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 |
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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); } } |
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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 |
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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 |
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Output:
1 3
Time Complexity: O(N + M).
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