Pair Sum in a Sorted and Rotated Array
Last Updated :
23 Jul, 2025
Given an array arr[] of size n, which is sorted and then rotated around an unknown pivot, the task is to check whether there exists a pair of elements in the array whose sum is equal to a given target value.
Examples :
Input: arr[] = [11, 15, 6, 8, 9, 10], target = 16
Output: true
Explanation: There is a pair (6, 10) with sum 16.
Input: arr[] = [11, 11, 15, 26, 38, 9, 10], target = 35
Output: true
Explanation: There is a pair (26, 9) with sum 35.
Input: arr[] = [9, 10, 10, 11, 15, 26, 38], target = 45
Output: false
Explanation: There is no pair with sum 45.
[Naive Approach] Using Hashing - O(n) Time and O(n) Space
We have discussed different solutions for finding a pair with given sum in an array (not sorted). The best complexities we can achieve is O(n) Time and O(n) auxiliary space in the hashing based solution.
C++
// C++ code to check whether any pair exists
// whose sum is equal to the given target value
#include <iostream>
#include <vector>
#include <unordered_set>
using namespace std;
bool pairInSortedRotated(vector<int> &arr, int target){
unordered_set<int> s;
for (int i = 0; i < arr.size(); i++){
// Calculate the complement that added to
// arr[i], equals the target
int complement = target - arr[i];
// Check if the complement exists in the set
if (s.find(complement) != s.end())
return true;
// Add the current element to the set
s.insert(arr[i]);
}
// If no pair is found
return false;
}
int main(){
vector<int> arr = {11, 15, 6, 8, 9, 10};
int target = 16;
if (pairInSortedRotated(arr, target))
cout << "true";
else
cout << "false";
return 0;
}
Java
// Java code to check whether any pair exists
// whose sum is equal to the given target value
import java.util.HashSet;
class GfG {
static boolean pairInSortedRotated(int[] arr, int target){
HashSet<Integer> set = new HashSet<>();
for (int i = 0; i < arr.length; i++) {
// Calculate the complement that added to
// arr[i], equals the target
int complement = target - arr[i];
// Check if the complement exists in the set
if (set.contains(complement)) {
return true;
}
// Add the current element to the set
set.add(arr[i]);
}
// If no pair is found
return false;
}
public static void main(String[] args) {
int[] arr = {11, 15, 6, 8, 9, 10};
int target = 16;
if (pairInSortedRotated(arr, target))
System.out.println("true");
else
System.out.println("false");
}
}
Python
# Python3 code to check whether any pair exists
# whose sum is equal to the given target value
def pairInSortedRotated(arr, target):
s = set()
for num in arr:
# Calculate the complement that added to
# num, equals the target
complement = target - num
# Check if the complement exists in the set
if complement in s:
return True
# Add the current element to the set
s.add(num)
# If no pair is found
return False
if __name__ == "__main__":
arr = [11, 15, 6, 8, 9, 10]
target = 16
if pairInSortedRotated(arr, target):
print("true")
else:
print("false")
C#
// C# code to check whether any pair exists
// whose sum is equal to the given target value
using System;
using System.Collections.Generic;
class GfG {
static bool pairInSortedRotated(int[] arr, int target){
HashSet<int> set = new HashSet<int>();
for (int i = 0; i < arr.Length; i++) {
// Calculate the complement that added to
// arr[i], equals the target
int complement = target - arr[i];
// Check if the complement exists in the set
if (set.Contains(complement))
return true;
// Add the current element to the set
set.Add(arr[i]);
}
// If no pair is found
return false;
}
static void Main(){
int[] arr = {11, 15, 6, 8, 9, 10};
int target = 16;
if (pairInSortedRotated(arr, target))
Console.WriteLine("true");
else
Console.WriteLine("false");
}
}
JavaScript
// Javascript code to check whether any pair exists
// whose sum is equal to the given target value
function pairInSortedRotated(arr, target) {
let set = new Set();
for (let num of arr) {
// Calculate the complement that added to
// num, equals the target
let complement = target - num;
// Check if the complement exists in the set
if (set.has(complement)) {
return true;
}
// Add the current element to the set
set.add(num);
}
// If no pair is found
return false;
}
// Driver Code
let arr = [11, 15, 6, 8, 9, 10];
let target = 16;
if (pairInSortedRotated(arr, target))
console.log("true");
else
console.log("false");
[Expected Approach] Two Pointer Technique - O(n) Time and O(1) Space
First find the largest element in an array which is the pivot point. The element just after the largest element is the smallest element. Once we have the indices of the largest and the smallest elements, we use two pointer technique to find the pair.
- Set the left pointer(l) to the smallest value and the right pointer(r) to the highest value.
- To handle the circular nature of the rotated array, we will use the modulo operation with the array size.
- While l ! = r, we shall keep checking if arr[l] + arr[r] = target.
- If arr[l] + arr[r] > target, update r = (r - 1 + n) % n.
- If arr[l] + arr[r] < target, update l = (l + 1) % n.
- If arr[l] + arr[r] = target, then return true.
- If no such pair is found after the iteration is complete, return false.
C++
// Cpp program to find a Pair Sum in a Sorted
// and Rotated Array using Two Pointer Technique
#include <iostream>
#include <vector>
using namespace std;
bool pairInSortedRotated(vector<int>& arr, int target) {
int n = arr.size();
// Find the pivot element
int i;
for (i = 0; i < n - 1; i++)
if (arr[i] > arr[i + 1])
break;
// l is now index of smallest element
int l = (i + 1) % n;
// r is now index of largest element
int r = i;
// Keep moving either l or r till they meet
while (l != r) {
// If we find a pair with sum target, return true
if (arr[l] + arr[r] == target)
return true;
// If current pair sum is less, move to higher sum
if (arr[l] + arr[r] < target)
l = (l + 1) % n;
// Move to lower sum
else
r = (r - 1 + n) % n;
}
return false;
}
int main() {
vector<int> arr = {11, 15, 6, 8, 9, 10};
int target = 16;
if (pairInSortedRotated(arr, target))
cout << "true";
else
cout << "false";
return 0;
}
Java
// Java program to find a Pair Sum in a Sorted
// and Rotated Array using Two Pointer Technique
class GfG {
static boolean pairInSortedRotated(int[] arr, int target) {
int n = arr.length;
// Find the pivot element
int i;
for (i = 0; i < n - 1; i++)
if (arr[i] > arr[i + 1])
break;
// l is now index of smallest element
int l = (i + 1) % n;
// r is now index of largest element
int r = i;
// Keep moving either l or r till they meet
while (l != r) {
// If we find a pair with sum target, return true
if (arr[l] + arr[r] == target)
return true;
// If current pair sum is less, move to higher sum
if (arr[l] + arr[r] < target)
l = (l + 1) % n;
// Move to lower sum side
else
r = (r - 1 + n) % n;
}
return false;
}
public static void main(String[] args) {
int[] arr = {11, 15, 6, 8, 9, 10};
int target = 16;
if (pairInSortedRotated(arr, target))
System.out.println("true");
else
System.out.println("false");
}
}
Python
# Python program to find a Pair Sum in a Sorted
# and Rotated Array using Two Pointer Technique
def pairInSortedRotated(arr, target):
n = len(arr)
# Find the pivot element
i = 0
for i in range(n - 1):
if arr[i] > arr[i + 1]:
break
# if whole array is sorted max
# element will be at last index
if arr[i] <= arr[i + 1]:
i += 1
# l is now index of smallest element
l = (i + 1) % n
# r is now index of largest element
r = i
# Keep moving either l or r till they meet
while l != r:
# If we find a pair with sum target, return true
if arr[l] + arr[r] == target:
return True
# If current pair sum is less, move to higher sum
if arr[l] + arr[r] < target:
l = (l + 1) % n
# Move to lower sum side
else:
r = (r - 1 + n) % n
return False
if __name__ == "__main__":
arr = [11, 15, 6, 8, 9, 10]
target = 16
if pairInSortedRotated(arr, target):
print("true")
else:
print("false")
C#
// C# program to find a Pair Sum in a Sorted
// and Rotated Array using Two Pointer Technique
using System;
using System.Collections.Generic;
class GfG {
static bool pairInSortedRotated(int[] arr, int target) {
int n = arr.Length;
// Find the pivot element
int i;
for (i = 0; i < n - 1; i++)
if (arr[i] > arr[i + 1])
break;
// l is now index of smallest element
int l = (i + 1) % n;
// r is now index of largest element
int r = i;
// Keep moving either l or r till they meet
while (l != r) {
// If we find a pair with sum target, return true
if (arr[l] + arr[r] == target)
return true;
// If current pair sum is less, move to higher sum
if (arr[l] + arr[r] < target)
l = (l + 1) % n;
// Move to lower sum side
else
r = (r - 1 + n) % n;
}
return false;
}
static void Main() {
int[] arr = { 11, 15, 6, 8, 9, 10 };
int target = 16;
if (pairInSortedRotated(arr, target))
Console.WriteLine("true");
else
Console.WriteLine("false");
}
}
JavaScript
// JavaScript program to find a Pair Sum in a Sorted
// and Rotated Array using Two Pointer Technique
function pairInSortedRotated(arr, target) {
let n = arr.length;
// Find the pivot element
let i;
for (i = 0; i < n - 1; i++)
if (arr[i] > arr[i + 1])
break;
// l is now index of smallest element
let l = (i + 1) % n;
// r is now index of largest element
let r = i;
// Keep moving either l or r till they meet
while (l !== r) {
// If we find a pair with sum target, return true
if (arr[l] + arr[r] === target)
return true;
// If current pair sum is less, move to higher sum
if (arr[l] + arr[r] < target)
l = (l + 1) % n;
// Move to lower sum side
else
r = (r - 1 + n) % n;
}
return false;
}
// Driver Code
let arr = [11, 15, 6, 8, 9, 10];
let target = 16;
if (pairInSortedRotated(arr, target))
console.log("true");
else
console.log("false");
Time Complexity: O(n)
Auxiliary Space: O(1)
Further Optimization : The above implementation find the pivot point using a linear search in O(n) Time. We can find the pivot point using Binary Search in O(Log n). Please refer Search in a sorted and rotated array for details. Please note that the overall time complexity remains same as we run a linear time two pointer algorithms after finding the pivot point.
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. Hereâs 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