Optimal Strategy for a Game | Special Gold Coin (original) (raw)

Last Updated : 24 Mar, 2023

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 are the steps to implement the above approach:

• Define a function getWinner that takes a string str and an integer len as input.
• Initialize a variable total to 0 to keep track of the number of silver coins.
• Check if the first or last character of the string is 'G'. If it is, the first player can pick up the gold coin on the first move and win. Return "First" in this case.
• Otherwise, loop through each character in the string and increment the total variable every time a silver coin is encountered.
• If the number of silver coins is odd, the first player can pick up the last silver coin and win. Return "First" in this case.
• Otherwise, if the number of silver coins is even, the second player can always win by picking up the last silver coin after the first player's move. Return "Second" in this case.
• If none of the above conditions are met, the function returns "Second" by default.
• In the main function, define a string str and its length len.
• Call the getWinner function with str and len as arguments and print the output.

Below is the implementation of the above approach:

C++ `

// 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;

}

Java

// 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

Python3

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

C#

// C# implementation of the approach using System;

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[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;

Console.WriteLine(getWinner(str, len));

} }

// This code is contributed by rrrtnx.

JavaScript

`

Time Complexity: O(n) where n is the size of the string.

Auxiliary Space: O(1)