time two players will play the game and one will spectate. When one game ends, the one who lost the game becomes the spectator in the next game and the one who was spectating plays against the winner. There cannot be any draws in any game. Player P1 and P2 will play the first game. Input is the number of games played n and in next line winner of n games.

Examples:

Input : No. of Games : 4 Winner of the Game Gi : 1 1 2 3 Output : YES Explanation : Game1 : P1 vs P2 : P1 wins Game2 : P1 vs P3 : P1 wins Game3 : P1 vs P2 : P2 wins Game4 : P3 vs P2 : P3 winsNone of the winners were invalidInput : No. of Games : 2 Winner of the Game Gi : 2 1 Output : NO Explanation : Game1 : P1 vs P2 : P2 wins Game2 : P2 vs P3 : P1 wins (Invalid winner)In Game2 P1 is spectator

**Approach :**

Start with P1 and P2 and continue the game while making the loser new spectator by subtracting the current spectator and winner from total sum of three players i.e. 6. An invalid entry will halt the process.

Below is the implementation for the above approach:

## C++

// CPP program to check if the game // is valid #include <bits/stdc++.h> using namespace std; string check_valid(int a[], int n) { // starting with player P1 and P2 // so making P3 spectator int spec = 3; for (int i = 0; i < n; i++) { // If spectator wins a game // then its not valid if (a[i] == spec) { return "Invalid"; } // subtracting the current spectator // and winner from total sum 6 which // makes losing player spectator spec = 6 - a[i] - spec; } // None of the winner is found spectator. return "Valid"; } // Driver program to test above functions int main() { int n = 4; int a[n] = {1, 1, 2, 3}; cout << check_valid(a, n); return 0; }

## Java

// java program to check if the game // is valid import java.io.*; class GFG { static String check_valid(int a[], int n) { // starting with player P1 and P2 // so making P3 spectator int spec = 3; for (int i = 0; i < n; i++) { // If spectator wins a game // then its not valid if (a[i] == spec) { return "Invalid"; } // subtracting the current spectator // and winner from total sum 6 which // makes losing player spectator spec = 6 - a[i] - spec; } // None of the winner is found spectator. return "Valid"; } // Driver program to test above functions public static void main (String[] args) { int a[] = {1, 1, 2, 3}; int n = a.length; System.out.println(check_valid(a, n)); } } // This code is contributed by vt_m

## Python3

# Python3 code to check if the game # is valid def check_valid( a , n ): # starting with player P1 and P2 # so making P3 spectator spec = 3 for i in range(n): # If spectator wins a game # then its not valid if a[i] == spec: return "Invalid" # subtracting the current spectator # and winner from total sum 6 which # makes losing player spectator spec = 6 - a[i] - spec # None of the winner is found spectator. return "Valid" # Driver code to test above functions n = 4 a = [1, 1, 2, 3] print(check_valid(a, n)) # This code is contributed by "Sharad_Bhardwaj".

## C#

// C# program to check if the game // is valid using System; class GFG { static String check_valid(int []a, int n) { // starting with player P1 and P2 // so making P3 spectator int spec = 3; for (int i = 0; i < n; i++) { // If spectator wins a game // then its not valid if (a[i] == spec) { return "Invalid"; } // subtracting the current spectator // and winner from total sum 6 which // makes losing player spectator spec = 6 - a[i] - spec; } // None of the winner is found spectator. return "Valid"; } // Driver program public static void Main () { int []a = {1, 1, 2, 3}; int n = a.Length; Console.WriteLine(check_valid(a, n)); } } // This code is contributed by vt_m

Output:

Valid

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.