Two Sum - Pair with given Sum
Last Updated :
26 Jul, 2025
Given an array arr[] of n integers and a target value, check if there exists a pair whose sum equals the target. This is a variation of the 2-Sum problem.
Examples:
Input: arr[] = [0, -1, 2, -3, 1], target = -2
Output: true
Explanation: There is a pair (1, -3) with the sum equal to given target, 1 + (-3) = -2.
Input: arr[] = [1, -2, 1, 0, 5], target = 0
Output: false
Explanation: There is no pair with sum equals to given target.
[Naive Approach] Generating all Possible Pairs - O(n2) time and O(1) space
The basic approach is to generate all the possible pairs and check if any of them add up to the target value. To generate all pairs, we simply run two nested loops.
C++
#include <iostream>
#include <vector>
using namespace std;
bool twoSum(vector<int> &arr, int target) {
int n = arr.size();
for (int i = 0; i < n; i++) {
// For each element arr[i], check every
// other element arr[j] that comes after it
for (int j = i + 1; j < n; j++) {
// Check if the sum of the current pair
// equals the target
if (arr[i] + arr[j] == target) {
return true;
}
}
}
// If no pair is found after checking
// all possibilities
return false;
}
int main() {
vector<int> arr = {0, -1, 2, -3, 1};
int target = -2;
if(twoSum(arr, target))
cout << "true";
else
cout << "false";
return 0;
}
#include <stdbool.h>
#include <stdio.h>
bool twoSum(int arr[], int n, int target){
for (int i = 0; i < n; i++){
// For each element arr[i], check every
// other element arr[j] that comes after it
for (int j = i + 1; j < n; j++){
// Check if the sum of the current pair
// equals the target
if (arr[i] + arr[j] == target)
return true;
}
}
// If no pair is found after checking
// all possibilities
return false;
}
int main(){
int arr[] = {0, -1, 2, -3, 1};
int target = -2;
int n = sizeof(arr) / sizeof(arr[0]);
// Call the twoSum function and print the result
if (twoSum(arr, n, target))
printf("true\n");
else
printf("false\n");
return 0;
}
class GfG {
static boolean twoSum(int[] arr, int target){
int n = arr.length;
for (int i = 0; i < n; i++) {
// For each element arr[i], check every
// other element arr[j] that comes after it
for (int j = i + 1; j < n; j++) {
// Check if the sum of the current pair
// equals the target
if (arr[i] + arr[j] == target) {
return true;
}
}
}
// If no pair is found after checking
// all possibilities
return false;
}
public static void main(String[] args){
int[] arr = { 0, -1, 2, -3, 1 };
int target = -2;
if (twoSum(arr, target))
System.out.println("true");
else
System.out.println("false");
}
}
def twoSum(arr, target):
n = len(arr)
for i in range(n):
# For each element arr[i], check every
# other element arr[j] that comes after it
for j in range(i + 1, n):
# Check if the sum of the current pair
# equals the target
if arr[i] + arr[j] == target:
return True
# If no pair is found after checking
# all possibilities
return False
if __name__ == "__main__":
arr = [0, -1, 2, -3, 1]
target = -2
if twoSum(arr, target):
print("true")
else:
print("false")
using System;
class GfG {
static bool twoSum(int[] arr, int target) {
int n = arr.Length;
for (int i = 0; i < n; i++) {
// For each element arr[i], check every
// other element arr[j] that comes after it
for (int j = i + 1; j < n; j++) {
// Check if the sum of the current pair
// equals the target
if (arr[i] + arr[j] == target) {
return true;
}
}
}
// If no pair is found after checking
// all possibilities
return false;
}
static void Main() {
int[] arr = { 0, -1, 2, -3, 1 };
int target = -2;
if (twoSum(arr, target))
Console.WriteLine("true");
else
Console.WriteLine("false");
}
}
function twoSum(arr, target) {
let n = arr.length;
for (let i = 0; i < n; i++) {
// For each element arr[i], check every
// other element arr[j] that comes after it
for (let j = i + 1; j < n; j++) {
// Check if the sum of the current pair
// equals the target
if (arr[i] + arr[j] === target) {
return true;
}
}
}
// If no pair is found after checking
// all possibilities
return false;
}
// Driver Code
let arr = [0, -1, 2, -3, 1];
let target = -2;
if (twoSum(arr, target))
console.log("true");
else
console.log("false");
[Better Approach 1] Sorting and Binary Search - O(n × log(n)) time and O(1) space
To check if a pair with a given sum exists in the array, we first sort the array. Then for each element, we compute the required complement (i.e., target - arr[i]) and perform binary search on the remaining subarray (from index i+1 to end) to find that complement.
Step By Step Implementation:
- Sort the array in non-decreasing order.
- Loop through each element arr[i] from index 0 to n-2.
- For each arr[i], calculate complement = target - arr[i].
- Perform binary search for complement in the subarray from index i+1 to n-1.
- If the complement is found, return true.
- If the loop completes without finding any valid pair, return false.
C++
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
// Function to perform binary search
bool binarySearch(vector<int> &arr, int left,
int right, int target){
while (left <= right){
int mid = left + (right - left) / 2;
if (arr[mid] == target)
return true;
if (arr[mid] < target)
left = mid + 1;
else
right = mid - 1;
}
return false;
}
bool twoSum(vector<int> &arr, int target){
sort(arr.begin(), arr.end());
for (int i = 0; i < arr.size(); i++){
int complement = target - arr[i];
// Use binary search to
// find the complement
if (binarySearch(arr, i + 1,
arr.size() - 1, complement))
return true;
}
// If no pair is found
return false;
}
int main(){
vector<int> arr = {0, -1, 2, -3, 1};
int target = -2;
if (twoSum(arr, target))
cout << "true";
else
cout << "false";
return 0;
}
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
// Comparison function for qsort
int compare(const void *a, const void *b){
return (*(int *)a - *(int *)b);
}
// Function to perform binary search
bool binarySearch(int arr[], int left,
int right, int target){
while (left <= right){
int mid = left + (right - left) / 2;
if (arr[mid] == target)
return true;
if (arr[mid] < target)
left = mid + 1;
else
right = mid - 1;
}
return false;
}
bool twoSum(int arr[], int n, int target){
qsort(arr, n, sizeof(int), compare);
for (int i = 0; i < n; i++){
int complement = target - arr[i];
// Use binary search to
// find the complement
if (binarySearch(arr, i + 1,
n - 1, complement))
return true;
}
// If no pair is found
return false;
}
int main(){
int arr[] = {0, -1, 2, -3, 1};
int target = -2;
int n = sizeof(arr) / sizeof(arr[0]);
if (twoSum(arr, n, target))
printf("true\n");
else
printf("false\n");
return 0;
}
import java.util.Arrays;
class GfG {
// Function to perform binary search
static boolean binarySearch(int[] arr, int left,
int right, int target){
while (left <= right) {
int mid = left + (right - left) / 2;
if (arr[mid] == target)
return true;
if (arr[mid] < target)
left = mid + 1;
else
right = mid - 1;
}
return false;
}
static boolean twoSum(int[] arr, int target){
Arrays.sort(arr);
for (int i = 0; i < arr.length; i++) {
int complement = target - arr[i];
// Use binary search to find the complement
if (binarySearch(arr, i + 1, arr.length - 1,
complement))
return true;
}
// If no pair is found
return false;
}
public static void main(String[] args){
int[] arr = { 0, -1, 2, -3, 1 };
int target = -2;
if (twoSum(arr, target)) {
System.out.println("true");
}
else {
System.out.println("false");
}
}
}
# Function to perform binary search
def binarySearch(arr, left, right, target):
while left <= right:
mid = left + (right - left) // 2
if arr[mid] == target:
return True
elif arr[mid] < target:
left = mid + 1
else:
right = mid - 1
return False
def twoSum(arr, target):
arr.sort()
for i in range(len(arr)):
complement = target - arr[i]
# Use binary search to find the complement
if binarySearch(arr, i + 1,
len(arr) - 1, complement):
return True
# If no pair is found
return False
if __name__ == "__main__":
arr = [0, -1, 2, -3, 1]
target = -2
if twoSum(arr, target):
print("true")
else:
print("false")
using System;
class GfG {
// Function to perform binary search
static bool binarySearch(int[] arr, int left,
int right, int target){
while (left <= right) {
int mid = left + (right - left) / 2;
if (arr[mid] == target)
return true;
if (arr[mid] < target)
left = mid + 1;
else
right = mid - 1;
}
return false;
}
static bool twoSum(int[] arr, int target){
Array.Sort(arr);
for (int i = 0; i < arr.Length; i++) {
int complement = target - arr[i];
// Use binary search to find the complement
if (binarySearch(arr, i + 1, arr.Length - 1,
complement))
return true;
}
// If no pair is found
return false;
}
static void Main(){
int[] arr = { 0, -1, 2, -3, 1 };
int target = -2;
if (twoSum(arr, target)) {
Console.WriteLine("true");
}
else {
Console.WriteLine("false");
}
}
}
// Function to perform binary search
function binarySearch(arr, left, right, target) {
while (left <= right) {
let mid = Math.floor(left + (right - left) / 2);
if (arr[mid] === target)
return true;
if (arr[mid] < target)
left = mid + 1;
else
right = mid - 1;
}
return false;
}
function twoSum(arr, target) {
arr.sort((a, b) => a - b);
for (let i = 0; i < arr.length; i++) {
let complement = target - arr[i];
// Use binary search to find the complement
if (binarySearch(arr, i + 1,
arr.length - 1, complement))
return true;
}
// If no pair is found
return false;
}
// Driver Code
let arr = [0, -1, 2, -3, 1];
let target = -2;
if (twoSum(arr, target)) {
console.log("true");
} else {
console.log("false");
}
[Better Approach 2] Sorting and Two-Pointer Technique - O(n × log(n)) time and O(1) space
The idea is to use the two-pointer technique but for using the two-pointer technique, the array must be sorted. Once the array is sorted then we can use this approach by keeping one pointer at the beginning (left) and another at the end (right) of the array.
Check the sum of the elements at these two pointers:
- If the sum equals the target, we’ve found the pair.
- If the sum is less than the target, move the left pointer to the right to increase the sum.
- If the sum is greater than the target, move the right pointer to the left to decrease the sum.
Note: This approach is the best approach for a sorted array. But if array is not sorted, then we use the below approach.
C++
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
bool twoSum(vector<int> &arr, int target){
sort(arr.begin(), arr.end());
int left = 0, right = arr.size() - 1;
// Iterate while left pointer
// is less than right
while (left < right){
int sum = arr[left] + arr[right];
// Check if the sum matches the target
if (sum == target)
return true;
else if (sum < target)
// Move left pointer to the right
left++;
else
// Move right pointer to the left
right--;
}
// If no pair is found
return false;
}
int main(){
vector<int> arr = {0, -1, 2, -3, 1};
int target = -2;
if (twoSum(arr, target))
cout << "true";
else
cout << "false";
return 0;
}
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
// Comparison function for qsort
int compare(const void *a, const void *b){
return (*(int *)a - *(int *)b);
}
bool twoSum(int arr[], int n, int target){
qsort(arr, n, sizeof(int), compare);
int left = 0, right = n - 1;
// Iterate while left pointer is less than right
while (left < right){
int sum = arr[left] + arr[right];
// Check if the sum matches the target
if (sum == target)
return true;
else if (sum < target)
// Move left pointer to the right
left++;
else
// Move right pointer to the left
right--;
}
// If no pair is found
return false;
}
int main(){
int arr[] = {0, -1, 2, -3, 1};
int target = -2;
int n = sizeof(arr) / sizeof(arr[0]);
if (twoSum(arr, n, target))
printf("true\n");
else
printf("false\n");
return 0;
}
import java.util.Arrays;
class GfG {
static boolean twoSum(int[] arr, int target){
Arrays.sort(arr);
int left = 0, right = arr.length - 1;
// Iterate while left pointer is less than right
while (left < right) {
int sum = arr[left] + arr[right];
// Check if the sum matches the target
if (sum == target)
return true;
else if (sum < target)
// Move left pointer to the right
left++;
else
// Move right pointer to the left
right--;
}
// If no pair is found
return false;
}
public static void main(String[] args){
int[] arr = { 0, -1, 2, -3, 1 };
int target = -2;
if (twoSum(arr, target)) {
System.out.println("true");
}
else {
System.out.println("false");
}
}
}
def twoSum(arr, target):
arr.sort()
left, right = 0, len(arr) - 1
# Iterate while left pointer is less than right
while left < right:
sum = arr[left] + arr[right]
# Check if the sum matches the target
if sum == target:
return True
elif sum < target:
# Move left pointer to the right
left += 1
else:
# Move right pointer to the left
right -= 1
# If no pair is found
return False
if __name__ == "__main__":
arr = [0, -1, 2, -3, 1]
target = -2
if twoSum(arr, target):
print("true")
else:
print("false")
using System;
using System.Linq;
class GfG {
static bool twoSum(int[] arr, int target){
Array.Sort(arr);
int left = 0, right = arr.Length - 1;
// Iterate while left pointer is less than right
while (left < right) {
int sum = arr[left] + arr[right];
// Check if the sum matches the target
if (sum == target)
return true;
else if (sum < target)
// Move left pointer to the right
left++;
else
// Move right pointer to the left
right--;
}
// If no pair is found
return false;
}
static void Main(){
int[] arr = { 0, -1, 2, -3, 1 };
int target = -2;
if (twoSum(arr, target))
Console.WriteLine("true");
else
Console.WriteLine("false");
}
}
function twoSum(arr, target)
{
arr.sort((a, b) => a - b);
let left = 0, right = arr.length - 1;
// Iterate while left pointer is less than right
while (left < right) {
let sum = arr[left] + arr[right];
// Check if the sum matches the target
if (sum === target)
return true;
else if (sum < target)
// Move left pointer to the right
left++;
else
// Move right pointer to the left
right--;
}
// If no pair is found
return false;
}
// Driver Code
let arr = [ 0, -1, 2, -3, 1 ];
let target = -2;
if (twoSum(arr, target)) {
console.log("true");
} else {
console.log("false");
}
[Expected Approach] Using Hash Set - O(n) time and O(n) space
Hashing provides a more efficient solution to the 2-Sum problem. Rather than checking every possible pair, we store each number in an unordered set during iterating over the array's elements. For each number, we calculate its complement (i.e., target - current number) and check if this complement exists in the set. If it does, we have successfully found the pair that sums to the target.
Step By Step Implementations:
- Create an empty Hash Set or Unordered Set
- Iterate through the array and for each number in the array:
=> Calculate the complement (target - current number).
=> Check if the complement exists in the set:
- If it is, then pair found.
- If it isn’t, add the current number to the set. - If the loop completes without finding a pair, return that no pair exists.
C++
#include <iostream>
#include <vector>
#include <unordered_set>
using namespace std;
bool twoSum(vector<int> &arr, int target){
// Create an unordered_set to store the elements
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 = {0, -1, 2, -3, 1};
int target = -2;
if (twoSum(arr, target))
cout << "true";
else
cout << "false";
return 0;
}
import java.util.HashSet;
class GfG {
static boolean twoSum(int[] arr, int target){
// Create a HashSet to store the elements
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 = { 0, -1, 2, -3, 1 };
int target = -2;
if (twoSum(arr, target))
System.out.println("true");
else
System.out.println("false");
}
}
def twoSum(arr, target):
# Create a set to store the elements
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 = [0, -1, 2, -3, 1]
target = -2
if twoSum(arr, target):
print("true")
else:
print("false")
using System;
using System.Collections.Generic;
class GfG {
static bool twoSum(int[] arr, int target){
// Create a HashSet to store the elements
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 = { 0, -1, 2, -3, 1 };
int target = -2;
if (twoSum(arr, target))
Console.WriteLine("true");
else
Console.WriteLine("false");
}
}
function twoSum(arr, target) {
// Create a Set to store the elements
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 = [0, -1, 2, -3, 1];
let target = -2;
if (twoSum(arr, target))
console.log("true");
else
console.log("false");
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