Ways to remove one element from a binary string so that XOR becomes zero

• Difficulty Level : Easy
• Last Updated : 29 Apr, 2021

Given a binary string, task is to erase exactly one integer in the array so that the XOR of the remaining numbers is zero. The task is to count number of ways to remove one element so that XOR of that string become ZERO.
Examples :

Input : 10000
Output : 1
We only have 1 ways to

Input : 10011
Output : 3
There are 3 ways to make XOR 0. We
can remove any of the three 1's.

Input : 100011100
Output : 5
There are 5 ways to make XOR 0. We
can remove any of the give 0's

A simple solution is to one by one remove an element, then compute XOR of remaining string. And count occurrences where removing an element makes XOR 0.
An efficient solution is based on following fact. If count of 1s is odd, then we must remove a 1 to make count 0 and we can remove any of the 1s. If count of 1s is even, then XOR is 0, We can remove any of the 0s and XOR will remain 0.

C++

 // C++ program to count number of ways to// remove an element so that XOR of remaining// string becomes 0.#include using namespace std; // Return number of ways in which XOR become ZERO// by remove 1 elementint xorZero(string str){    int one_count = 0, zero_count = 0;    int n = str.length();     // Counting number of 0 and 1    for (int i = 0; i < n; i++)        if (str[i] == '1')            one_count++;        else            zero_count++;         // If count of ones is even    // then return count of zero    // else count of one    if (one_count % 2 == 0)        return zero_count;    return one_count;} // Driver Codeint main(){    string str = "11111";    cout << xorZero(str) << endl;    return 0;}

Java

 // Java program to count number of ways to// remove an element so that XOR of remaining// string becomes 0.import java.util.*;  class CountWays{    // Returns number of ways in which XOR become    // ZERO by remove 1 element    static int xorZero(String s)    {        int one_count = 0, zero_count = 0;        char[] str=s.toCharArray();        int n = str.length;              // Counting number of 0 and 1        for (int i = 0; i < n; i++)            if (str[i] == '1')                one_count++;            else                zero_count++;                  // If count of ones is even        // then return count of zero        // else count of one        if (one_count % 2 == 0)            return zero_count;        return one_count;    }     // Driver Code to test above function    public static void main(String[] args)    {        String s = "11111";        System.out.println(xorZero(s));     }} // This code is contributed by Mr. Somesh Awasthi

Python3

 # Python 3 program to count number of# ways to remove an element so that# XOR of remaining string becomes 0. # Return number of ways in which XOR# become ZERO by remove 1 elementdef xorZero(str):    one_count = 0    zero_count = 0    n = len(str)     # Counting number of 0 and 1    for i in range(0, n, 1):        if (str[i] == '1'):            one_count += 1        else:            zero_count += 1         # If count of ones is even    # then return count of zero    # else count of one    if (one_count % 2 == 0):        return zero_count    return one_count # Driver Codeif __name__ == '__main__':    str = "11111"    print(xorZero(str)) # This code is contributed by# Surendra_Gangwar

C#

 // C# program to count number// of ways to remove an element// so that XOR of remaining// string becomes 0.using System; class GFG{    // Returns number of ways    // in which XOR become    // ZERO by remove 1 element    static int xorZero(string s)    {        int one_count = 0,            zero_count = 0;                 int n = s.Length;             // Counting number of 0 and 1        for (int i = 0; i < n; i++)            if (s[i] == '1')                one_count++;            else                zero_count++;                 // If count of ones is even        // then return count of zero        // else count of one        if (one_count % 2 == 0)            return zero_count;        return one_count;    }     // Driver Code    public static void Main()    {        string s = "11111";        Console.WriteLine(xorZero(s));    }} // This code is contributed by anuj_67.



Javascript



Output :

5

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