Find starting index for every occurence of given array B in array A using Z-Algorithm

Given two array A and B, the task is to find the starting index for every occurence of array B in array A using Z-Algorithm.

Examples:

Input: A = {1, 2, 3, 2, 3}, B = {2, 3}
Output: 1 3
Explanation:
In array A, array B occurs at index 1 and index 3. Thus the answer is {1, 3}.



Input: A = {1, 1, 1, 1, 1}, B = {1}
Output: 0 1 2 3 4
In array A, array B occur at index {0, 1, 2, 3, 4}.

In Z-Algorithm, we construct a Z-Array.

What is Z-Array?

For a arr[0..n-1], Z array is an array, of same length as the string array arr, where each element Z[i] of Z array stores length of the longest substring starting from arr[i] which is also a prefix of arr[0..n-1]. The first entry of Z array is meaning less as complete array is always prefix of itself.

For example: For a given array arr[] = { 1, 2, 3, 0, 1, 2, 3, 5}

Approach:

  • Merge array B and array A with a separator in between into a new array C. Here separator can be any special character.
  • Create Z-array using array C.
  • Iterate over the Z-array and print all those indices whose value is greater than or equal to the length of the array B.

Below is the implementation of the above approach.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP implementation for pattern
// searching in an array using Z-Algorithm
#include<bits/stdc++.h>
using namespace std;
  
// Function to calculate Z-Array
vector<int> zArray(vector<int> arr)
{
    int n = arr.size();
    vector<int> z(n);
    int r = 0, l = 0;
  
    // Loop to calculate Z-Array
    for (int k = 1; k < n; k++) {
  
        // Outside the Z-box
        if (k > r) {
            r = l = k;
            while (r < n
                && arr[r] == arr[r - l])
                r++;
            z[k] = r - l;
            r--;
        }
  
        // Inside Z-box
        else {
            int k1 = k - l;
  
            if (z[k1] < r - k + 1)
                z[k] = z[k1];
  
            else {
                l = k;
                while (r < n
                    && arr[r] == arr[r - l])
                    r++;
                z[k] = r - l;
                r--;
            }
        }
    }
    return z;
}
  
// Helper function to merge two
// arrays and create a single array
vector<int> mergeArray(vector<int> A, vector<int> B)
{
    int n = A.size();
    int m = B.size();
    vector<int> z;
  
    // Array to store merged array
    vector<int> c(n + m + 1);
  
    // Copying array B
    for (int i = 0; i < m; i++)
        c[i] = B[i];
  
    // Adding a seperator
    c[m] = INT_MAX;
  
    // Copying array A
    for (int i = 0; i < n; i++)
        c[m + i + 1] = A[i];
  
    // Calling Z-function
    z = zArray(c);
    return z;
}
  
// Function to help compute the Z array
void findZArray(vector<int>A,vector<int>B, int n)
{
    int flag = 0;
    vector<int> z;
    z = mergeArray(A, B);
  
    // Printing indexes where array B occur
    for (int i = 0; i < z.size(); i++) {
        if (z[i] == n) {
  
            cout << (i - n - 1) << " ";
            flag = 1;
        }
    }
    if (flag == 0) {
        cout << ("Not Found");
    }
}
  
// Driver Code
int main()
{
    vector<int>A{ 1, 2, 3, 2, 3, 2 };
    vector<int>B{ 2, 3 };
    int n = B.size();
  
    findZArray(A, B, n);
}
  
// This code is contributed by Surendra_Gangwar

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implementation for pattern
// searching in an array using Z-Algorithm
  
import java.io.*;
import java.util.*;
  
class GfG {
  
    // Function to calculate Z-Array
    private static int[] zArray(int arr[])
    {
        int z[];
        int n = arr.length;
        z = new int[n];
        int r = 0, l = 0;
  
        // Loop to calculate Z-Array
        for (int k = 1; k < n; k++) {
  
            // Outside the Z-box
            if (k > r) {
                r = l = k;
                while (r < n
                       && arr[r] == arr[r - l])
                    r++;
                z[k] = r - l;
                r--;
            }
  
            // Inside Z-box
            else {
                int k1 = k - l;
  
                if (z[k1] < r - k + 1)
                    z[k] = z[k1];
  
                else {
                    l = k;
                    while (r < n
                           && arr[r] == arr[r - l])
                        r++;
                    z[k] = r - l;
                    r--;
                }
            }
        }
        return z;
    }
  
    // Helper function to merge two
    // arrays and create a single array
    private static int[] mergeArray(int A[],
                                    int B[])
    {
        int n = A.length;
        int m = B.length;
        int z[];
  
        // Array to store merged array
        int c[] = new int[n + m + 1];
  
        // Copying array B
        for (int i = 0; i < m; i++)
            c[i] = B[i];
  
        // Adding a seperator
        c[m] = Integer.MAX_VALUE;
  
        // Copying array A
        for (int i = 0; i < n; i++)
            c[m + i + 1] = A[i];
  
        // Calling Z-function
        z = zArray(c);
        return z;
    }
  
    // Function to help compute the Z array
    private static void findZArray(int A[], int B[], int n)
    {
        int flag = 0;
        int z[];
        z = mergeArray(A, B);
  
        // Printing indexes where array B occur
        for (int i = 0; i < z.length; i++) {
            if (z[i] == n) {
  
                System.out.print((i - n - 1)
                                 + " ");
                flag = 1;
            }
        }
        if (flag == 0) {
            System.out.println("Not Found");
        }
    }
  
    // Driver Code
    public static void main(String args[])
    {
        int A[] = { 1, 2, 3, 2, 3, 2 };
        int B[] = { 2, 3 };
        int n = B.length;
  
        findZArray(A, B, n);
    }
}

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 implementation for pattern 
# searching in an array using Z-Algorithm 
import sys;
  
# Function to calculate Z-Array 
def zArray(arr) :
    n = len(arr); 
    z = [0]*n;
    r = 0
    l = 0;
      
    # Loop to calculate Z-Array
    for k in range(1, n) :
          
        # Outside the Z-box
        if (k > r) :
            r = l = k;
            while (r < n and arr[r] == arr[r - l]) :
                r += 1;
            z[k] = r - l;
            r -= 1;
                  
        # Inside Z-box
        else :
            k1 = k - l;
              
            if (z[k1] < r - k + 1) :
                z[k] = z[k1];
                  
            else :
                l = k;
                while (r < n and arr[r] == arr[r - l]) :
                    r += 1 ;
                z[k] = r - l;
                r -= 1;
                      
    return z; 
  
# Helper function to merge two 
# arrays and create a single array 
def mergeArray(A,B) : 
  
    n = len(A); 
    m = len(B); 
  
    # Array to store merged array 
    c = [0]*(n + m + 1); 
  
    # Copying array B 
    for i in range(m) :
        c[i] = B[i]; 
  
    # Adding a seperator 
    c[m] = sys.maxsize; 
  
    # Copying array A 
    for i in range(n) : 
        c[m + i + 1] = A[i]; 
  
    # Calling Z-function 
    z = zArray(c); 
    return z; 
  
# Function to help compute the Z array 
def findZArray( A,B, n) :
    flag = 0;
    z = mergeArray(A, B);
      
    # Printing indexes where array B occur
    for i in range(len(z)) :
        if (z[i] == n) :
            print(i - n - 1, end= " ");
            flag = 1;
              
    if (flag == 0) :
        print("Not Found"); 
  
# Driver Code 
if __name__ == "__main__" :
      
    A = [ 1, 2, 3, 2, 3, 2];
    B = [ 2, 3 ];
    n = len(B);
    findZArray(A, B, n); 
  
# This code is contributed by AnkitRai01

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implementation for pattern 
// searching in an array using Z-Algorithm 
using System;
  
class GfG 
  
    // Function to calculate Z-Array 
    private static int[] zArray(int []arr) 
    
        int []z; 
        int n = arr.Length; 
        z = new int[n]; 
        int r = 0, l = 0; 
  
        // Loop to calculate Z-Array 
        for (int k = 1; k < n; k++) 
        
  
            // Outside the Z-box 
            if (k > r)
            
                r = l = k; 
                while (r < n 
                    && arr[r] == arr[r - l]) 
                    r++; 
                z[k] = r - l; 
                r--; 
            
  
            // Inside Z-box 
            else
            
                int k1 = k - l; 
  
                if (z[k1] < r - k + 1) 
                    z[k] = z[k1]; 
  
                else
                
                    l = k; 
                    while (r < n 
                        && arr[r] == arr[r - l]) 
                        r++; 
                    z[k] = r - l; 
                    r--; 
                
            
        
        return z; 
    
  
    // Helper function to merge two 
    // arrays and create a single array 
    private static int[] mergeArray(int []A, 
                                    int []B) 
    
        int n = A.Length; 
        int m = B.Length; 
        int []z; 
  
        // Array to store merged array 
        int []c = new int[n + m + 1]; 
  
        // Copying array B 
        for (int i = 0; i < m; i++) 
            c[i] = B[i]; 
  
        // Adding a seperator 
        c[m] = int.MaxValue; 
  
        // Copying array A 
        for (int i = 0; i < n; i++) 
            c[m + i + 1] = A[i]; 
  
        // Calling Z-function 
        z = zArray(c); 
        return z; 
    
  
    // Function to help compute the Z array 
    private static void findZArray(int []A, int []B, int n) 
    
        int flag = 0; 
        int []z; 
        z = mergeArray(A, B); 
  
        // Printing indexes where array B occur 
        for (int i = 0; i < z.Length; i++) 
        
            if (z[i] == n)
            
  
                Console.Write((i - n - 1) 
                                + " "); 
                flag = 1; 
            
        
        if (flag == 0) 
        
            Console.WriteLine("Not Found"); 
        
    
  
    // Driver Code 
    public static void Main() 
    
        int []A = { 1, 2, 3, 2, 3, 2 }; 
        int []B = { 2, 3 }; 
        int n = B.Length; 
  
        findZArray(A, B, n); 
    
  
// This code is contributed by AnkitRai01

chevron_right


Output:

1 3

Time Complexity: O(N + M).

GeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details




My Personal Notes arrow_drop_up

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.



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.