Count distinct elements from a range of a sorted sequence from a given frequency array
Last Updated :
23 Jul, 2025
Given two integers L and R and an array arr[] consisting of N positive integers( 1-based indexing ) such that the frequency of ith element of a sorted sequence, say A[], is arr[i]. The task is to find the number of distinct elements from the range [L, R] in the sequence A[].
Examples:
Input: arr[] = {3, 6, 7, 1, 8}, L = 3, R = 7
Output: 2
Explanation: From the given frequency array, the sorted array will be {1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, ....}. Now, the number of distinct elements from the range [3, 7] is 2( = {1, 2}).
Input: arr[] = {1, 2, 3, 4}, L = 3, R = 4
Output: 2
Naive Approach: The simplest approach to solve the given problem is to construct the sorted sequence from the given array arr[] using the given frequencies and then traverse the constructed array over the range [L, R] to count the number of distinct elements.
Code-
C++
// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;
// Function to count the number of
// distinct elements over the range
// [L, R] in the sorted sequence
void countDistinct(vector<int> arr,
int L, int R)
{
vector<int> vec;
for(int i=0;i<arr.size();i++){
int temp=arr[i];
for(int j=0;j<temp;j++){
vec.push_back(i+1);
}
}
int curr=INT_MIN;
int count=0;
for(int i=L-1;i<R;i++){
if(curr!=vec[i]){
count++;
curr=vec[i];
}
}
cout<<count<<endl;
}
// Driver Code
int main()
{
vector<int> arr{ 3, 6, 7, 1, 8 };
int L = 3;
int R = 7;
countDistinct(arr, L, R);
}
import java.util.*;
class GFG {
// Function to count the number of
// distinct elements over the range
// [L, R] in the sorted sequence
static void countDistinct(ArrayList<Integer> arr, int L,
int R)
{
ArrayList<Integer> vec = new ArrayList<Integer>();
for (int i = 0; i < arr.size(); i++) {
int temp = arr.get(i);
for (int j = 0; j < temp; j++) {
vec.add(i + 1);
}
}
int curr = Integer.MIN_VALUE;
int count = 0;
for (int i = L - 1; i < R; i++) {
if (curr != vec.get(i)) {
count++;
curr = vec.get(i);
}
}
System.out.println(count);
}
// Driver Code
public static void main(String[] args)
{
ArrayList<Integer> arr = new ArrayList<Integer>(
Arrays.asList(3, 6, 7, 1, 8));
int L = 3;
int R = 7;
countDistinct(arr, L, R);
}
}
# Python program for the above approach
def countDistinct(arr, L, R):
# create a new vector
vec = []
for i in range(len(arr)):
temp = arr[i]
for j in range(temp):
vec.append(i+1)
curr = float('-inf')
count = 0
for i in range(L-1, R):
if curr != vec[i]:
count += 1
curr = vec[i]
print(count)
# Driver Code
if __name__ == '__main__':
arr = [3, 6, 7, 1, 8]
L = 3
R = 7
countDistinct(arr, L, R)
using System;
using System.Collections.Generic;
class GFG
{
// Function to count the number of distinct elements over the range
// [L, R] in the sorted sequence
static void CountDistinct(List<int> arr, int L, int R)
{
List<int> vec = new List<int>();
// Create a sorted sequence with occurrences of elements from the input array
foreach (int temp in arr)
{
for (int j = 0; j < temp; j++)
{
vec.Add(arr.IndexOf(temp) + 1);
}
}
int curr = int.MinValue;
int count = 0;
// Count the number of distinct elements in the range [L, R]
for (int i = L - 1; i < R; i++)
{
if (curr != vec[i])
{
count++;
curr = vec[i];
}
}
Console.WriteLine(count);
}
// Driver Code
static void Main()
{
List<int> arr = new List<int> { 3, 6, 7, 1, 8 };
int L = 3;
int R = 7;
CountDistinct(arr, L, R);
}
}
// Function to count the number of
// distinct elements over the range
// [L, R] in the sorted sequence
function countDistinct(arr, L, R) {
// creating sorted sequence
let vec = [];
for (let i = 0; i < arr.length; i++) {
let temp = arr[i];
for (let j = 0; j < temp; j++) {
vec.push(i + 1);
}
}
// Counting distinct elements
let curr = Number.MIN_SAFE_INTEGER;
let count = 0;
for (let i = L - 1; i < R; i++) {
if (curr !== vec[i]) {
count++;
curr = vec[i];
}
}
console.log(count);
}
// test case
let arr = [3, 6, 7, 1, 8];
let L = 3;
let R = 7;
countDistinct(arr, L, R);
Time Complexity: O(S + R - L)
Auxiliary Space: O(S), where S is the sum of the array elements.
Efficient Approach: The above approach can be optimized by using the Binary Search and the prefix sum technique to find the number of distinct elements over the range [L, R]. Follow the steps below to solve the given problem:
- Initialize an auxiliary array, say prefix[] that stores the prefix sum of the given array elements.
- Find the prefix sum of the given array and stored it in the array prefix[].
- By using binary search, find the first index at which the value in prefix[] is at least L, say left.
- By using binary search, find the first index at which the value in prefix[] is at least R, say right.
- After completing the above steps, print the value of (right - left + 1) as the result.
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;
// Function to find the first index
// with value is at least element
int binarysearch(int array[], int right,
int element)
{
// Update the value of left
int left = 1;
// Update the value of right
// Binary search for the element
while (left <= right)
{
// Find the middle element
int mid = (left + right / 2);
if (array[mid] == element)
{
return mid;
}
// Check if the value lies
// between the elements at
// index mid - 1 and mid
if (mid - 1 > 0 && array[mid] > element &&
array[mid - 1] < element)
{
return mid;
}
// Check in the right subarray
else if (array[mid] < element)
{
// Update the value
// of left
left = mid + 1;
}
// Check in left subarray
else
{
// Update the value of
// right
right = mid - 1;
}
}
return 1;
}
// Function to count the number of
// distinct elements over the range
// [L, R] in the sorted sequence
void countDistinct(vector<int> arr,
int L, int R)
{
// Stores the count of distinct
// elements
int count = 0;
// Create the prefix sum array
int pref[arr.size() + 1];
for(int i = 1; i <= arr.size(); ++i)
{
// Update the value of count
count += arr[i - 1];
// Update the value of pref[i]
pref[i] = count;
}
// Calculating the first index
// of L and R using binary search
int left = binarysearch(pref, arr.size() + 1, L);
int right = binarysearch(pref, arr.size() + 1, R);
// Print the resultant count
cout << right - left + 1;
}
// Driver Code
int main()
{
vector<int> arr{ 3, 6, 7, 1, 8 };
int L = 3;
int R = 7;
countDistinct(arr, L, R);
}
// This code is contributed by ipg2016107
// Java program for the above approach
import java.io.*;
import java.util.*;
class GFG {
// Function to find the first index
// with value is at least element
static int binarysearch(int array[],
int element)
{
// Update the value of left
int left = 1;
// Update the value of right
int right = array.length - 1;
// Binary search for the element
while (left <= right) {
// Find the middle element
int mid = (int)(left + right / 2);
if (array[mid] == element) {
return mid;
}
// Check if the value lies
// between the elements at
// index mid - 1 and mid
if (mid - 1 > 0
&& array[mid] > element
&& array[mid - 1] < element) {
return mid;
}
// Check in the right subarray
else if (array[mid] < element) {
// Update the value
// of left
left = mid + 1;
}
// Check in left subarray
else {
// Update the value of
// right
right = mid - 1;
}
}
return 1;
}
// Function to count the number of
// distinct elements over the range
// [L, R] in the sorted sequence
static void countDistinct(int arr[],
int L, int R)
{
// Stores the count of distinct
// elements
int count = 0;
// Create the prefix sum array
int pref[] = new int[arr.length + 1];
for (int i = 1; i <= arr.length; ++i) {
// Update the value of count
count += arr[i - 1];
// Update the value of pref[i]
pref[i] = count;
}
// Calculating the first index
// of L and R using binary search
int left = binarysearch(pref, L);
int right = binarysearch(pref, R);
// Print the resultant count
System.out.println(
(right - left) + 1);
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 3, 6, 7, 1, 8 };
int L = 3;
int R = 7;
countDistinct(arr, L, R);
}
}
# Python3 program for the above approach
# Function to find the first index
# with value is at least element
def binarysearch(array, right,
element):
# Update the value of left
left = 1
# Update the value of right
# Binary search for the element
while (left <= right):
# Find the middle element
mid = (left + right // 2)
if (array[mid] == element):
return mid
# Check if the value lies
# between the elements at
# index mid - 1 and mid
if (mid - 1 > 0 and array[mid] > element and
array[mid - 1] < element):
return mid
# Check in the right subarray
elif (array[mid] < element):
# Update the value
# of left
left = mid + 1
# Check in left subarray
else:
# Update the value of
# right
right = mid - 1
return 1
# Function to count the number of
# distinct elements over the range
# [L, R] in the sorted sequence
def countDistinct(arr, L, R):
# Stores the count of distinct
# elements
count = 0
# Create the prefix sum array
pref = [0] * (len(arr) + 1)
for i in range(1, len(arr) + 1):
# Update the value of count
count += arr[i - 1]
# Update the value of pref[i]
pref[i] = count
# Calculating the first index
# of L and R using binary search
left = binarysearch(pref, len(arr) + 1, L)
right = binarysearch(pref, len(arr) + 1, R)
# Print the resultant count
print(right - left + 1)
# Driver Code
if __name__ == "__main__":
arr = [ 3, 6, 7, 1, 8 ]
L = 3
R = 7
countDistinct(arr, L, R)
# This code is contributed by ukasp
// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG{
// Function to find the first index
// with value is at least element
static int binarysearch(int []array, int right,
int element)
{
// Update the value of left
int left = 1;
// Update the value of right
// Binary search for the element
while (left <= right)
{
// Find the middle element
int mid = (left + right / 2);
if (array[mid] == element)
{
return mid;
}
// Check if the value lies
// between the elements at
// index mid - 1 and mid
if (mid - 1 > 0 && array[mid] > element &&
array[mid - 1] < element)
{
return mid;
}
// Check in the right subarray
else if (array[mid] < element)
{
// Update the value
// of left
left = mid + 1;
}
// Check in left subarray
else
{
// Update the value of
// right
right = mid - 1;
}
}
return 1;
}
// Function to count the number of
// distinct elements over the range
// [L, R] in the sorted sequence
static void countDistinct(List<int> arr,
int L, int R)
{
// Stores the count of distinct
// elements
int count = 0;
// Create the prefix sum array
int []pref = new int[arr.Count + 1];
for(int i = 1; i <= arr.Count; ++i)
{
// Update the value of count
count += arr[i - 1];
// Update the value of pref[i]
pref[i] = count;
}
// Calculating the first index
// of L and R using binary search
int left = binarysearch(pref, arr.Count + 1, L);
int right = binarysearch(pref, arr.Count + 1, R);
// Print the resultant count
Console.Write(right - left + 1);
}
// Driver Code
public static void Main()
{
List<int> arr = new List<int>(){ 3, 6, 7, 1, 8 };
int L = 3;
int R = 7;
countDistinct(arr, L, R);
}
}
// This code is contributed by SURENDRA_GANGWAR
<script>
// Javascript program for the above approach
// Function to find the first index
// with value is at least element
function binarysearch(array, right, element)
{
// Update the value of left
let left = 1;
// Update the value of right
// Binary search for the element
while (left <= right)
{
// Find the middle element
let mid = Math.floor((left + right / 2));
if (array[mid] == element)
{
return mid;
}
// Check if the value lies
// between the elements at
// index mid - 1 and mid
if (mid - 1 > 0 && array[mid] > element &&
array[mid - 1] < element)
{
return mid;
}
// Check in the right subarray
else if (array[mid] < element)
{
// Update the value
// of left
left = mid + 1;
}
// Check in left subarray
else
{
// Update the value of
// right
right = mid - 1;
}
}
return 1;
}
// Function to count the number of
// distinct elements over the range
// [L, R] in the sorted sequence
function countDistinct(arr, L, R)
{
// Stores the count of distinct
// elements
let count = 0;
// Create the prefix sum array
let pref = Array.from(
{length: arr.length + 1}, (_, i) => 0);
for(let i = 1; i <= arr.length; ++i)
{
// Update the value of count
count += arr[i - 1];
// Update the value of pref[i]
pref[i] = count;
}
// Calculating the first index
// of L and R using binary search
let left = binarysearch(pref, arr.length + 1, L);
let right = binarysearch(pref, arr.length + 1, R);
// Print the resultant count
document.write((right - left) + 1);
}
// Driver Code
let arr = [ 3, 6, 7, 1, 8 ];
let L = 3;
let R = 7;
countDistinct(arr, L, R);
// This code is contributed by susmitakundugoaldanga
</script>
Time Complexity: O(log(N))
Auxiliary Space: O(N)
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