Count of cyclic permutations having XOR with other binary string as 0

Given two binary strings A and B. Let S be set of all the cyclic permutations of string B. The task is to find how many strings in set S when XORed with A give 0 as result.

Examples:

Input: A = “101”, B = “101”
Output: 1
S = {“101”, “011”, “110”}
Only “101” XOR “101” = 0

Input: A = “111”, B = “111”
Output: 3



Approach: Concatenate B with B so that it contains all of it’s cyclic permutations as sub-strings. Now the problem is reduced to find the number of occurrences of pattern A in string B which can be solved using Z algorithm (for linear time pattern searching).

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find bitwise XOR between binary
// string A and all the cyclic permutations
// of binary string B
#include <bits/stdc++.h>
using namespace std;
  
// Implementation of Z-algorithm
// for linear time pattern searching
void compute_z(string s, int z[])
{
    int l = 0, r = 0;
    int n = s.length();
    for (int i = 1; i <= n - 1; i++) {
        if (i > r) {
            l = i, r = i;
            while (r < n && s[r - l] == s[r])
                r++;
            z[i] = r - l;
            r--;
        }
        else {
            int k = i - l;
            if (z[k] < r - i + 1) {
                z[i] = z[k];
            }
            else {
                l = i;
                while (r < n && s[r - l] == s[r])
                    r++;
                z[i] = r - l;
                r--;
            }
        }
    }
}
  
// Function to get the count of the cyclic
// permutations of b that given 0 when XORed with a
int countPermutation(string a, string b)
{
    // concatenate b with b
    b = b + b;
  
    // new b now contains all the cyclic
    // permutations of old b as it's sub-strings
    b = b.substr(0, b.size() - 1);
  
    // concatenate pattern with text
    int ans = 0;
    string s = a + "$" + b;
    int n = s.length();
  
    // Fill z array used in Z algorithm   
    int z[n];
    compute_z(s, z);
  
    for (int i = 1; i <= n - 1; i++) {
  
        // pattern occurs at index i since
        // z value of i equals pattern length
        if (z[i] == a.length())
            ans++;
    }
    return ans;
}
  
// Driver code
int main()
{
    string a = "101";
    string b = "101";
  
    cout << countPermutation(a, b) << endl;
  
    return 0;
}

chevron_right






                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// Java program to find bitwise XOR between binary 


// string A and all the cyclic permutations 


// of binary string B 


  


public class GFG{ 


      


    // Implementation of Z-algorithm 


    // for linear time pattern searching 


    static void compute_z(String s, int z[]) 


    { 


        int l = 0, r = 0; 


        int n = s.length(); 


        for (int i = 1; i <= n - 1; i++) { 


            if (i > r) { 


                l = i; 


                r = i; 


                while (r < n && s.charAt(r - l) == s.charAt(r)) 


                    r++; 


                z[i] = r - l; 


                r--; 


            } 


            else { 


                int k = i - l; 


                if (z[k] < r - i + 1) { 


                    z[i] = z[k]; 


                } 


                else { 


                    l = i; 


                    while (r < n && s.charAt(r - l) == s.charAt(r)) 


                        r++; 


                    z[i] = r - l; 


                    r--; 


                } 


            } 


        } 


    } 


      


    // Function to get the count of the cyclic 


    // permutations of b that given 0 when XORed with a 


    static int countPermutation(String a, String b) 


    { 


        // concatenate b with b 


        b = b + b; 


        // new b now contains all the cyclic 


        // permutations of old b as it's sub-strings 


        b = b.substring(0, b.length() - 1); 


      


        // concatenate pattern with text 


        int ans = 0; 


        String s = a + "$" + b; 


        int n = s.length(); 


      


        // Fill z array used in Z algorithm    


        int z[] = new int[n]; 


        compute_z(s, z); 


      


        for (int i = 1; i <= n - 1; i++) { 


      


            // pattern occurs at index i since 


            // z value of i equals pattern length 


            if (z[i] == a.length()) 


                ans++; 


        } 


        return ans; 


    } 


      


      


    // Driver Code 


     public static void main(String []args){ 


           


               String a = "101"; 


               String b = "101"; 


               System.out.println(countPermutation(a, b)) ; 


     } 


     // This code is contributed by ANKITRAI1 


} 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// C# program to find bitwise XOR between  


// binary string A and all the cyclic  


// permutations of binary string B  


using System; 


  


class GFG 


{ 


  


// Implementation of Z-algorithm  


// for linear time pattern searching  


public static void compute_z(string s,  


                             int[] z) 


{ 


    int l = 0, r = 0; 


    int n = s.Length; 


    for (int i = 1; i <= n - 1; i++) 


    { 


        if (i > r) 


        { 


            l = i; 


            r = i; 


            while (r < n && s[r - l] == s[r]) 


            { 


                r++; 


            } 


            z[i] = r - l; 


            r--; 


        } 


        else


        { 


            int k = i - l; 


            if (z[k] < r - i + 1) 


            { 


                z[i] = z[k]; 


            } 


            else


            { 


                l = i; 


                while (r < n && s[r - l] == s[r]) 


                { 


                    r++; 


                } 


                z[i] = r - l; 


                r--; 


            } 


        } 


    } 


} 


  


// Function to get the count of the  


// cyclic permutations of b that 


// given 0 when XORed with a  


public static int countPermutation(string a,  


                                   string b) 


{ 


    // concatenate b with b  


    b = b + b; 


      


    // new b now contains all the cyclic  


    // permutations of old b as it's sub-strings  


    b = b.Substring(0, b.Length - 1); 


  


    // concatenate pattern with text  


    int ans = 0; 


    string s = a + "$" + b; 


    int n = s.Length; 


  


    // Fill z array used in Z algorithm  


    int[] z = new int[n]; 


    compute_z(s, z); 


  


    for (int i = 1; i <= n - 1; i++) 


    { 


  


        // pattern occurs at index i since  


        // z value of i equals pattern length  


        if (z[i] == a.Length) 


        { 


            ans++; 


        } 


    } 


    return ans; 


} 


  


// Driver Code  


public static void Main(string[] args) 


{ 


    string a = "101"; 


    string b = "101"; 


    Console.WriteLine(countPermutation(a, b)); 


} 


} 


  


// This code is contributed by Shrikant13 



















                        chevron_right







                        filter_none











Output:


1






          
          
          
          

            

    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts:
VishalBachchas
Check out this Author's contributed articles.
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on  the "Improve Article" button below.


Improved By :  Ryuga, shrikanth13