Intersection of Two Sorted Arrays with Distinct Elements
Last Updated :
23 Jul, 2025
Given two sorted arrays a[] and b[] with distinct elements of size n and m respectively, the task is to find intersection (or common elements) of the two arrays. We need to return the intersection in sorted order.
Note: Intersection of two arrays can be defined as a set containing distinct common elements between the two arrays.
Examples:
Input: a[] = { 1, 2, 4, 5, 6 }, b[] = { 2, 4, 7, 9 }
Output: { 2, 4 }
Explanation: The common elements in both arrays are 2 and 4.
Input: a[] = { 2, 3, 4, 5 }, b[] = { 1, 7 }
Output: { }
Explanation: There are no common elements in array a[] and b[].
Approaches Same as Unsorted Arrays with distinct elements – Best Time O(n+m) and O(n) Space
The idea is to use the same approaches as discussed in Intersection of Two Arrays with Distinct Elements. The most optimal approach among them is to use Hash Set which has a time complexity of O(n+m) and Auxiliary Space of O(n).
[Expected Approach] Using Merge Step of Merge Sort - O(n+m) Time and O(1) Space
The idea is to find the intersection of two sorted arrays using merge step of merge sort. We maintain two pointers to traverse both arrays simultaneously.
- If the element in first array is smaller, move the pointer of first array forward because this element cannot be part of the intersection.
- If the element in second array is smaller, move the pointer of second array forward.
- If both elements are equal, add one of them and move both the pointers forward.
This continues until one of the pointers reaches the end of its array.
C++
// C++ program for intersection of
// two sorted arrays with distinct elements
#include <iostream>
#include <vector>
using namespace std;
vector<int> intersection(vector<int>& a, vector<int>& b) {
vector<int> res;
int i=0;
int j=0;
// Start simultaneous traversal on both arrays
while (i < a.size() && j < b.size()) {
// if a[i] is smaller, then move in a[]
// towards larger value
if(a[i] < b[j]) {
i++;
}
// if b[j] is smaller, then move in b[]
// towards larger value
else if (a[i] > b[j]) {
j++;
}
// if a[i] == b[j], then this element is common
// add it to result array and move in both arrays
else {
res.push_back(a[i]);
i++;
j++;
}
}
return res;
}
int main() {
vector<int> a = {1, 2, 4, 5, 6};
vector<int> b = {2, 4, 7, 9};
vector<int> res = intersection(a, b);
for (int i = 0; i < res.size(); i++)
cout << res[i] << " ";
return 0;
}
// C program for intersection of
// two sorted arrays with distinct elements
#include <stdio.h>
int* intersection(int a[], int b[], int n, int m, int *size) {
int* res = (int*) malloc(n * sizeof(int));
*size = 0;
int i = 0;
int j = 0;
// Start simultaneous traversal on both arrays
while (i < n && j < m) {
// if a[i] is smaller, then move in a[]
// towards larger value
if (a[i] < b[j]) {
i++;
}
// if b[j] is smaller, then move in b[]
// towards larger value
else if (a[i] > b[j]) {
j++;
}
// if a[i] == b[j], then this element is common
// add it to result array and move in both arrays
else {
res[(*size)++] = a[i];
i++;
j++;
}
}
return res;
}
int main() {
int a[] = {1, 2, 4, 5, 6};
int b[] = {2, 4, 7, 9};
int size;
int* res = intersection(a, b, 5, 4, &size);
for (int i = 0; i < size; i++)
printf("%d ", res[i]);
return 0;
}
// Java program for intersection of
// two sorted arrays with distinct elements
import java.util.ArrayList;
class GfG {
static ArrayList<Integer> intersection(int[] a, int[] b) {
ArrayList<Integer> res = new ArrayList<>();
int i = 0;
int j = 0;
// Start simultaneous traversal on both arrays
while (i < a.length && j < b.length) {
// if a[i] is smaller, then move in a[]
// towards larger value
if (a[i] < b[j]) {
i++;
}
// if b[j] is smaller, then move in b[]
// towards larger value
else if (a[i] > b[j]) {
j++;
}
// if a[i] == b[j], then this element is common
// add it to result array and move in both arrays
else {
res.add(a[i]);
i++;
j++;
}
}
return res;
}
public static void main(String[] args) {
int[] a = {1, 2, 4, 5, 6};
int[] b = {2, 4, 7, 9};
ArrayList<Integer> res = intersection(a, b);
for (int i = 0; i < res.size(); i++)
System.out.print(res.get(i) + " ");
}
}
# Python program for intersection of
# two sorted arrays with distinct elements
def intersection(a, b):
res = []
i = 0
j = 0
# Start simultaneous traversal on both arrays
while i < len(a) and j < len(b):
# if a[i] is smaller, then move in a[]
# towards larger value
if a[i] < b[j]:
i += 1
# if b[j] is smaller, then move in b[]
# towards larger value
elif a[i] > b[j]:
j += 1
# if a[i] == b[j], then this element is common
# add it to result array and move in both arrays
else:
res.append(a[i])
i += 1
j += 1
return res
if __name__ == "__main__":
a = [1, 2, 4, 5, 6]
b = [2, 4, 7, 9]
res = intersection(a, b)
for i in range(len(res)):
print(res[i], end=" ")
// C# program for intersection of
// two sorted arrays with distinct elements
using System;
using System.Collections.Generic;
class GfG {
static List<int> intersection(int[] a, int[] b) {
List<int> res = new List<int>();
int i = 0;
int j = 0;
// Start simultaneous traversal on both arrays
while (i < a.Length && j < b.Length) {
// if a[i] is smaller, then move in a[]
// towards larger value
if (a[i] < b[j]) {
i++;
}
// if b[j] is smaller, then move in b[]
// towards larger value
else if (a[i] > b[j]) {
j++;
}
// if a[i] == b[j], then this element is common
// add it to result array and move in both arrays
else {
res.Add(a[i]);
i++;
j++;
}
}
return res;
}
static void Main() {
int[] a = {1, 2, 4, 5, 6};
int[] b = {2, 4, 7, 9};
List<int> res = intersection(a, b);
for (int i = 0; i < res.Count; i++)
Console.Write(res[i] + " ");
}
}
// JavaScript program for intersection of
// two sorted arrays with distinct elements
function intersection(a, b) {
const res = [];
let i = 0;
let j = 0;
// Start simultaneous traversal on both arrays
while (i < a.length && j < b.length) {
// if a[i] is smaller, then move in a[]
// towards larger value
if (a[i] < b[j]) {
i++;
}
// if b[j] is smaller, then move in b[]
// towards larger value
else if (a[i] > b[j]) {
j++;
}
// if a[i] == b[j], then this element is common
// add it to result array and move in both arrays
else {
res.push(a[i]);
i++;
j++;
}
}
return res;
}
const a = [1, 2, 4, 5, 6];
const b = [2, 4, 7, 9];
const res = intersection(a, b);
console.log(res.join(' '));
Time Complexity: O(n + m), where n and m are size of array a[] and b[] respectively.
Auxiliary Space: O(1)
[Alternate Approach 1] Using Binary Search - O(n * log (m)) Time and O(1) Space
The idea is to check each element of array a[] and see if it is in array b[]. If it is, we add it to the result array. Since b[] is already sorted, we can use binary search to find the elements in log(n) time.
C++
// C++ program for intersection of two sorted arrays
// with distinct elements using Binary Search
#include <iostream>
#include <vector>
using namespace std;
// Function to perform binary search
int binarySearch(vector<int> &arr, int lo, int hi, int target) {
while (lo <= hi){
int mid = lo + (hi - lo) / 2;
if (arr[mid] == target)
return mid;
if (arr[mid] < target)
lo = mid + 1;
else
hi = mid - 1;
}
return -1;
}
vector<int> intersection(vector<int>& a, vector<int>& b) {
vector<int> res;
// Traverse through array a[] and search every
// element a[i] in array b[]
for (int i = 0; i < a.size(); i++) {
// If found in b[], then add this
// element to result array
if (binarySearch(b, 0, b.size()-1, a[i]) != -1) {
res.push_back(a[i]);
}
}
return res;
}
int main() {
vector<int> a = {1, 2, 4, 5, 6};
vector<int> b = {2, 4, 7, 9};
vector<int> res = intersection(a, b);
for (int i = 0; i < res.size(); i++)
cout << res[i] << " ";
return 0;
}
// C program for intersection of two sorted arrays
// with distinct elements using Binary Search
#include <stdio.h>
int binarySearch(int arr[], int lo, int hi, int target) {
while (lo <= hi) {
int mid = lo + (hi - lo) / 2;
if (arr[mid] == target)
return mid;
if (arr[mid] < target)
lo = mid + 1;
else
hi = mid - 1;
}
return -1;
}
int* intersection(int a[], int b[], int n, int m, int *size) {
*size = 0;
int* res = (int*) malloc(n * sizeof(int));
// Traverse through array a[] and search every
// element a[i] in array b[]
for (int i = 0; i < n; i++) {
// If found in b[], then add this
// element to result array
if (binarySearch(b, 0, m - 1, a[i]) != -1) {
res[(*size)++] = a[i];
}
}
return res;
}
int main() {
int a[] = {1, 2, 4, 5, 6};
int b[] = {2, 4, 7, 9};
int size;
int* res = intersection(a, b, 5, 4, &size);
for (int i = 0; i < size; i++)
printf("%d ", res[i]);
return 0;
}
// Java program for intersection of two sorted arrays
// with distinct elements using Binary Search
import java.util.ArrayList;
class GfG {
// Function to perform binary search
static int binarySearch(int[] arr, int lo, int hi, int target) {
while (lo <= hi) {
int mid = lo + (hi - lo) / 2;
if (arr[mid] == target)
return mid;
if (arr[mid] < target)
lo = mid + 1;
else
hi = mid - 1;
}
return -1;
}
static ArrayList<Integer> intersection(int[] a, int[] b) {
ArrayList<Integer> res = new ArrayList<>();
// Traverse through array a[] and search every
// element a[i] in array b[]
for (int i = 0; i < a.length; i++) {
// If found in b[], then add this
// element to result array
if (binarySearch(b, 0, b.length - 1, a[i]) != -1) {
res.add(a[i]);
}
}
return res;
}
public static void main(String[] args) {
int[] a = {1, 2, 4, 5, 6};
int[] b = {2, 4, 7, 9};
ArrayList<Integer> res = intersection(a, b);
for (int i = 0; i < res.size(); i++)
System.out.print(res.get(i) + " ");
}
}
# Python program for intersection of two sorted arrays
# with distinct elements using Binary Search
def binarySearch(arr, lo, hi, target):
while lo <= hi:
mid = lo + (hi - lo) // 2
if arr[mid] == target:
return mid
if arr[mid] < target:
lo = mid + 1
else:
hi = mid - 1
return -1
def intersection(a, b):
res = []
# Traverse through array a[] and search every
# element a[i] in array b[]
for i in range(len(a)):
# If found in b[], then add this
# element to result array
if binarySearch(b, 0, len(b) - 1, a[i]) != -1:
res.append(a[i])
return res
if __name__ == "__main__":
a = [1, 2, 4, 5, 6]
b = [2, 4, 7, 9]
res = intersection(a, b)
for i in range(len(res)):
print(res[i], end=" ")
// C# program for intersection of two sorted arrays
// with distinct elements using Binary Search
using System;
using System.Collections.Generic;
class GfG {
// Function to perform binary search
static int binarySearch(int[] arr, int lo, int hi, int target) {
while (lo <= hi) {
int mid = lo + (hi - lo) / 2;
if (arr[mid] == target)
return mid;
if (arr[mid] < target)
lo = mid + 1;
else
hi = mid - 1;
}
return -1;
}
static List<int> intersection(int[] a, int[] b) {
List<int> res = new List<int>();
// Traverse through array a[] and search every
// element a[i] in array b[]
for (int i = 0; i < a.Length; i++) {
// If found in b[], then add this
// element to result array
if (binarySearch(b, 0, b.Length - 1, a[i]) != -1) {
res.Add(a[i]);
}
}
return res;
}
static void Main() {
int[] a = {1, 2, 4, 5, 6};
int[] b = {2, 4, 7, 9};
List<int> res = intersection(a, b);
for (int i = 0; i < res.Count; i++)
Console.Write(res[i] + " ");
}
}
// JavaScript program for intersection of two sorted arrays
// with distinct elements using Binary Search
function binarySearch(arr, lo, hi, target) {
while (lo <= hi) {
const mid = lo + Math.floor((hi - lo) / 2);
if (arr[mid] === target)
return mid;
if (arr[mid] < target)
lo = mid + 1;
else
hi = mid - 1;
}
return -1;
}
function intersection(a, b) {
const res = [];
// Traverse through array a[] and search every
// element a[i] in array b[]
for (let i = 0; i < a.length; i++) {
// If found in b[], then add this
// element to result array
if (binarySearch(b, 0, b.length - 1, a[i]) !== -1) {
res.push(a[i]);
}
}
return res;
}
const a = [1, 2, 4, 5, 6];
const b = [2, 4, 7, 9];
const res = intersection(a, b);
console.log(res.join(' '));
Time Complexity: O(n * log (m)), where n and m are size of array a[] and b[] respectively.
Auxiliary Space: O(1)
Related Articles:
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem