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

Given two arrays A and B, the task is to find the starting index for every occurrence 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 the 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 the 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 meaningless 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++

// 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 separator
    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

Java

// 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 separator
        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);
    }
}

Python3

# 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 separator
    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

C#

// 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 separator
        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

Javascript

<script>

// JavaScript implementation for pattern
// searching in an array using Z-Algorithm


// Function to calculate Z-Array
function zArray(arr) {
    let n = arr.length;
    let z = new Array(n);
    let r = 0, l = 0;

    // Loop to calculate Z-Array
    for (let 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 {
            let 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
function mergeArray(A, B) {
    let n = A.length;
    let m = B.length;
    let z = new Array();

    // Array to store merged array
    let c = new Array(n + m + 1);

    // Copying array B
    for (let i = 0; i < m; i++)
        c[i] = B[i];

    // Adding a separator
    c[m] = Number.MAX_SAFE_INTEGER;

    // Copying array A
    for (let 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
function findZArray(A, B, n) {
    let flag = 0;
    let z = [];
    z = mergeArray(A, B);

    // Printing indexes where array B occur
    for (let i = 0; i < z.length; i++) {
        if (z[i] == n) {

            document.write((i - n - 1) + " ");
            flag = 1;
        }
    }
    if (flag == 0) {
        document.write("Not Found");
    }
}

// Driver Code

let A = [1, 2, 3, 2, 3, 2];
let B = [2, 3];
let n = B.length;

findZArray(A, B, n);

// This code is contributed by gfgking

</script>

Output:

1 3

Time Complexity: O(N + M).
Auxiliary Space: O(N + M), where N and M are the sizes of the given vectors A and B respectively.