Cumulative frequency of count of each element in an unsorted array

Given an unsorted array. The task is to calculate the cumulative frequency of each element of the array using count array.

Examples:

Input : arr[] = [1, 2, 2, 1, 3, 4]
Output :1->2
        2->4
        3->5
        4->6

Input : arr[] = [1, 1, 1, 2, 2, 2]
Output :1->3
        2->6

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

A simple solution is to use two nested loops, the outer loops picks an element from left to right that are not visited. The inner loop counts its occurrences and mark occurrences as visited. Time complexity of this solution is O(n*n) and auxiliary space required is O(n).

A better solution is to use sorting. We sort the array so that same elements come together. After sorting, we linearly traverse elements and count their frequencies.

An efficient solution is to use hashing. Insert the element and its frequency in a set of pairs. As the set stores unique values in a sorted order, it will store all the elements with their frequencies in a sorted order. Iterate in the set and print the frequencies by adding the previous ones at every step.

Below is the implementation of the above approach.

C++

// CPP program to count cumlative 
// frequencies of elements in an unsorted array. 
#include <bits/stdc++.h> 
using namespace std; 
  
void countFreq(int a[], int n) 
{ 
    // Insert elements and their 
    // frequencies in hash map. 
    unordered_map<int, int> hm; 
    for (int i = 0; i < n; i++) 
        hm[a[i]]++; 
  
    // Declare a set 
    set<pair<int, int> > st; 
  
    // insert the element and 
    // and insert its frequency in a set 
    for (auto x : hm) { 
        st.insert({ x.first, x.second }); 
    } 
  
    int cumul = 0; 
  
    // iterate the set and print the 
    // cumulative frequency 
    for (auto x : st) { 
        cumul += x.second; 
        cout << x.first << " " << cumul << endl; 
    } 
} 
  
// Driver Code 
int main() 
{ 
    int a[] = { 1, 3, 2, 4, 2, 1 }; 
    int n = sizeof(a) / sizeof(a[0]); 
    countFreq(a, n); 
    return 0; 
} 

Java

// Java program to count cumlative  
// frequencies of elements in an unsorted array.  
import java.util.*; 
  
class GFG  
{ 
    static void countFreq(int[] a, int n)  
    { 
  
        // Insert elements and their 
        // frequencies in hash map. 
        HashMap<Integer,  
                Integer> hm = new HashMap<>(); 
        for (int i = 0; i < n; i++) 
            hm.put(a[i], hm.get(a[i]) == null ?  
                     1 : hm.get(a[i]) + 1); 
  
        // Declare a Map 
        SortedMap<Integer, Integer> st = new TreeMap<>(); 
  
        // insert the element and 
        // and insert its frequency in a set 
        for (HashMap.Entry<Integer, 
                           Integer> x : hm.entrySet())  
        { 
            st.put(x.getKey(), x.getValue()); 
        } 
  
        int cumul = 0; 
  
        // iterate the set and print the 
        // cumulative frequency 
        for (SortedMap.Entry<Integer,  
                             Integer> x : st.entrySet()) 
        { 
            cumul += x.getValue(); 
            System.out.println(x.getKey() + " " + cumul); 
        } 
    } 
  
    // Driver Code 
    public static void main(String[] args)  
    { 
        int[] a = { 1, 3, 2, 4, 2, 1 }; 
        int n = a.length; 
        countFreq(a, n); 
    } 
} 
  
// This code is contributed by 
// sanjeev2552 

Python3

# Python3 program to count cumlative  
# frequencies of elements in an unsorted array.  
def countFreq(a, n):  
  
    # Insert elements and their  
    # frequencies in hash map.  
    hm = {}  
    for i in range(0, n):  
        hm[a[i]] = hm.get(a[i], 0) + 1
  
    # Declare a set  
    st = set()  
  
    # Insert the element and  
    # its frequency in a set  
    for x in hm:  
        st.add((x, hm[x]))  
  
    cumul = 0
  
    # Iterate the set and print  
    # the cumulative frequency  
    for x in sorted(st):  
        cumul += x[1]  
        print(x[0], cumul)  
  
# Driver Code  
if __name__ == "__main__": 
  
    a = [1, 3, 2, 4, 2, 1]  
    n = len(a)  
    countFreq(a, n) 
      
# This code is contributed by Rituraj Jain 

Output:

Time complexity of the solution is O(n log n).

What if we need frequencies of elements according to the order of the first occurrence?
For example, an array [2, 4, 1, 2, 1, 3, 4], the frequency of 2 should be printed first, then of 4, then 1 and finally 3.
Approach: Hash the count of occurrences of an element. Traverse in the array and print the cumulative frequency. Once the element and its cumulative frequency has been printed, hash the occurrence of that element as 0 so that it not printed again if it appears in the latter half of array while traversal.

Below is the implementation of the above approach:

C++

// CPP program to print the cumulative frequency  
// according to the order given  
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to print the cumulative frequency  
// according to the order given  
void countFreq(int a[], int n) 
{ 
    // Insert elements and their  
    // frequencies in hash map. 
    unordered_map<int, int> hm; 
    for (int i=0; i<n; i++) 
        hm[a[i]]++; 
    int cumul = 0; 
      
   // traverse in the array  
   for(int i=0;i<n;i++) 
   { 
       // add the frequencies  
       cumul += hm[a[i]];  
         
       // if the element has not been  
       // visited previously  
       if(hm[a[i]]) 
       { 
           cout << a[i] << "->" << cumul << endl; 
       } 
       // mark the hash 0  
       // as the element's cumulative frequency  
       // has been printed  
       hm[a[i]]=0; 
   } 
} 
  
// Driver Code 
int main() 
{ 
    int a[] = {1, 3, 2, 4, 2, 1}; 
    int n = sizeof(a)/sizeof(a[0]); 
    countFreq(a, n); 
    return 0; 
} 

Java

// Java program to print the cumulative frequency  
// according to the order given  
class GFG 
{ 
  
// Function to print the cumulative frequency  
// according to the order given  
static void countFreq(int a[], int n) 
{ 
    // Insert elements and their  
    // frequencies in hash map. 
    int hm[] = new int[n]; 
    for (int i = 0; i < n; i++) 
        hm[a[i]]++; 
    int cumul = 0; 
      
// traverse in the array  
for(int i = 0; i < n; i++) 
{ 
    // add the frequencies  
    cumul += hm[a[i]];  
          
    // if the element has not been  
    // visited previously  
    if(hm[a[i]] != 0) 
    { 
        System.out.println(a[i] + "->" + cumul); 
    } 
    // mark the hash 0  
    // as the element's cumulative frequency  
    // has been printed  
    hm[a[i]] = 0; 
} 
} 
  
// Driver Code 
public static void main(String[] args)  
{ 
    int a[] = {1, 3, 2, 4, 2, 1}; 
    int n = a.length; 
    countFreq(a, n); 
} 
}  
  
// This code has been contributed by 29AjayKumar 

Python3

# Python3 program to prthe cumulative  
# frequency according to the order given 
  
# Function to prthe cumulative frequency 
# according to the order given 
def countFreq(a, n): 
  
    # Insert elements and their 
    # frequencies in hash map. 
    hm = dict() 
    for i in range(n): 
        hm[a[i]] = hm.get(a[i], 0) + 1
  
    cumul = 0
  
    # traverse in the array 
    for i in range(n): 
  
    # add the frequencies 
        cumul += hm[a[i]] 
  
    # if the element has not been 
    # visited previously 
        if(hm[a[i]] > 0): 
            print(a[i], "->", cumul) 
              
    # mark the hash 0 
    # as the element's cumulative  
    # frequency has been printed 
        hm[a[i]] = 0
  
# Driver Code 
a = [1, 3, 2, 4, 2, 1] 
n = len(a) 
countFreq(a, n) 
  
# This code is contributed by mohit kumar 

C#

// C# program to print the cumulative frequency  
// according to the order given  
using System; 
  
class GFG  
{  
  
// Function to print the cumulative frequency  
// according to the order given  
static void countFreq(int []a, int n)  
{  
    // Insert elements and their  
    // frequencies in hash map.  
    int []hm = new int[n];  
    for (int i = 0; i < n; i++)  
        hm[a[i]]++;  
    int cumul = 0;  
      
// traverse in the array  
for(int i = 0; i < n; i++)  
{  
    // add the frequencies  
    cumul += hm[a[i]];  
          
    // if the element has not been  
    // visited previously  
    if(hm[a[i]] != 0)  
    {  
        Console.WriteLine(a[i] + "->" + cumul);  
    }  
      
    // mark the hash 0  
    // as the element's cumulative frequency  
    // has been printed  
    hm[a[i]] = 0;  
}  
}  
  
// Driver Code  
public static void Main(String[] args)  
{  
    int []a = {1, 3, 2, 4, 2, 1};  
    int n = a.Length;  
    countFreq(a, n);  
}  
}  
  
/* This code contributed by PrinciRaj1992 */

Output:

1->2
3->3
2->5
4->6

This article is contributed by Himanshu Ranjan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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