Optimal Strategy for a Game | Special Gold Coin

Given a row of silver coins among which a special gold coin is present. Two players play the game, and with each move, a player has to remove a coin from either the left or the right end of the row and the player who removes the special coin wins the game. The task is to find the winner of the game.

Examples:

Input: str = “GSSS”
Output: First
The first player directly removes the special gold coin.



Input: str = “SGS”
Output: Second
Irrespective of which coin the first player removes, the special
gold coin becomes exposed and is removed by the second player.

Approach: It can be observed by taking a few examples that if the count of the silver coins is odd then the first player wins the game otherwise the player two wins the game. In special case when Gold coin is in corner, First player will be the winner regardless the count of silver coins.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the
// winner of the game
string getWinner(string str, int len)
{
      
    // To store the count of silver coins
    int total = 0;
      
    if(str[0]=='G' ||str[len-1]=='G')
        return "First";
    else{
        for (int i = 0; i < len; i++) {
  
            // Update the position of
           // the gold coin
            if (str[i] == 'S') {
                total++;
            }
        }
  
        // First player will win the game
        if ((total % 2) == 1)
            return "First";
        return "Second";
    }
}
  
// Driver code
int main()
{
    string str = "GSSS";
    int len = str.length();
  
    cout << getWinner(str, len);
  
    return 0;
}

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Java

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// Java implementation of the approach
import java.util.*;
  
class GFG
{
  
// Function to return the
// winner of the game
static String getWinner(String str, int len)
{
  
    // To store the count of silver coins
    int total = 0;
    for (int i = 0; i < len; i++) 
    {
  
        // Update the position of
        // the gold coin
        if (str.charAt(i) == 'S')
        {
            total++;
        }
    }
  
    // First player will win the game
    if ((total % 2) == 1)
        return "First";
    return "Second";
}
  
// Driver code
public static void main(String []args)
{
    String str = "GSSS";
    int len = str.length();
  
    System.out.println(getWinner(str, len));
}
}
  
// This code is contributed by Surendra_Gangwar

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Python3

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# Python3 implementation of the approach 
  
# Function to return the 
# winner of the game 
def getWinner(string, length) :
  
    # To store the count of silver coins 
    total = 0
    for i in range(length) : 
  
        # Update the position of 
        # the gold coin 
        if (string[i] == 'S') :
            total += 1
  
    # First player will win the game 
    if ((total % 2) == 1) :
        return "First"
    return "Second"
  
# Driver code 
if __name__ == "__main__"
  
    string = "GSSS"
    length = len(string); 
  
    print(getWinner(string, length)); 
      
# This code is contributed by kanugargng

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Output:

First

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