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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



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;
}

/div>

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:

1 2
2 4
3 5
4 6

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

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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