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 a 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 loop picks an element from left to right that is not visited. The inner loop counts its occurrences and marks occurrences as visited. The time complexity of this solution is O(n*n) and the auxiliary space required is O(n).

A better solution is to use sorting. We sort the array so that the 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++

#include <bits/stdc++.h>
using namespace std;

// Function to print the cumulative frequency according to
// the order given
void countFreq(int a[], int n)
{

    // Declaring a map so values get inserted in a sorted
    // manner
    map<int, int> m;

    // Inserting values into the map
    for (int i = 0; i < n; i++) {
        m[a[i]]++;
    }

    // Variable to store the count of previous number
    // cumulative frequency
    int cumul = 0;
    for (auto v : m) {
        cout << v.first << " " << v.second + cumul
             << endl;
        cumul += v.second;
    }
}

int main()
{
    int arr[] = { 1, 3, 2, 4, 2, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    countFreq(arr, n);
    return 0;
}

// This code is contributed by Vinayak Pareek (Kargil)

Java

// Java program to count cumulative
// 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 cumulative
# 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

C#

// C# program to count cumulative
// frequencies of elements in an
// unsorted array.
using System;
using System.Collections.Generic;
using System.Linq;

class GFG{

static void countFreq(int[] a, int n)
{

    // Insert elements and their
    // frequencies in hash map.
    Dictionary<int,
               int> hm = new Dictionary<int,
                                        int>();
    for(int i = 0; i < n; i++)
    {
        if (hm.ContainsKey(a[i]))
        {
            hm[a[i]]++;
        }
        else
        {
            hm[a[i]] = 1;
        }
    }

    int cumul = 0;

    // Iterate the set and print the
    // cumulative frequency
    foreach(KeyValuePair<int,
                         int> x in hm.OrderBy(key => key.Key))
    {
        cumul += x.Value;
        Console.Write(x.Key + " " + cumul + "\n");
    }
}

// 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 rutvik_56

Javascript

<script>
// Javascript program to count cumulative
// frequencies of elements in an unsorted array.

    function countFreq(a,n)
    {
        // Insert elements and their
        // frequencies in hash map.
        let hm = new Map();
        for (let i = 0; i < n; i++)
            hm.set(a[i], hm.get(a[i]) == null ?
                     1 : hm.get(a[i]) + 1);

        // Declare a Map
        let st = new Set();

        // insert the element and
        // and insert its frequency in a set
        for (let [key, value] of hm.entries())
        {
            st.add([key, value]);
        }
          st=[...st.entries()].sort()
        let cumul = 0;

        // iterate the set and print the
        // cumulative frequency
        for (let [key, value] of st.entries())
        {
            cumul += value[1][1];
            document.write(value[1][0] + " " + cumul+"<br>");
        }
    }

    // Driver Code
    let a=[1, 3, 2, 4, 2, 1];
    let n = a.length;
    countFreq(a, n);


// This code is contributed by unknown2108
</script>

Output:

1 2
2 4
3 5
4 6

Time Complexity: O(n log n), where n is the size of the given array
Auxiliary Space: O(n), as extra space of size n is used to create a map

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++

// C++ 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 print the cumulative
# frequency according to the order given

# Function to print the 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 */

Javascript

<script>
// Javascript program to print the cumulative frequency
// according to the order given

// Function to print the cumulative frequency
// according to the order given
function countFreq(a,n) {
    // Insert elements and their
    // frequencies in hash map.
    let hm = new Array(n);
    for(let i=0;i<hm.length;i++)
    {
        hm[i]=0;
    }
    for (let i = 0; i < n; i++)
        hm[a[i]]++;
    let cumul = 0;

    // traverse in the array
    for(let 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)
        {
            document.write(a[i] + "->" + cumul+"<br>");
        }
        // mark the hash 0
        // as the element's cumulative frequency
        // has been printed
        hm[a[i]] = 0;
    }

}

// Driver Code
let a=[1, 3, 2, 4, 2, 1];
let n = a.length;
countFreq(a, n);


// This code is contributed by patel2127
</script>

Output:

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

Time Complexity: O(n), where n is the size of the given array
Auxiliary Space: O(n), as extra space of size n is used to create a map

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