# Find the player with least 0s after emptying a Binary String by removing non-empty substrings

In this article, we'll examine an interesting problem from the field of string manipulation and game theory: "Find the player with the least 0s after emptying a binary string by removing non-empty substrings". This problem explores the concept of competitive game playing between two players using binary strings. Our goal is to identify the player who ends up with the least number of 0s after the game ends. We'll discuss the problem, provide a C++ code implementation, and clarify the concept with an example.

## Understanding the Problem Statement

Two players are given a binary string, and they play a game in turns. In each turn, a player removes a non-empty substring that contains at least one '1'. The game ends when the string becomes empty or no '1' is left in the string. The player who is unable to make a move loses the game. The task is to find the player who ends up with the least number of 0s.

## Approach

To solve this problem, we need to count the number of segments separated by '0's that have at least one '1'. The player who starts the game will always choose the segment with the most '1's. Therefore, the first player can always ensure that they remove more '1's than the second player, except when the number of segments is even. In that case, both players can remove an equal number of '1's.

## C++ Implementation

### Example

Here is the C++ code that implements the above strategy:

#include<bits/stdc++.h>
using namespace std;

int findWinner(string s) {
int segments = 0;
for (int i = 0; i < s.size();) {
if (s[i] == '1') {
segments++;
while (i < s.size() && s[i] == '1') {
i++;
}
}
i++;
}
return segments % 2 == 0 ? 2 : 1;
}

int main() {
string s = "100101";
int winner = findWinner(s);
cout << "Player " << winner << " wins";
return 0;
}


### Output

Player 1 wins


This code iterates over the string, counts the number of segments, and then checks if the number of segments is even or odd to decide the winner.

## Test Case

Let's consider the binary string "100101". The segments in this string are "1", "1", and "1". Since the number of segments is odd, the first player will win the game, as they will be able to remove more '1's than the second player.

## Conclusion

In this article, we investigated the problem of finding the player with the least 0s after emptying a binary string by removing non-empty substrings. The problem presents a fascinating crossover of string manipulation and game theory. We explored the problem, outlined an approach to solve it, provided a C++ code implementation, and elaborated on the concept using an example.

Updated on: 17-May-2023

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