Find All Occurrences of Subarray in Array
Last Updated :
26 Nov, 2024
Given two arrays a[] and b[], the task is to find all starting indices of b[] as a subarray in a[].
Examples:
Input: a[] = [2, 3, 0, 3, 0, 3, 0], b[] = [3, 0, 3, 0]
Output: [1, 3]
Explanation: The subarray a[1...4] = b[] and subarray a[3...6] = b[].
Input : a[] = [1, 2, 3, 4, 5], b[] = [2, 5, 6]
Output: []
Explanation: No subarray of a[] matches with b[].
[Naive Approach] Comparing All Subarrays - O(n*m) Time and O(1) Space
The idea is to check for all possible indices in a[] as starting index of subarray b[]. For each index, compare the subarray of a[] with b[] using a nested loop. If all the elements match, store the starting index in result. If any element does not match, break and check for next starting index.
C++
// C++ Program to search for subarray by matching
// with every possible subarray
#include <iostream>
#include <vector>
using namespace std;
vector<int> search(vector<int> &a, vector<int> &b) {
int n = a.size(), m = b.size();
vector<int> res;
// Iterate over all possible starting indices
for(int i = 0; i < n - m + 1; i++) {
bool isSame = true;
for(int j = 0; j < m; j++) {
// If any character does not match, break
// and begin from the next starting index
if(a[i + j] != b[j]) {
isSame = false;
break;
}
}
// If all characters are matched, store the
// starting index
if(isSame)
res.push_back(i);
}
return res;
}
int main() {
vector<int> a = {2, 3, 0, 3, 0, 3, 0};
vector<int> b = {3, 0, 3, 0};
vector<int> res = search(a, b);
for(int idx: res)
cout << idx << " ";
}
Java
// Java Program to search for subarray by matching
// with every possible subarray
import java.util.ArrayList;
import java.util.List;
class GfG {
static List<Integer> search(int[] a, int[] b) {
int n = a.length, m = b.length;
List<Integer> res = new ArrayList<>();
// Iterate over all possible starting indices
for (int i = 0; i < n - m + 1; i++) {
boolean isSame = true;
// If any character does not match, break
// and begin from the next starting index
for (int j = 0; j < m; j++) {
if (a[i + j] != b[j]) {
isSame = false;
break;
}
}
// If all characters are matched, store
// the starting index
if (isSame)
res.add(i);
}
return res;
}
public static void main(String[] args) {
int[] a = {2, 3, 0, 3, 0, 3, 0};
int[] b = {3, 0, 3, 0};
List<Integer> res = search(a, b);
for (int idx : res)
System.out.print(idx + " ");
}
}
Python
# Python Program to search for subarray by matching
# with every possible subarray
def search(a, b):
n = len(a)
m = len(b)
res = []
# Iterate over all possible starting indices
for i in range(n - m + 1):
isSame = True
for j in range(m):
# If any character does not match, break
# and begin from the next starting index
if a[i + j] != b[j]:
isSame = False
break
# If all characters are matched, store the starting index
if isSame:
res.append(i)
return res
if __name__ == "__main__":
a = [2, 3, 0, 3, 0, 3, 0]
b = [3, 0, 3, 0]
res = search(a, b)
for idx in res:
print(idx, end=" ")
C#
// C# Program to search for subarray by matching
// with every possible subarray
using System;
using System.Collections.Generic;
class GfG {
static List<int> Search(int[] a, int[] b) {
int n = a.Length, m = b.Length;
List<int> res = new List<int>();
// Iterate over all possible starting indices
for (int i = 0; i < n - m + 1; i++) {
bool isSame = true;
for (int j = 0; j < m; j++) {
// If any character does not match, break
// and begin from the next starting index
if (a[i + j] != b[j]) {
isSame = false;
break;
}
}
// If all characters are matched, store the starting index
if (isSame)
res.Add(i);
}
return res;
}
static void Main() {
int[] a = { 2, 3, 0, 3, 0, 3, 0 };
int[] b = { 3, 0, 3, 0 };
List<int> res = Search(a, b);
foreach (int idx in res) {
Console.Write(idx + " ");
}
}
}
JavaScript
// JavaScript Program to search for subarray by matching
// with every possible subarray
function search(a, b) {
let n = a.length, m = b.length;
let res = [];
// Iterate over all possible starting indices
for (let i = 0; i < n - m + 1; i++) {
let isSame = true;
for (let j = 0; j < m; j++) {
// If any character does not match, break
// and begin from the next starting index
if (a[i + j] !== b[j]) {
isSame = false;
break;
}
}
// If all characters are matched, store the starting index
if (isSame)
res.push(i);
}
return res;
}
// Driver code
let a = [2, 3, 0, 3, 0, 3, 0];
let b = [3, 0, 3, 0];
let res = search(a, b);
for (let idx of res) {
console.log(idx + " ");
}
Time Complexity: O(n*m), where n and m are the sizes of the arrays a[] and b[], respectively.
Space Complexity: O(1) as we are not using any additional space to store the arrays or any other variables.
[Expected Approach] Using KMP Algorithm - O(n+m) Time and O(m) Space
The idea is to use KMP Algorithm with a[] as the text and b[] as the pattern. So, instead of comparing characters, we can compare numbers of the array to construct the lps[] array and find all occurrences of b[] in a[].
C++
// C++ Program to search for subarray using KMP Algorithm
#include <iostream>
#include <vector>
using namespace std;
void constructLps(vector<int> &pat, vector<int> &lps) {
// len stores the length of longest prefix which
// is also a suffix for the previous index
int len = 0;
// lps[0] is always 0
lps[0] = 0;
int i = 1;
while (i < pat.size()) {
// If numbers match, increment the size of lps
if (pat[i] == pat[len]) {
len++;
lps[i] = len;
i++;
}
// If there is a mismatch
else {
if (len != 0) {
// Update len to the previous lps value
// to avoid reduntant comparisons
len = lps[len - 1];
}
else {
// If no matching prefix found, set lps[i] to 0
lps[i] = 0;
i++;
}
}
}
}
vector<int> search(vector<int> &a, vector<int> &b) {
int n = a.size();
int m = b.size();
vector<int> lps(m);
vector<int> res;
constructLps(b, lps);
// Pointers i and j, for traversing a[] and b[]
int i = 0;
int j = 0;
while (i < n) {
// If elements match, move both pointers forward
if (a[i] == b[j]) {
i++;
j++;
// If all elements of b[] are matched
// store the start index in result
if (j == m) {
res.push_back(i - j);
// Use LPS of previous index to
// skip unnecessary comparisons
j = lps[j - 1];
}
}
// If there is a mismatch
else {
// Use lps value of previous index
// to avoid redundant comparisons
if (j != 0)
j = lps[j - 1];
else
i++;
}
}
return res;
}
int main() {
vector<int> a = {2, 3, 0, 3, 0, 3, 0};
vector<int> b = {3, 0, 3, 0};
vector<int> res = search(a, b);
for(int idx: res)
cout << idx << " ";
}
Java
// Java Program to search for subarray using KMP Algorithm
import java.util.ArrayList;
import java.util.List;
class GfG {
// Function to construct LPS array
static void constructLps(int[] pat, int[] lps) {
// len stores the length of longest prefix which
// is also a suffix for the previous index
int len = 0;
// lps[0] is always 0
lps[0] = 0;
int i = 1;
while (i < pat.length) {
// If numbers match, increment the size of lps
if (pat[i] == pat[len]) {
len++;
lps[i] = len;
i++;
}
// If there is a mismatch
else {
if (len != 0) {
// Update len to the previous lps value
// to avoid redundant comparisons
len = lps[len - 1];
} else {
// If no matching prefix found, set lps[i] to 0
lps[i] = 0;
i++;
}
}
}
}
// Function to search for the subarray using KMP algorithm
static List<Integer> search(int[] a, int[] b) {
int n = a.length;
int m = b.length;
int[] lps = new int[m];
List<Integer> res = new ArrayList<>();
constructLps(b, lps);
// Pointers i and j, for traversing a[] and b[]
int i = 0;
int j = 0;
while (i < n) {
// If elements match, move both pointers forward
if (a[i] == b[j]) {
i++;
j++;
// If all elements of b[] are matched
// store the start index in result
if (j == m) {
res.add(i - j);
// Use LPS of previous index to
// skip unnecessary comparisons
j = lps[j - 1];
}
}
// If there is a mismatch
else {
// Use lps value of previous index
// to avoid redundant comparisons
if (j != 0)
j = lps[j - 1];
else
i++;
}
}
return res;
}
public static void main(String[] args) {
int[] a = {2, 3, 0, 3, 0, 3, 0};
int[] b = {3, 0, 3, 0};
List<Integer> res = search(a, b);
for (int idx : res)
System.out.print(idx + " ");
}
}
Python
# Python Program to search for subarray using KMP Algorithm
def constructLps(pat, lps):
# len stores the length of longest prefix which
# is also a suffix for the previous index
length = 0
# lps[0] is always 0
lps[0] = 0
i = 1
while i < len(pat):
# If numbers match, increment the size of lps
if pat[i] == pat[length]:
length += 1
lps[i] = length
i += 1
# If there is a mismatch
else:
if length != 0:
# Update length to the previous lps value
# to avoid redundant comparisons
length = lps[length - 1]
else:
# If no matching prefix found, set lps[i] to 0
lps[i] = 0
i += 1
def search(a, b):
n = len(a)
m = len(b)
lps = [0] * m
res = []
constructLps(b, lps)
# Pointers i and j, for traversing a[] and b[]
i = 0
j = 0
while i < n:
# If elements match, move both pointers forward
if a[i] == b[j]:
i += 1
j += 1
# If all elements of b[] are matched
# store the start index in result
if j == m:
res.append(i - j)
# Use LPS of previous index to
# skip unnecessary comparisons
j = lps[j - 1]
else:
# If there is a mismatch
# Use lps value of previous index
# to avoid redundant comparisons
if j != 0:
j = lps[j - 1]
else:
i += 1
return res
if __name__ == "__main__":
a = [2, 3, 0, 3, 0, 3, 0]
b = [3, 0, 3, 0]
res = search(a, b)
for idx in res:
print(idx, end=" ")
C#
// C# Program to search for subarray using KMP Algorithm
using System;
using System.Collections.Generic;
class GfG {
// Function to construct the LPS array (Longest Prefix Suffix)
static void ConstructLps(int[] pat, int[] lps) {
// len stores the length of the longest prefix which
// is also a suffix for the previous index
int len = 0;
// lps[0] is always 0
lps[0] = 0;
int i = 1;
while (i < pat.Length) {
// If numbers match, increment the size of lps
if (pat[i] == pat[len]) {
len++;
lps[i] = len;
i++;
}
// If there is a mismatch
else {
if (len != 0) {
// Update len to the previous lps value
// to avoid redundant comparisons
len = lps[len - 1];
}
else {
// If no matching prefix found, set lps[i] to 0
lps[i] = 0;
i++;
}
}
}
}
// Function to search for the subarray
static List<int> Search(int[] a, int[] b) {
int n = a.Length;
int m = b.Length;
int[] lps = new int[m];
List<int> res = new List<int>();
ConstructLps(b, lps);
// Pointers i and j, for traversing a[] and b[]
int i = 0;
int j = 0;
while (i < n) {
// If elements match, move both pointers forward
if (a[i] == b[j]) {
i++;
j++;
// If all elements of b[] are matched
// store the start index in result
if (j == m) {
res.Add(i - j);
// Use LPS of previous index to
// skip unnecessary comparisons
j = lps[j - 1];
}
}
// If there is a mismatch
else {
// Use lps value of previous index
// to avoid redundant comparisons
if (j != 0)
j = lps[j - 1];
else
i++;
}
}
// Convert the List<int> to an int[] before returning
return res;
}
static void Main() {
int[] a = { 2, 3, 0, 3, 0, 3, 0 };
int[] b = { 3, 0, 3, 0 };
List<int> res = Search(a, b);
foreach (int idx in res) {
Console.Write(idx + " ");
}
}
}
JavaScript
// JavaScript Program to search for subarray using KMP Algorithm
function constructLps(pat, lps) {
// len stores the length of longest prefix which
// is also a suffix for the previous index
let len = 0;
// lps[0] is always 0
lps[0] = 0;
let i = 1;
while (i < pat.length) {
// If numbers match, increment the size of lps
if (pat[i] === pat[len]) {
len++;
lps[i] = len;
i++;
}
// If there is a mismatch
else {
if (len !== 0) {
// Update len to the previous lps value
// to avoid redundant comparisons
len = lps[len - 1];
}
else {
// If no matching prefix found, set lps[i] to 0
lps[i] = 0;
i++;
}
}
}
}
function search(a, b) {
let n = a.length;
let m = b.length;
let lps = new Array(m);
let res = [];
constructLps(b, lps);
// Pointers i and j, for traversing a[] and b[]
let i = 0;
let j = 0;
while (i < n) {
// If elements match, move both pointers forward
if (a[i] === b[j]) {
i++;
j++;
// If all elements of b[] are matched
// store the start index in result
if (j === m) {
res.push(i - j);
// Use LPS of previous index to
// skip unnecessary comparisons
j = lps[j - 1];
}
}
// If there is a mismatch
else {
// Use lps value of previous index
// to avoid redundant comparisons
if (j !== 0)
j = lps[j - 1];
else
i++;
}
}
return res;
}
// Driver Code
let a = [2, 3, 0, 3, 0, 3, 0];
let b = [3, 0, 3, 0];
let res = search(a, b);
for (let idx of res) {
console.log(idx + " ");
}
Time Complexity: O(n+m), where n and m are the sizes of the arrays a[] and b[], respectively.
Auxiliary Space: O(m), for lps[] array.
Related Topic: Subarrays, Subsequences, and Subsets in Array
Similar Reads
DSA Tutorial - Learn Data Structures and Algorithms DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. Data structures manage how data is stored and accessed, while algorithms focus on
7 min read
Quick Sort QuickSort is a sorting algorithm based on the Divide and Conquer that picks an element as a pivot and partitions the given array around the picked pivot by placing the pivot in its correct position in the sorted array. It works on the principle of divide and conquer, breaking down the problem into s
12 min read
Merge Sort - Data Structure and Algorithms Tutorials Merge sort is a popular sorting algorithm known for its efficiency and stability. It follows the divide-and-conquer approach. It works by recursively dividing the input array into two halves, recursively sorting the two halves and finally merging them back together to obtain the sorted array. Merge
14 min read
Bubble Sort Algorithm Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst-case time complexity are quite high.We sort the array using multiple passes. After the fir
8 min read
Data Structures Tutorial Data structures are the fundamental building blocks of computer programming. They define how data is organized, stored, and manipulated within a program. Understanding data structures is very important for developing efficient and effective algorithms. What is Data Structure?A data structure is a st
2 min read
Breadth First Search or BFS for a Graph Given a undirected graph represented by an adjacency list adj, where each adj[i] represents the list of vertices connected to vertex i. Perform a Breadth First Search (BFS) traversal starting from vertex 0, visiting vertices from left to right according to the adjacency list, and return a list conta
15+ min read
Binary Search Algorithm - Iterative and Recursive Implementation Binary Search Algorithm is a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(log N). Binary Search AlgorithmConditions to apply Binary Searc
15 min read
Insertion Sort Algorithm Insertion sort is a simple sorting algorithm that works by iteratively inserting each element of an unsorted list into its correct position in a sorted portion of the list. It is like sorting playing cards in your hands. You split the cards into two groups: the sorted cards and the unsorted cards. T
9 min read
Dijkstra's Algorithm to find Shortest Paths from a Source to all Given a weighted undirected graph represented as an edge list and a source vertex src, find the shortest path distances from the source vertex to all other vertices in the graph. The graph contains V vertices, numbered from 0 to V - 1.Note: The given graph does not contain any negative edge. Example
12 min read
Selection Sort Selection Sort is a comparison-based sorting algorithm. It sorts an array by repeatedly selecting the smallest (or largest) element from the unsorted portion and swapping it with the first unsorted element. This process continues until the entire array is sorted.First we find the smallest element an
8 min read