A Binary String Game

Given a Binary String S. The task is to determine the winner of the game when two players play a game optimally with the string as per the given conditions:

• Player 1 always starts first.
• Two players take turns choosing a whole block of consecutive equal characters and deleting them from a given binary String S.
• Player 1 can choose only an odd number of consecutive equal characters and Player 2 can choose only an even number of consecutive equal characters. The player may choose nothing and count it as their turn only if it is impossible to choose anything.
• After all the characters are removed, the player with maximum scores wins the game and if scores are equal then print “-1”

Input: S = “1110011001010”
Output: Player 1
Explanation:
The selected characters will be in bold and Player 1’s score is Score_1 and Player 2’s score is Score_2 :
Turn 1 : (Player 1) “1110011001010” → “0011001010” Score_1 = 3
Turn 2 : (Player 2) “0011001010” → “00001010” Score_2 = 2
Turn 3 : (Player 1) “00001010”→ “0000010” Score_1 = 4
Turn 4: (Player 2) “0000010” 
He cannot do anything as only one ‘1’ is present which is an odd number. 
Also, he can’t choose the ‘0’s as they are odd (5 and 1), Therefore, Score_2 =2
Turn 5:(Player 1) “0000010”→ “000000” Score_1=5
Turn 6:(Player 2) “000000” → “” Score_2 = 2 (No ‘1’ was deleted in this turn)

Final scores: Score_1 = 5 and Score_2 = 2
Therefore, Player 1 wins.

Input : S = “11111101”
Output: Player 2
Explanation: 
Turn 1 : (Player 1) “11111101” → “1111110” Score_1 = 3
Turn 2 : (Player 2) “1111110” → “0” Score_2 = 6
Turn 3 : (Player 1) “0” → “” Score_1 = 3

Final scores: Score_1 = 3 and Score_2 = 6
Therefore, Player 2 wins.

Approach: 

1. If we observe this game carefully, we understand that the only consecutive 1s are contributing to the scores of these players.
2. Create a list to store the lengths of the consecutive 1s in the string.
3. Sort the list in descending order.
4. Now iterate over the list and if the list element is odd it will be added to the score of the Player 1 and if it is even it will be added to the score of the Player 2.
5. Now if the score of the Player 1 is greater than the score of the Player 2 then print “Player 1” and if the score of the Player 2 is greater than the score of the Player 1 then print “Player 2”.
6. Print “-1” if there is a tie i.e., scores are the same.

Below is the implementation of the above approach.

C++

// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;

// Function to return the result of
// the game
string gameMax(string S)
{

    // length of the string
    int N = S.length();

    // List to maintain the lengths of
    // consecutive '1's in the string
    vector<int> list;

    // Variable that keeps a track of
    // the current length of the block
    // of consecutive '1's
    int one = 0;

    for(int i = 0; i < N; i++)
    {
        if (S[i] == '1')
        {
            one++;
        }
        else
        {

            // Adds non-zero lengths
            if (one != 0)
            {
                list.push_back(one);
            }
            one = 0;
        }
    }

    // This takes care of the case
    // when the last character is '1'
    if (one != 0)
    {
        list.push_back(one);
    }

    // Sorts the lengths in
    // descending order
    sort(list.begin(), list.end(),
         greater<int>());

    // Scores of the 2 players
    int score_1 = 0, score_2 = 0;

    for(int i = 0; i < list.size(); i++)
    {

        // For player 1
        if (list[i] % 2 == 1)
        {
            score_1 += list[i];
        }

        // For player 2
        else
        {
            score_2 += list[i];
        }
    }

    // In case of a tie
    if (score_1 == score_2)
        return "-1";

    // Print the result
    return (score_1 > score_2) ? "Player 1" :
                                 "Player 2";
}

// Driver Code
int main()
{

    // Given string S
    string S = "11111101";

    // Function call
    cout << gameMax(S);
}

// This code is contributed by rutvik_56

Java

// Java program for the above approach
import java.io.*;
import java.util.*;

class GFG {

    // Function to return the result of
    // the game
    public static String gameMax(String S)
    {
        // length of the string
        int N = S.length();

        // List to maintain the lengths of
        // consecutive '1's in the string
        List<Integer> list = new ArrayList<>();

        // Variable that keeps a track of
        // the current length of the block
        // of consecutive '1's
        int one = 0;

        for (int i = 0; i < N; i++) {

            if (S.charAt(i) == '1') {
                one++;
            }
            else {

                // Adds non-zero lengths
                if (one != 0) {
                    list.add(one);
                }
                one = 0;
            }
        }

        // This takes care of the case
        // when the last character is '1'
        if (one != 0) {
            list.add(one);
        }

        // Sorts the lengths in
        // descending order
        Collections.sort(list,
                         Collections.reverseOrder());

        // Scores of the 2 players
        int score_1 = 0, score_2 = 0;

        for (int i = 0; i < list.size(); i++) {

            // For player 1
            if (list.get(i) % 2 == 1) {
                score_1 += list.get(i);
            }

            // For player 2
            else {
                score_2 += list.get(i);
            }
        }

        // In case of a tie
        if (score_1 == score_2)
            return "-1";

        // Print the result
        return (score_1 > score_2) ? "Player 1"
                                   : "Player 2";
    }

    // Driver Code
    public static void main(String[] args)
    {
        // Given string S
        String S = "11111101";

        // Function Call
        System.out.println(gameMax(S));
    }
}

Python3

# Python3 program for
# the above approach

# Function to return the
# result of the game
def gameMax(S):

    # Length of the string
    N = len(S)

    # List to maintain the lengths of
    # consecutive '1's in the string
    list = []

    # Variable that keeps a track of
    # the current length of the block
    # of consecutive '1's
    one = 0

    for i in range(N):
        if(S[i] == '1'):
            one += 1
        else:

            # Adds non-zero lengths
            if(one != 0):
                list.append(one)
            one = 0

    # This takes care of the case
    # when the last character is '1'
    if(one != 0):
        list.append(one)

    # Sorts the lengths in
    # descending order
    list.sort(reverse = True)

    # Scores of the 2 players
    score_1 = 0
    score_2 = 0

    for i in range(len(list)):

        # For player 1
        if(list[i] % 2 == 1):
            score_1 += list[i]

        # For player 2
        else:
            score_2 += list[i]

    # In case of a tie
    if(score_1 == score_2):
        return '-1'

    # Print the result
    if(score_1 > score_2):
        return "Player 1"
    else:
        return "Player 2"

# Driver Code

# Given string S
S = "11111101"

# Function call
print(gameMax(S))

# This code is contributed by avanitrachhadiya2155

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

// Function to return the result of
// the game
public static String gameMax(String S)
{

    // length of the string
    int N = S.Length;

    // List to maintain the lengths of
    // consecutive '1's in the string
    List<int> list = new List<int>();

    // Variable that keeps a track of
    // the current length of the block
    // of consecutive '1's
    int one = 0;

    for(int i = 0; i < N; i++)
    {
        if (S[i] == '1')
        {
            one++;
        }
        else
        {

            // Adds non-zero lengths
            if (one != 0)
            {
                list.Add(one);
            }
            one = 0;
        }
    }

    // This takes care of the case
    // when the last character is '1'
    if (one != 0)
    {
        list.Add(one);
    }

    // Sorts the lengths in
    // descending order
    list.Sort();
    list.Reverse();

    // Scores of the 2 players
    int score_1 = 0, score_2 = 0;

    for(int i = 0; i < list.Count; i++)
    {

        // For player 1
        if (list[i] % 2 == 1)
        {
            score_1 += list[i];
        }

        // For player 2
        else
        {
            score_2 += list[i];
        }
    }

    // In case of a tie
    if (score_1 == score_2)
        return "-1";

    // Print the result
    return (score_1 > score_2) ?
         "Player 1" : "Player 2";
}

// Driver Code
public static void Main(String[] args)
{

    // Given string S
    String S = "11111101";

    // Function Call
    Console.WriteLine(gameMax(S));
}
}

// This code is contributed by Amit Katiyar

Javascript

<script>
// javascript program for the
// above approach

// Function to return the result of
// the game
function gameMax(S)
{

    // length of the string
    let N = S.length;

    // List to maintain the lengths of
    // consecutive '1's in the string
    let list = [];

    // Variable that keeps a track of
    // the current length of the block
    // of consecutive '1's
    let one = 0;

    for(let i = 0; i < N; i++)
    {
        if (S[i] == '1')
        {
            one++;
        }
        else
        {

            // Adds non-zero lengths
            if (one != 0)
            {
                list.push(one);
            }
            one = 0;
        }
    }

    // This takes care of the case
    // when the last character is '1'
    if (one != 0)
    {
        list.push(one);
    }

    // Sorts the lengths in
    // descending order
    list.sort();
    list.reverse();

    // Scores of the 2 players
    let score_1 = 0, score_2 = 0;

    for(let i = 0; i < list.length; i++)
    {

        // For player 1
        if (list[i] % 2 == 1)
        {
            score_1 += list[i];
        }

        // For player 2
        else
        {
            score_2 += list[i];
        }
    }

    // In case of a tie
    if (score_1 == score_2)
        return "-1";

    // Print the result
    return (score_1 > score_2) ?
         "Player 1" : "Player 2";
}

// Driver Code

    // Given string S
    let S = "11111101";

    // Function Call
    document.write(gameMax(S));

   // This code is contributed by target_2.
</script>

Output: 

Player 2

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