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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 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.
Implementation
Example
Here are the programs that implements the above strategy −
#include <stdio.h>
#include <string.h>
// Function to find the winner based on the string pattern
int findWinner(char *s) {
int segments = 0;
// Count of consecutive '1' segments
for (int i = 0; i < strlen(s);) {
// Loop through the string
if (s[i] == '1') {
// If current character is '1'
segments++; // Increment segment count
while (i < strlen(s) && s[i] == '1') {
i++; // Move to the next character while it's '1'
}
}
i++; // Move to the next character
}
return segments % 2 == 0 ? 2 : 1; // If even segments, player 2 wins; else player 1 wins
}
int main() {
char s[] = "100101";
int winner = findWinner(s);
printf("Player %d wins\n", winner);
return 0;
}
Output
Player 1 wins
#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
public class Main {
static int findWinner(String s) {
int segments = 0;
// Count of consecutive '1' segments
for (int i = 0; i < s.length();) {
// Loop through the string
if (s.charAt(i) == '1') {
// If current character is '1'
segments++;
// Increment segment count
while (i < s.length() && s.charAt(i) == '1') {
i++; // Move to the next character while it's '1'
}
}
i++; // Move to the next character
}
return segments % 2 == 0 ? 2 : 1; // If even segments, player 2 wins; else player 1 wins
}
public static void main(String[] args) {
String s = "100101";
int winner = findWinner(s);
System.out.println("Player " + winner + " wins");
}
}
Output
Player 1 wins
def findWinner(s):
segments = 0 # Count of consecutive '1' segments
i = 0
while i < len(s): # Loop through the string
if s[i] == '1': # If current character is '1'
segments += 1 # Increment segment count
while i < len(s) and s[i] == '1':
i += 1 # Move to the next character while it's '1'
i += 1 # Move to the next character
return 2 if segments % 2 == 0 else 1 # If even segments, player 2 wins; else player 1 wins
def main():
s = "100101"
winner = findWinner(s)
print(f"Player {winner} wins")
if __name__ == "__main__":
main()
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 code implementation, and elaborated on the concept using an example.
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