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Frequency Measuring Techniques for Competitive Programming
  • Difficulty Level : Medium
  • Last Updated : 16 Jun, 2021

Measuring the frequency of elements in an array is a really handy skill and is required a lot of competitive coding problems. We, in a lot of problems, are required to measure the frequency of various elements like numbers, alphabets, symbols, etc. as a part of our problem.

Naive method

Examples:  

Input :  arr[] = {10, 20, 20, 10, 10, 20, 5, 20}
Output : 10 3
         20 4
         5  1

Input : arr[] = {10, 20, 20}
Output : 10 2
         20 1

We run two loops. For every item count number of times it occurs. To avoid duplicate printing, keep track of processed items. 

C++




// C++ program to count frequencies of array items
#include <bits/stdc++.h>
using namespace std;
  
void countFreq(int arr[], int n)
{
    // Mark all array elements as not visited
    vector<int> visited(n, false);
  
    // Traverse through array elements and
    // count frequencies
    for (int i = 0; i < n; i++) {
  
        // Skip this element if already processed
        if (visited[i] == true)
            continue;
  
        // Count frequency
        int count = 1;
        for (int j = i + 1; j < n; j++) {
            if (arr[i] == arr[j]) {
                visited[j] = true;
                count++;
            }
        }
        cout << arr[i] << " " << count << endl;
    }
}
  
int main()
{
    int arr[] = { 10, 20, 20, 10, 10, 20, 5, 20 };
    int n = sizeof(arr) / sizeof(arr[0]);
    countFreq(arr, n);
    return 0;
}

Java




// Java program to count frequencies
// of array items
import java.util.*;
 
class GFG
{
static void countFreq(int arr[], int n)
{
    // Mark all array elements as not visited
    boolean []visited = new boolean[n];
 
    // Traverse through array elements and
    // count frequencies
    for (int i = 0; i < n; i++)
    {
 
        // Skip this element if already processed
        if (visited[i] == true)
            continue;
 
        // Count frequency
        int count = 1;
        for (int j = i + 1; j < n; j++)
        {
            if (arr[i] == arr[j])
            {
                visited[j] = true;
                count++;
            }
        }
        System.out.println(arr[i] + " " + count);
    }
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 10, 20, 20, 10, 10, 20, 5, 20 };
    int n = arr.length;
    countFreq(arr, n);
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python program to count frequencies
# of array items
def countFreq(arr, n):
     
    # mark all array elements as not visited
    visited = [False for i in range(n)]
     
    # Traverse through array elements
    # and count frequencies
    for i in range(n):
         
        # Skip this element if already processed
        if visited[i] == True:
            continue
             
        # count frequency
        count = 1
         
        for j in range(i + 1, n):
            if arr[i] == arr[j]:
                visited[j] = True
                count += 1
        print(arr[i], count)
     
# Driver code
a = [10, 20, 20, 10, 10, 20, 5, 20]
 
n = len(a)
 
countFreq(a, n)
 
# This code is contributed
# by Mohit kumar 29

C#




// C# program to count frequencies
// of array items
using System;
     
class GFG
{
static void countFreq(int []arr, int n)
{
    // Mark all array elements as not visited
    Boolean []visited = new Boolean[n];
 
    // Traverse through array elements and
    // count frequencies
    for (int i = 0; i < n; i++)
    {
 
        // Skip this element if already processed
        if (visited[i] == true)
            continue;
 
        // Count frequency
        int count = 1;
        for (int j = i + 1; j < n; j++)
        {
            if (arr[i] == arr[j])
            {
                visited[j] = true;
                count++;
            }
        }
        Console.WriteLine(arr[i] + " " + count);
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    int []arr = { 10, 20, 20, 10,
                  10, 20, 5, 20 };
    int n = arr.Length;
    countFreq(arr, n);
}
}
 
// This code is contributed by Rajput-Ji

Javascript




<script>
    // Javascript program to count frequencies of array items
     
    function countFreq(arr, n)
    {
        // Mark all array elements as not visited
        let visited = new Array(n);
        visited.fill(false);
 
        // Traverse through array elements and
        // count frequencies
        for (let i = 0; i < n; i++) {
 
            // Skip this element if already processed
            if (visited[i] == true)
                continue;
 
            // Count frequency
            let count = 1;
            for (let j = i + 1; j < n; j++) {
                if (arr[i] == arr[j]) {
                    visited[j] = true;
                    count++;
                }
            }
            document.write(arr[i] + " " + count + "</br>");
        }
    }
 
    let arr = [ 10, 20, 20, 10, 10, 20, 5, 20 ];
    let n = arr.length;
    countFreq(arr, n);
     
    // This code is contributed by mukesh07.
</script>
Output: 



10 3
20 4
5 1

 

Optimized methods :

Measuring frequencies when elements are limited by value 
If our input array has small values, we can use array elements as index in a count array and increment count. In below example, elements are maximum 10. 

Input :  arr[] = {5, 5, 6, 6, 5, 6, 1, 2, 3, 10, 10}
         limit = 10
Output : 1 1
         2 1
         3 1
         5 3
         6 3
         10 2

C++




// C++ program to count frequencies of array items
// having small values.
#include <bits/stdc++.h>
using namespace std;
  
void countFreq(int arr[], int n, int limit)
{
    // Create an array to store counts. The size
    // of array is limit+1 and all values are
    // initially 0
    vector<int> count(limit+1, 0);
  
    // Traverse through array elements and
    // count frequencies (assuming that elements
    // are limited by limit)
    for (int i = 0; i < n; i++)
        count[arr[i]]++;
  
    for (int i = 0; i <= limit; i++)
       if (count[i] > 0)
        cout << i << " " << count[i] << endl;
     
}
  
int main()
{
    int arr[] = {5, 5, 6, 6, 5, 6, 1, 2, 3, 10, 10};
    int n = sizeof(arr) / sizeof(arr[0]);
    int limit = 10;
    countFreq(arr, n, limit);
    return 0;
}

Java




// Java program to count frequencies of array items
// having small values.
class GFG
{
     
static void countFreq(int arr[], int n, int limit)
{
    // Create an array to store counts. The size
    // of array is limit+1 and all values are
    // initially 0
    int []count = new int[limit + 1];
 
    // Traverse through array elements and
    // count frequencies (assuming that elements
    // are limited by limit)
    for (int i = 0; i < n; i++)
        count[arr[i]]++;
 
    for (int i = 0; i <= limit; i++)
    if (count[i] > 0)
            System.out.println(i + " " + count[i]);
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = {5, 5, 6, 6, 5, 6, 1, 2, 3, 10, 10};
    int n = arr.length;
    int limit = 10;
    countFreq(arr, n, limit);
}
}
 
// This code is contributed by PrinciRaj1992

Python3




# Python3 program to count frequencies of
# array items having small values.
def countFreq(arr, n, limit):
     
    # Create an array to store counts.
    # The size of array is limit+1 and
    # all values are initially 0
    count = [0 for i in range(limit + 1)]
 
    # Traverse through array elements and
    # count frequencies (assuming that
    # elements are limited by limit)
    for i in range(n):
        count[arr[i]] += 1
 
    for i in range(limit + 1):
        if (count[i] > 0):
            print(i, count[i])
 
# Driver Code
arr = [ 5, 5, 6, 6, 5, 6,
        1, 2, 3, 10, 10 ]
n = len(arr)
limit = 10
 
countFreq(arr, n, limit)
 
# This code is contributed by avanitrachhadiya2155

C#




// C# program to count frequencies of
// array items having small values.
using System;
     
class GFG
{
     
static void countFreq(int []arr,
                      int n, int limit)
{
    // Create an array to store counts.
    // The size of array is limit+1 and
    // all values are initially 0
    int []count = new int[limit + 1];
 
    // Traverse through array elements and
    // count frequencies (assuming that
    // elements are limited by limit)
    for (int i = 0; i < n; i++)
        count[arr[i]]++;
 
    for (int i = 0; i <= limit; i++)
    if (count[i] > 0)
            Console.WriteLine(i + " " +
                              count[i]);
}
 
// Driver Code
public static void Main(String[] args)
{
    int []arr = {5, 5, 6, 6, 5, 6,
                 1, 2, 3, 10, 10};
    int n = arr.Length;
    int limit = 10;
    countFreq(arr, n, limit);
}
}
 
// This code is contributed
// by Princi Singh

Javascript




<script>
 
// Javascript program to count frequencies
// of array items having small values.
function countFreq(arr, n, limit)
{
     
    // Create an array to store counts.
    // The size of array is limit+1 and
    // all values are initially 0
    let count = new Array(limit + 1);
    count.fill(0);
 
    // Traverse through array elements and
    // count frequencies (assuming that
    // elements are limited by limit)
    for(let i = 0; i < n; i++)
        count[arr[i]]++;
 
    for(let i = 0; i <= limit; i++)
        if (count[i] > 0)
            document.write(i + " " +
                           count[i] + "</br>");
}
 
// Driver code
let arr = [ 5, 5, 6, 6, 5, 6,
            1, 2, 3, 10, 10 ];
let n = arr.length;
let limit = 10;
 
countFreq(arr, n, limit);
 
// This code is contributed by rameshtravel07  
 
</script>
Output: 
1 1
2 1
3 1
5 3
6 3
10 2

 

C++




// C++ program to count frequencies of array items
#include <bits/stdc++.h>
using namespace std;
 
const int limit = 255;
 
void countFreq(string str)
{
    // Create an array to store counts. The size
    // of array is limit+1 and all values are
    // initially 0
    vector<int> count(limit+1, 0);
  
    // Traverse through string characters and
    // count frequencies
    for (int i = 0; i < str.length(); i++)
        count[str[i]]++;
  
    for (int i = 0; i <= limit; i++)
       if (count[i] > 0)
        cout << (char)i << " " << count[i] << endl;
     
}
  
int main()
{
    string str = "GeeksforGeeks";
    countFreq(str);
    return 0;
}

Java




// Java program to count frequencies of array items
class GFG
{
static int limit = 255;
 
static void countFreq(String str)
{
    // Create an array to store counts. The size
    // of array is limit+1 and all values are
    // initially 0
    int []count= new int[limit + 1];
 
    // Traverse through string characters and
    // count frequencies
    for (int i = 0; i < str.length(); i++)
        count[str.charAt(i)]++;
 
    for (int i = 0; i <= limit; i++)
    if (count[i] > 0)
        System.out.println((char)i + " " + count[i]);
}
 
// Driver Code
public static void main(String[] args)
{
    String str = "GeeksforGeeks";
    countFreq(str);
}
}
 
// This code is contributed by PrinciRaj1992

Python3




# Python3 program to count frequencies of array items
limit = 255
def countFreq(Str) :
 
    # Create an array to store counts. The size
    # of array is limit+1 and all values are
    # initially 0
    count = [0] * (limit + 1)
   
    # Traverse through string characters and
    # count frequencies
    for i in range(len(Str)) :
        count[ord(Str[i])] += 1
   
    for i in range(limit + 1) :
       if (count[i] > 0) :
        print(chr(i), count[i])
  
Str = "GeeksforGeeks"
countFreq(Str)
 
# This code is contributed by divyeshrabadiya07

C#




// C# program to count frequencies
// of array items
using System;
     
class GFG
{
static int limit = 25;
 
static void countFreq(String str)
{
    // Create an array to store counts.
    // The size of array is limit+1 and
    // all values are initially 0
    int []count = new int[limit + 1];
 
    // Traverse through string characters
    // and count frequencies
    for (int i = 0; i < str.Length; i++)
        count[str[i] - 'A']++;
 
    for (int i = 0; i <= limit; i++)
    if (count[i] > 0)
        Console.WriteLine((char)(i + 'A') +
                          " " + count[i]);
}
 
// Driver Code
public static void Main(String[] args)
{
    String str = "GEEKSFORGEEKS";
    countFreq(str);
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
 
// Javascript program to count frequencies of array items
     
    let limit = 255;
     
function countFreq(str)
{
        // Create an array to store counts. The size
    // of array is limit+1 and all values are
    // initially 0
    let count= new Array(limit + 1);
    for(let i=0;i<count.length;i++)
    {
        count[i]=0;
    }
  
    // Traverse through string characters and
    // count frequencies
    for (let i = 0; i < str.length; i++)
        count[str[i].charCodeAt(0)]++;
  
    for (let i = 0; i <= limit; i++)
    {    if (count[i] > 0)
            document.write(String.fromCharCode(i) + " " + count[i]+"<br>");
    }
}
 
// Driver Code
let str = "GeeksforGeeks";
countFreq(str);
     
     
    // This code is contributed by unknown2108
</script>
Output: 
G 2
e 4
f 1
k 2
o 1
r 1
s 2

 

Measuring frequencies when elements are in limited range 
For example consider a string containing only upper case alphabets. Elements of string are limited in range from ‘A’ to ‘Z’. The idea is to subtract smallest element (‘A’ in this example) to get index of the element. 

C++




// C++ program to count frequencies of array items
#include <bits/stdc++.h>
using namespace std;
 
const int limit = 25;
 
void countFreq(string str)
{
    // Create an array to store counts. The size
    // of array is limit+1 and all values are
    // initially 0
    vector<int> count(limit+1, 0);
  
    // Traverse through string characters and
    // count frequencies
    for (int i = 0; i < str.length(); i++)
        count[str[i] - 'A']++;
  
    for (int i = 0; i <= limit; i++)
       if (count[i] > 0)
        cout << (char)(i + 'A') << " " << count[i] << endl;
     
}
  
int main()
{
    string str = "GEEKSFORGEEKS";
    countFreq(str);
    return 0;
}

Java




// Java program to count frequencies
// of array items
import java.util.*;
 
class GFG
{
static int limit = 25;
 
static void countFreq(String str)
{
    // Create an array to store counts.
    // The size of array is limit+1 and
    // all values are initially 0
    int []count = new int[limit + 1];
 
    // Traverse through string characters
    // and count frequencies
    for (int i = 0; i < str.length(); i++)
        count[str.charAt(i) - 'A']++;
 
    for (int i = 0; i <= limit; i++)
    if (count[i] > 0)
        System.out.println((char)(i + 'A') +
                           " " + count[i]);
}
 
// Driver Code
public static void main(String[] args)
{
    String str = "GEEKSFORGEEKS";
    countFreq(str);
}
}
 
// This code is contributed by PrinciRaj1992

Python3




# Python3 program to count frequencies of array items
limit = 25;
def countFreq(str):
     
    # Create an array to store counts. The size
    # of array is limit+1 and all values are
    # initially 0
    count = [0 for i in range(limit + 1)]
   
    # Traverse through string characters and
    # count frequencies
    for i in range(len(str)):  
        count[ord(str[i]) - ord('A')] += 1
   
    for i in range(limit + 1):
       if (count[i] > 0):
           print(chr(i + ord('A')), count[i])
 
# Driver code
if __name__=='__main__':
     
    str = "GEEKSFORGEEKS";
    countFreq(str);
     
# This code is contributed by Pratham76

C#




// C# program to count frequencies
// of array items
using System;
     
class GFG
{
static int limit = 25;
  
static void countFreq(String str)
{
    // Create an array to store counts.
    // The size of array is limit+1 and
    // all values are initially 0
    int []count = new int[limit + 1];
  
    // Traverse through string characters
    // and count frequencies
    for (int i = 0; i < str.Length; i++)
        count[str[i] - 'A']++;
  
    for (int i = 0; i <= limit; i++)
    if (count[i] > 0)
        Console.WriteLine((char)(i + 'A') +
                           " " + count[i]);
}
  
// Driver Code
public static void Main(String[] args)
{
    String str = "GEEKSFORGEEKS";
    countFreq(str);
}
}
  
// This code contributed by PrinciRaj1992

Javascript




<script>
 
// JavaScript program to count frequencies
// of array items
 
let limit = 25;
function countFreq(str)
{
    // Create an array to store counts.
    // The size of array is limit+1 and
    // all values are initially 0
    let count = new Array(limit + 1);
    for(let i=0;i<limit+1;i++)
    {
        count[i]=0;
    }
  
    // Traverse through string characters
    // and count frequencies
    for (let i = 0; i < str.length; i++)
        count[str[i].charCodeAt(0) - 'A'.charCodeAt(0)]++;
  
    for (let i = 0; i <= limit; i++)
    if (count[i] > 0)
        document.write(String.fromCharCode(i + 'A'.charCodeAt(0)) +
                           " " + count[i]+"<br>");
}
 
// Driver Code
let str = "GEEKSFORGEEKS";
countFreq(str);
 
// This code is contributed by rag2127
 
</script>
Output: 
E 4
F 1
G 2
K 2
O 1
R 1
S 2

 

Measuring frequencies if no range and no limit 
The idea is to use hashing (unordered_map in C++ and HashMap in Java) to get frequencies. 

C++




// C++ program to count frequencies of array items
#include <bits/stdc++.h>
using namespace std;
 
void countFreq(int arr[], int n)
{
    unordered_map<int, int> mp;
 
    // Traverse through array elements and
    // count frequencies
    for (int i = 0; i < n; i++)
        mp[arr[i]]++;
 
    // Traverse through map and print frequencies
    for (auto x : mp)
        cout << x.first << " " << x.second << endl;
}
 
int main()
{
    int arr[] = { 10, 20, 20, 10, 10, 20, 5, 20 };
    int n = sizeof(arr) / sizeof(arr[0]);
    countFreq(arr, n);
    return 0;
}

Java




// Java program to count frequencies of array items
import java.util.*;
class GFG
{
static void countFreq(int arr[], int n)
{
    HashMap<Integer,
            Integer>mp = new HashMap<Integer,
                                     Integer>();
                                      
    // Traverse through array elements and
    // count frequencies
    for (int i = 0 ; i < n; i++)
    {
        if(mp.containsKey(arr[i]))
        {
            mp.put(arr[i], mp.get(arr[i]) + 1);
        }
        else
        {
            mp.put(arr[i], 1);
        }
    }
     
    // Traverse through map and print frequencies
    for (Map.Entry<Integer,
                   Integer> entry : mp.entrySet())
        System.out.println(entry.getKey() + " " +
                           entry.getValue());
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 10, 20, 20, 10, 10, 20, 5, 20 };
    int n = arr.length;
    countFreq(arr, n);   
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python3 program to count frequencies of array items
def countFreq(arr, n):
 
    mp = {}
  
    # Traverse through array elements and
    # count frequencies
    for i in range(n):
        if arr[i] in mp:
            mp[arr[i]] += 1
        else:
            mp[arr[i]] = 1
  
    # Traverse through map and print frequencies
    for x in sorted(mp):
        print(x, mp[x])
 
# Driver Code
arr = [ 10, 20, 20, 10, 10, 20, 5, 20 ]
n = len(arr)
 
countFreq(arr, n)
 
# This code is contributed by divyesh072019

C#




// C# program to count frequencies of array items
using System;
using System.Collections.Generic;
 
class GFG
{
static void countFreq(int []arr, int n)
{
    Dictionary<int,
               int> mp = new Dictionary<int,
                                        int>();
                                     
    // Traverse through array elements and
    // count frequencies
    for (int i = 0 ; i < n; i++)
    {
        if(mp.ContainsKey(arr[i]))
        {
            var val = mp[arr[i]];
            mp.Remove(arr[i]);
            mp.Add(arr[i], val + 1);
        }
        else
        {
            mp.Add(arr[i], 1);
        }
    }
     
    // Traverse through map and print frequencies
    foreach(KeyValuePair<int, int> entry in mp)
        Console.WriteLine(entry.Key + " " +
                          entry.Value);
}
 
// Driver Code
public static void Main(String[] args)
{
    int []arr = { 10, 20, 20, 10,
                  10, 20, 5, 20 };
    int n = arr.Length;
    countFreq(arr, n);
}
}
 
// This code is contributed by Princi Singh
Output: 



5 1
10 3
20 4

 

Time Complexity : O(n) 
Auxiliary Space : O(n)

In above efficient solution, how to print elements in same order as they appear in input?  

C++




// C++ program to count frequencies of array items
#include <bits/stdc++.h>
using namespace std;
 
void countFreq(int arr[], int n)
{
    unordered_map<int, int> mp;
 
    // Traverse through array elements and
    // count frequencies
    for (int i = 0; i < n; i++)
        mp[arr[i]]++;
 
    // To print elements according to first
    // occurrence, traverse array one more time
    // print frequencies of elements and mark
    // frequencies as -1 so that same element
    // is not printed multiple times.
    for (int i = 0; i < n; i++) {
      if (mp[arr[i]] != -1)
      {
          cout << arr[i] << " " << mp[arr[i]] << endl;
          mp[arr[i]] = -1;
      }
    }
}
 
int main()
{
    int arr[] = { 10, 20, 20, 10, 10, 20, 5, 20 };
    int n = sizeof(arr) / sizeof(arr[0]);
    countFreq(arr, n);
    return 0;
}

Java




// Java program to count frequencies of array items
import java.util.*;
 
class GFG
{
static void countFreq(int arr[], int n)
{
    HashMap<Integer,
            Integer> mp = new HashMap<Integer,
                                      Integer>();
 
    // Traverse through array elements and
    // count frequencies
    for (int i = 0 ; i < n; i++)
    {
        if(mp.containsKey(arr[i]))
        {
            mp.put(arr[i], mp.get(arr[i]) + 1);
        }
        else
        {
            mp.put(arr[i], 1);
        }
    }
     
    // To print elements according to first
    // occurrence, traverse array one more time
    // print frequencies of elements and mark
    // frequencies as -1 so that same element
    // is not printed multiple times.
    for (int i = 0; i < n; i++)
    {
        if (mp.get(arr[i]) != -1)
        {
            System.out.println(arr[i] + " " +
                               mp.get(arr[i]));
            mp. put(arr[i], -1);
        }
    }
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 10, 20, 20, 10, 10, 20, 5, 20 };
    int n = arr.length;
    countFreq(arr, n);
}
}
 
// This code is contributed by Princi Singh

Python3




# Python3 program to count frequencies of array items
def countFreq(arr, n):
    mp = {}
     
    # Traverse through array elements and
    # count frequencies
    for i in range(n):
        if arr[i] not in mp:
            mp[arr[i]] = 1
        else:
            mp[arr[i]] += 1
 
    # To print elements according to first
    # occurrence, traverse array one more time
    # print frequencies of elements and mark
    # frequencies as -1 so that same element
    # is not printed multiple times.
    for i in range(n):
        if(mp[arr[i]] != -1):
            print(arr[i], mp[arr[i]])
            mp[arr[i]] = -1
 
# Driver code
arr = [10, 20, 20, 10, 10, 20, 5, 20 ]
n = len(arr)
countFreq(arr, n)
 
# This code is contributed by rag2127

C#




// C# program to count frequencies of array items
using System;
using System.Collections.Generic;
     
class GFG
{
static void countFreq(int []arr, int n)
{
    Dictionary<int,
               int> mp = new Dictionary<int,
                                        int>();
 
    // Traverse through array elements and
    // count frequencies
    for (int i = 0 ; i < n; i++)
    {
        if(mp.ContainsKey(arr[i]))
        {
            mp[arr[i]] = mp[arr[i]] + 1;
        }
        else
        {
            mp.Add(arr[i], 1);
        }
    }
     
    // To print elements according to first
    // occurrence, traverse array one more time
    // print frequencies of elements and mark
    // frequencies as -1 so that same element
    // is not printed multiple times.
    for (int i = 0; i < n; i++)
    {
        if (mp[arr[i]] != -1)
        {
            Console.WriteLine(arr[i] + " " +
                              mp[arr[i]]);
            mp[arr[i]] = - 1;
        }
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    int []arr = { 10, 20, 20, 10,
                  10, 20, 5, 20 };
    int n = arr.Length;
    countFreq(arr, n);
}
}
 
// This code is contributed by Rajput-Ji
Output: 
10 3
20 4
5 1

 

Time Complexity : O(n) 
Auxiliary Space : O(n)

In Java, we can get elements in same order using LinkedHashMap. Therefore we do not need an extra loop.
Lot of problems are based on frequency measurement and will be a cheesecake if we know how to calculate frequency of various elements in a given array. For example try the given below problems which are based on frequency measurement: 

  1. Anagrams
  2. Sorting Elements of an Array by Frequency
  3. Single Number

This article is contributed by Aditya Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

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