Count number of triplets in an array having sum in the range [a, b]
Last Updated :
11 Jul, 2025
Given an array of distinct integers and a range [a, b], the task is to count the number of triplets having a sum in the range [a, b].
Examples:
Input : arr[] = {8, 3, 5, 2}
range = [7, 11]
Output : 1
There is only one triplet {2, 3, 5}
having sum 10 in range [7, 11].
Input : arr[] = {2, 7, 5, 3, 8, 4, 1, 9}
range = [8, 16]
Output : 36
A naive approach is to run three loops to consider all the triplets one by one. Find the sum of each triplet and increment the count if the sum lies in a given range [a, b].
Below is the implementation of the above approach:
C++
// C++ program to count triplets with
// sum that lies in given range [a, b].
#include <bits/stdc++.h>
using namespace std;
// Function to count triplets
int countTriplets(int arr[], int n, int a, int b)
{
// Initialize result
int ans = 0;
// Fix the first element as A[i]
for (int i = 0; i < n - 2; i++) {
// Fix the second element as A[j]
for (int j = i + 1; j < n - 1; j++) {
// Now look for the third number
for (int k = j + 1; k < n; k++)
if (arr[i] + arr[j] + arr[k] >= a
&& arr[i] + arr[j] + arr[k] <= b)
ans++;
}
}
return ans;
}
// Driver Code
int main()
{
int arr[] = { 2, 7, 5, 3, 8, 4, 1, 9 };
int n = sizeof arr / sizeof arr[0];
int a = 8, b = 16;
cout << countTriplets(arr, n, a, b) << endl;
return 0;
}
// Java program to count triplets
// with sum that lies in given
// range [a, b].
import java.util.*;
class GFG
{
// Function to count triplets
public static int countTriplets(int []arr, int n,
int a, int b)
{
// Initialize result
int ans = 0;
// Fix the first
// element as A[i]
for (int i = 0; i < n - 2; i++)
{
// Fix the second
// element as A[j]
for (int j = i + 1; j < n - 1; j++)
{
// Now look for the
// third number
for (int k = j + 1; k < n; k++)
{
if (arr[i] + arr[j] + arr[k] >= a &&
arr[i] + arr[j] + arr[k] <= b)
{ans++;}
}
}
}
return ans;
}
// Driver Code
public static void main(String[] args)
{
int[] arr = { 2, 7, 5, 3, 8, 4, 1, 9 };
int n = arr.length;
int a = 8, b = 16;
System.out.println("" + countTriplets(arr, n,
a, b));
}
}
// This code is contributed
// by Harshit Saini
# Python3 program to count
# triplets with sum that
# lies in given range [a, b].
# Function to count triplets
def countTriplets(arr, n, a, b):
# Initialize result
ans = 0
# Fix the first
# element as A[i]
for i in range(0, n - 2):
# Fix the second
# element as A[j]
for j in range(i + 1, n - 1):
# Now look for
# the third number
for k in range(j + 1, n):
if ((arr[i] + arr[j] + arr[k] >= a)
and (arr[i] + arr[j] + arr[k] <= b)):
ans += 1
return ans
# Driver code
if __name__ == "__main__":
arr = [ 2, 7, 5, 3, 8, 4, 1, 9 ]
n = len(arr)
a = 8; b = 16
print(countTriplets(arr, n, a, b))
# This code is contributed
# by Harshit Saini
// C# program to count triplets
// with sum that lies in given
// range [a, b].
using System;
class GFG
{
// Function to count triplets
public static int countTriplets(int []arr, int n,
int a, int b)
{
// Initialize result
int ans = 0;
// Fix the first
// element as A[i]
for (int i = 0;
i < n - 2; i++)
{
// Fix the second
// element as A[j]
for (int j = i + 1;
j < n - 1; j++)
{
// Now look for the
// third number
for (int k = j + 1;
k < n; k++)
{
if (arr[i] + arr[j] + arr[k] >= a &&
arr[i] + arr[j] + arr[k] <= b)
{ans++;}
}
}
}
return ans;
}
// Driver Code
public static void Main()
{
int[] arr = {2, 7, 5, 3, 8, 4, 1, 9};
int n = arr.Length;
int a = 8, b = 16;
Console.WriteLine("" + countTriplets(arr, n,
a, b));
}
}
// This code is contributed
// by Akanksha Rai(Abby_akku)
<?php
// PHP program to count triplets with
// sum that lies in given range [a, b].
// Function to count triplets
function countTriplets($arr, $n, $a, $b)
{
// Initialize result
$ans = 0;
// Fix the first element as A[i]
for ($i = 0; $i < $n - 2; $i++)
{
// Fix the second element as A[j]
for ($j = $i + 1; $j < $n - 1; $j++)
{
// Now look for the third number
for ($k = $j + 1; $k < $n; $k++)
if ($arr[$i] + $arr[$j] + $arr[$k] >= $a &&
$arr[$i] + $arr[$j] + $arr[$k] <= $b)
$ans++;
}
}
return $ans;
}
// Driver Code
$arr = array( 2, 7, 5, 3, 8, 4, 1, 9 );
$n = sizeof($arr);
$a = 8; $b = 16;
echo countTriplets($arr, $n, $a, $b) . "\n";
// This code is contributed
// by Akanksha Rai(Abby_akku)
?>
<script>
// Javascript program to count triplets with
// sum that lies in given range [a, b].
// Function to count triplets
function countTriplets( arr, n, a, b)
{
// Initialize result
var ans = 0;
// Fix the first element as A[i]
for (var i = 0; i < n - 2; i++) {
// Fix the second element as A[j]
for (var j = i + 1; j < n - 1; j++) {
// Now look for the third number
for (var k = j + 1; k < n; k++)
if (arr[i] + arr[j] + arr[k] >= a
&& arr[i] + arr[j] + arr[k] <= b)
ans++;
}
}
return ans;
}
// Driver Code
var arr = [ 2, 7, 5, 3, 8, 4, 1, 9 ];
var n = arr.length;
var a = 8, b = 16;
document.write( countTriplets(arr, n, a, b) );
</script>
Time complexity: O(n3)
Auxiliary Space: O(1) An efficient solution is to first find the count of triplets having a sum less than or equal to upper limit b in the range [a, b]. This count of triplets will also include triplets having a sum less than the lower limit a. Subtract the count of triplets having a sum less than a. The final result is the count of triplets having a sum in the range [a, b].
The algorithm is as follows:
- Find count of triplets having a sum less than or equal to b. Let this count be x.
- Find count of triplets having a sum less than a. Let this count be y.
- Final result is x-y.
To find the count of triplets having a sum less than or equal to the given value, refer Count triplets with sum smaller than a given value
Below is the implementation of the above approach:
C++
// C++ program to count triplets with
// sum that lies in given range [a, b].
#include <bits/stdc++.h>
using namespace std;
// Function to find count of triplets having
// sum less than or equal to val.
int countTripletsLessThan(int arr[], int n, int val)
{
// sort the input array.
sort(arr, arr + n);
// Initialize result
int ans = 0;
int j, k;
// to store sum
int sum;
// Fix the first element
for (int i = 0; i < n - 2; i++) {
// Initialize other two elements as
// corner elements of subarray arr[j+1..k]
j = i + 1;
k = n - 1;
// Use Meet in the Middle concept.
while (j != k) {
sum = arr[i] + arr[j] + arr[k];
// If sum of current triplet
// is greater, then to reduce it
// decrease k.
if (sum > val)
k--;
// If sum is less than or equal
// to given value, then add
// possible triplets (k-j) to result.
else {
ans += (k - j);
j++;
}
}
}
return ans;
}
// Function to return count of triplets having
// sum in range [a, b].
int countTriplets(int arr[], int n, int a, int b)
{
// to store count of triplets.
int res;
// Find count of triplets having sum less
// than or equal to b and subtract count
// of triplets having sum less than or
// equal to a-1.
res = countTripletsLessThan(arr, n, b) -
countTripletsLessThan(arr, n, a - 1);
return res;
}
// Driver Code
int main()
{
int arr[] = { 2, 7, 5, 3, 8, 4, 1, 9 };
int n = sizeof arr / sizeof arr[0];
int a = 8, b = 16;
cout << countTriplets(arr, n, a, b) << endl;
return 0;
}
// Java program to count triplets
// with sum that lies in given
// range [a, b].
import java.util.*;
class GFG
{
// Function to find count of
// triplets having sum less
// than or equal to val.
public static int countTripletsLessThan(int []arr,
int n, int val)
{
// sort the input array.
Arrays.sort(arr);
// Initialize result
int ans = 0;
int j, k;
// to store sum
int sum;
// Fix the first element
for (int i = 0; i < n - 2; i++)
{
// Initialize other two elements
// as corner elements of subarray
// arr[j+1..k]
j = i + 1;
k = n - 1;
// Use Meet in the
// Middle concept.
while (j != k)
{
sum = arr[i] + arr[j] + arr[k];
// If sum of current triplet
// is greater, then to reduce it
// decrease k.
if (sum > val)
k--;
// If sum is less than or
// equal to given value,
// then add possible
// triplets (k-j) to result.
else
{
ans += (k - j);
j++;
}
}
}
return ans;
}
// Function to return count
// of triplets having sum
// in range [a, b].
public static int countTriplets(int arr[], int n,
int a, int b)
{
// to store count
// of triplets.
int res;
// Find count of triplets
// having sum less than or
// equal to b and subtract
// count of triplets having
// sum less than or equal
// to a-1.
res = countTripletsLessThan(arr, n, b) -
countTripletsLessThan(arr, n, a - 1);
return res;
}
// Driver Code
public static void main(String[] args)
{
int[] arr = {2, 7, 5, 3,
8, 4, 1, 9};
int n = arr.length;
int a = 8, b = 16;
System.out.println("" + countTriplets(arr, n,
a, b));
}
}
// This code is contributed
// by Harshit Saini
# Python program to count
# triplets with sum that
# lies in given range [a, b].
# Function to find count of
# triplets having sum less
# than or equal to val.
def countTripletsLessThan(arr, n, val):
# sort the input array.
arr.sort()
# Initialize result
ans = 0
j = 0; k = 0
# to store sum
sum = 0
# Fix the first element
for i in range(0,n-2):
# Initialize other two
# elements as corner
# elements of subarray
# arr[j+1..k]
j = i + 1
k = n - 1
# Use Meet in the
# Middle concept.
while j != k :
sum = arr[i] + arr[j] + arr[k]
# If sum of current triplet
# is greater, then to reduce it
# decrease k.
if sum > val:
k-=1
# If sum is less than or
# equal to given value,
# then add possible
# triplets (k-j) to result.
else :
ans += (k - j)
j += 1
return ans
# Function to return
# count of triplets having
# sum in range [a, b].
def countTriplets(arr, n, a, b):
# to store count of triplets.
res = 0
# Find count of triplets
# having sum less than or
# equal to b and subtract
# count of triplets having
# sum less than or equal to a-1.
res = (countTripletsLessThan(arr, n, b) -
countTripletsLessThan(arr, n, a - 1))
return res
# Driver code
if __name__ == "__main__":
arr = [ 2, 7, 5, 3, 8, 4, 1, 9 ]
n = len(arr)
a = 8; b = 16
print(countTriplets(arr, n, a, b))
# This code is contributed by
# Harshit Saini
// C# program to count triplets
// with sum that lies in given
// range [a, b].
using System;
class GFG
{
// Function to find count of
// triplets having sum less
// than or equal to val.
public static int countTripletsLessThan(int[] arr,
int n, int val)
{
// sort the input array.
Array.Sort(arr);
// Initialize result
int ans = 0;
int j, k;
// to store sum
int sum;
// Fix the first element
for (int i = 0; i < n - 2; i++)
{
// Initialize other two elements
// as corner elements of subarray
// arr[j+1..k]
j = i + 1;
k = n - 1;
// Use Meet in the
// Middle concept.
while (j != k)
{
sum = arr[i] + arr[j] + arr[k];
// If sum of current triplet
// is greater, then to reduce it
// decrease k.
if (sum > val)
k--;
// If sum is less than or
// equal to given value,
// then add possible
// triplets (k-j) to result.
else
{
ans += (k - j);
j++;
}
}
}
return ans;
}
// Function to return count
// of triplets having sum
// in range [a, b].
public static int countTriplets(int[] arr, int n,
int a, int b)
{
// to store count
// of triplets.
int res;
// Find count of triplets
// having sum less than or
// equal to b and subtract
// count of triplets having
// sum less than or equal
// to a-1.
res = countTripletsLessThan(arr, n, b) -
countTripletsLessThan(arr, n, a - 1);
return res;
}
// Driver Code
public static void Main()
{
int[] arr = {2, 7, 5, 3,
8, 4, 1, 9};
int n = arr.Length;
int a = 8, b = 16;
Console.WriteLine("" + countTriplets(arr, n,
a, b));
}
}
// This code is contributed
// by Akanksha Rai(Abby_akku)
<?php
// PHP program to count triplets with
// sum that lies in given range [a, b].
// Function to find count of triplets
// having sum less than or equal to val.
function countTripletsLessThan($arr, $n, $val)
{
// sort the input array.
sort($arr);
// Initialize result
$ans = 0;
// to store sum
$sum;
// Fix the first element
for ($i = 0; $i < $n - 2; $i++)
{
// Initialize other two elements as
// corner elements of subarray arr[j+1..k]
$j = $i + 1;
$k = $n - 1;
// Use Meet in the Middle concept.
while ($j != $k)
{
$sum = $arr[$i] + $arr[$j] + $arr[$k];
// If sum of current triplet is greater,
// then to reduce it decrease k.
if ($sum > $val)
$k--;
// If sum is less than or equal
// to given value, then add possible
// triplets (k-j) to result.
else
{
$ans += ($k - $j);
$j++;
}
}
}
return $ans;
}
// Function to return count of triplets
// having sum in range [a, b].
function countTriplets($arr, $n, $a, $b)
{
// to store count of triplets.
$res;
// Find count of triplets having sum less
// than or equal to b and subtract count
// of triplets having sum less than or
// equal to a-1.
$res = countTripletsLessThan($arr, $n, $b) -
countTripletsLessThan($arr, $n, $a - 1);
return $res;
}
// Driver Code
$arr = array( 2, 7, 5, 3, 8, 4, 1, 9 );
$n = sizeof($arr);
$a = 8;
$b = 16;
echo countTriplets($arr, $n, $a, $b), "\n";
// This code is contributed by Sachin
?>
<script>
// JavaScript program to count triplets
// with sum that lies in given
// range [a, b].
// Function to find count of
// triplets having sum less
// than or equal to val.
function countTripletsLessThan(arr, n, val) {
// sort the input array.
arr.sort();
// Initialize result
var ans = 0;
var j, k;
// to store sum
var sum;
// Fix the first element
for (var i = 0; i < n - 2; i++) {
// Initialize other two elements
// as corner elements of subarray
// arr[j+1..k]
j = i + 1;
k = n - 1;
// Use Meet in the
// Middle concept.
while (j != k) {
sum = arr[i] + arr[j] + arr[k];
// If sum of current triplet
// is greater, then to reduce it
// decrease k.
if (sum > val) k--;
// If sum is less than or
// equal to given value,
// then add possible
// triplets (k-j) to result.
else {
ans += k - j;
j++;
}
}
}
return ans;
}
// Function to return count
// of triplets having sum
// in range [a, b].
function countTriplets(arr, n, a, b) {
// to store count
// of triplets.
var res;
// Find count of triplets
// having sum less than or
// equal to b and subtract
// count of triplets having
// sum less than or equal
// to a-1.
res =
countTripletsLessThan(arr, n, b) -
countTripletsLessThan(arr, n, a - 1);
return res;
}
// Driver Code
var arr = [2, 7, 5, 3, 8, 4, 1, 9];
var n = arr.length;
var a = 8,
b = 16;
document.write("" + countTriplets(arr, n, a, b));
</script>
Time complexity: O(n2)
Auxiliary space: O(1)
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