Find frequency of each element in a limited range array in less than O(n) time

• Difficulty Level : Medium
• Last Updated : 13 Jan, 2022

Given a sorted array of positive integers, the count number of occurrences for each element in the array. Assume all elements in the array are less than some constant M.
Do this without traversing the complete array. i.e. expected time complexity is less than O(n).

Examples:

Input: arr[] = [1, 1, 1, 2, 3, 3, 5,
5, 8, 8, 8, 9, 9, 10]
Output:
Element 1 occurs 3 times
Element 2 occurs 1 times
Element 3 occurs 2 times
Element 5 occurs 2 times
Element 8 occurs 3 times
Element 9 occurs 2 times
Element 10 occurs 1 times

Input: arr[] = [2, 2, 6, 6, 7, 7, 7, 11]
Output:
Element 2 occurs 2 times
Element 6 occurs 2 times
Element 7 occurs 3 times
Element 11 occurs 1 times

Method 1: This method uses the technique of Linear Search without using auxiliary space.

• Approach:  The idea is to traverse the input array and increment the frequency of the element if the current element and the previous element are same, otherwise reset the frequency and print the element and its frequency.
• Algorithm:
• Initialise frequency to 1 and index to 1.
• Traverse the array from the index position and check if the current element  is equal to previous element.
• If yes, increment the frequency and index and repeat the step 2. Otherwise, print the element and its frequency and repeat step 2.
• At last(corner case), print the last element and its frequency.
• Implementation:

C++

 // C++ program to count number of occurrences of// each element in the array in O(n) time and O(1) space #include using namespace std;void findFrequencies(int ele[], int n){    int freq = 1;    int idx = 1;    int element = ele;    while (idx < n) {        // check if the current element is equal to        // previous element.        if (ele[idx - 1] == ele[idx]) {            freq++;            idx++;        }        else {            cout << element << " " << freq << endl;            element = ele[idx];            idx++;                       // reset the frequency            freq = 1;        }    }       // print the last element and its frequency    cout << element << " " << freq;} int main(){    cout << "---frequencies in a sorted array----" << endl;    int arr[]        = { 10, 20, 30, 30, 30, 40, 50, 50, 50, 50, 70 };    int n = sizeof(arr) / sizeof(arr);    findFrequencies(arr, n);} // This code is contributed by anushkaseehh

Java

 // Java program to count number of occurrences of// each element in the array in O(n) time and O(1) space      function void findFrequencies(ele)    {        var freq = 1;        var idx = 1;        var element = ele;        while (idx < ele.length) {            // check if the current element is equal to            // previous element.            if (ele[idx - 1] == ele[idx]) {                freq++;                idx++;            }            else {                document.write(element + " " + freq+ "
");                element = ele[idx];                idx++;                // reset the frequency                freq = 1;            }        }        // print the last element and its frequency        document.write(element + " " + freq +"
");    }    // Driver code             document.write(            "---frequencies in a sorted array----"+"
");        findFrequencies(new Array (10, 20, 30, 30, 30, 40,                                    50, 50, 50, 50, 70 ));     //this code is contributed by shivanisinghss2110

Python3

 # python program to count number of occurrences of# each element in the array in O(n) time and O(1) spacedef findFrequencies(ele, n):     freq = 1    idx = 1    element = ele    while (idx < n):               # check if the current element is equal to        # previous element.        if (ele[idx - 1] == ele[idx]):            freq += 1            idx += 1                 else:            print(element , " " ,freq);            element = ele[idx]            idx += 1                       # reset the frequency            freq = 1             # print the last element and its frequency    print(element , " " , freq); print( "---frequencies in a sorted array----" );arr = [10, 20, 30, 30, 30, 40, 50, 50, 50, 50, 70 ];n = len(arr)findFrequencies(arr, n) # This code is contributed by shivanisinghss2110

C#

 // C# program to count number of occurrences of// each element in the array in O(n) time and O(1) spaceusing System;class GFG {     public static void findFrequencies(int[] ele)    {        int freq = 1;        int idx = 1;        int element = ele;        while (idx < ele.Length)        {                       // check if the current element is equal to            // previous element.            if (ele[idx - 1] == ele[idx]) {                freq++;                idx++;            }            else {                Console.WriteLine(element + " " + freq);                element = ele[idx];                idx++;                               // reset the frequency                freq = 1;            }        }               // print the last element and its frequency        Console.WriteLine(element + " " + freq);    }       // Driver code    public static void Main(String[] args)    {        Console.WriteLine(            "---frequencies in a sorted array----");        findFrequencies(new int[] { 10, 20, 30, 30, 30, 40,                                    50, 50, 50, 50, 70 });    }}

Javascript


Output
---frequencies in a sorted array----
10 1
20 1
30 3
40 1
50 4
70 1

Method 2: This method uses the technique of Linear Search to solve the following.

• Approach: The idea is to traverse the input array and for each distinct element of the array, store its frequency in a HashMap, and finally print the HashMap.
• Algorithm:
1. Create a HashMap to map the frequency to element, i.e to store element-frequency pair.
2. Traverse the array from start to end.
3. For each element in the array update the frequency, i.e hm[array[i]]++
4. Traverse the HashMap and print the element frequency pair.
• Implementation:

C++

 // C++ program to count number of occurrences of// each element in the array #include #include using namespace std; // It prints number of// occurrences of each element in the array.void findFrequency(int arr[], int n){    // HashMap to store frequencies    unordered_map mp;     // traverse the array    for (int i = 0; i < n; i++) {        // update the frequency        mp[arr[i]]++;    }     // traverse the hashmap    for (auto i : mp) {        cout << "Element " << i.first << " occurs "             << i.second << " times" << endl;    }} // Driver functionint main(){    int arr[] = { 1, 1, 1, 2, 3, 3, 5, 5,                  8, 8, 8, 9, 9, 10 };    int n = sizeof(arr) / sizeof(arr);     findFrequency(arr, n);     return 0;}

Java

 // Java program to count number// of occurrences of each// element in the arrayimport java.io.*;import java.util.*;class GFG{   // It prints number of  // occurrences of each  // element in the array.  static void findFrequency(int [] arr,                            int n)  {    Map mp      = new HashMap();     // traverse the array    for (int i = 0; i < n; i++)    {       // update the frequency      if (!mp.containsKey(arr[i]))        mp.put(arr[i],0);       mp.put(arr[i],mp.get(arr[i])+1);    }     // traverse the hashmap    for (Map.Entry kvp : mp.entrySet())    {      System.out.println("Element " + kvp.getKey() +                         " occurs " + kvp.getValue() +                         " times");    }  }   // Driver function  public static void main (String[] args) {      int [] arr = {1, 1, 1, 2,                  3, 3, 5, 5,                  8, 8, 8, 9,                  9, 10};    int n = arr.length;    findFrequency(arr, n);  }} // This code is contributed by avanitrachhadiya2155

Python3

 # Python program to count number of occurrences of# each element in the array #include  # It prints number of# occurrences of each element in the array.def findFrequency(arr, n):         # HashMap to store frequencies    mp = {}     # traverse the array    for i in range(n):         # update the frequency        if arr[i] not in mp:            mp[arr[i]] = 0        mp[arr[i]] += 1             # traverse the hashmap    for i in mp:        print("Element", i, "occurs", mp[i], "times")     # Driver functionarr = [1, 1, 1, 2, 3, 3, 5, 5,8, 8, 8, 9, 9, 10]n = len(arr) findFrequency(arr, n)     # This code is contributed by shubhamsingh10

C#

 // C# program to count number// of occurrences of each// element in the arrayusing System;using System.Collections.Generic;class GFG{ // It prints number of// occurrences of each// element in the array.static void findFrequency(int [] arr,                          int n){  // HashMap to store frequencies  Dictionary mp =              new Dictionary();   // traverse the array  for (int i = 0; i < n; i++)  {    // update the frequency    if (!mp.ContainsKey(arr[i]))      mp[arr[i]] = 0;     mp[arr[i]]++;  }   // traverse the hashmap  foreach(KeyValuePair kvp in mp)    Console.WriteLine("Element " + kvp.Key +                      " occurs " + kvp.Value +                      " times");} // Driver functionpublic static void Main(){  int [] arr = {1, 1, 1, 2,                3, 3, 5, 5,                8, 8, 8, 9,                9, 10};  int n = arr.Length;  findFrequency(arr, n);}} // This code is contributed by Chitranayal

Javascript


Output
Element 10 occurs 1 times
Element 2 occurs 1 times
Element 9 occurs 2 times
Element 1 occurs 3 times
Element 8 occurs 3 times
Element 3 occurs 2 times
Element 5 occurs 2 times

Complexity Analysis:

• Time Complexity:O(n), only one traversal of the array is needed.
• Space Complexity:O(n), to store the elements in the HashMap O(n) extra space is needed.

Method 3: This method uses the technique of Binary Search to arrive at the solution.

• Approach: The problem can be solved in less than O(n) time if all its elements are sorted, i.e. if similar elements exist in the array then the elements are in a contiguous subarray or it can be said that if ends of a subarray are same then all the elements inside the subarray are equal. So the count of that element is the size of the subarray and all the elements of that subarray need not be counted.

• Algorithm:
1. Create a HashMap (hm) to store the frequency of elements.
2. Create a recursive function that accepts an array and size.
3. Check if the first element of the array is equal to the last element. If equal then all the elements are the same and update the frequency by hm[array+=size
4. Else divide the array into two equal halves and call the function recursively for both the halves.
5. Traverse the hashmap and print the element frequency pair.
• Implementation:

C++

 // C++ program to count number of occurrences of// each element in the array in less than O(n) time#include #include using namespace std; // A recursive function to count number of occurrences// for each element in the array without traversing// the whole arrayvoid findFrequencyUtil(int arr[], int low, int high,                       vector& freq){    // If element at index low is equal to element    // at index high in the array    if (arr[low] == arr[high]) {        // increment the frequency of the element        // by count of elements between high and low        freq[arr[low]] += high - low + 1;    }    else {        // Find mid and recurse for left and right        // subarray        int mid = (low + high) / 2;        findFrequencyUtil(arr, low, mid, freq);        findFrequencyUtil(arr, mid + 1, high, freq);    }} // A wrapper over recursive function// findFrequencyUtil(). It print number of// occurrences of each element in the array.void findFrequency(int arr[], int n){    // create a empty vector to store frequencies    // and initialize it by 0. Size of vector is    // maximum value (which is last value in sorted    // array) plus 1.    vector freq(arr[n - 1] + 1, 0);     // Fill the vector with frequency    findFrequencyUtil(arr, 0, n - 1, freq);     // Print the frequencies    for (int i = 0; i <= arr[n - 1]; i++)        if (freq[i] != 0)            cout << "Element " << i << " occurs "                 << freq[i] << " times" << endl;} // Driver functionint main(){    int arr[] = { 1, 1, 1, 2, 3, 3, 5, 5,                  8, 8, 8, 9, 9, 10 };    int n = sizeof(arr) / sizeof(arr);     findFrequency(arr, n);     return 0;}

Java

 // Java program to count number of occurrences of// each element in the array in less than O(n) timeimport java.util.*; class GFG {     // A recursive function to count number of occurrences    // for each element in the array without traversing    // the whole array    static void findFrequencyUtil(int arr[], int low,                                  int high, int[] freq)    {        // If element at index low is equal to element        // at index high in the array        if (arr[low] == arr[high]) {            // increment the frequency of the element            // by count of elements between high and low            freq[arr[low]] += high - low + 1;        }        else {            // Find mid and recurse for left and right            // subarray            int mid = (low + high) / 2;            findFrequencyUtil(arr, low, mid, freq);            findFrequencyUtil(arr, mid + 1, high, freq);        }    }     // A wrapper over recursive function    // findFrequencyUtil(). It print number of    // occurrences of each element in the array.    static void findFrequency(int arr[], int n)    {        // create a empty vector to store frequencies        // and initialize it by 0. Size of vector is        // maximum value (which is last value in sorted        // array) plus 1.        int[] freq = new int[arr[n - 1] + 1];         // Fill the vector with frequency        findFrequencyUtil(arr, 0, n - 1, freq);         // Print the frequencies        for (int i = 0; i <= arr[n - 1]; i++)            if (freq[i] != 0)                System.out.println("Element " + i + " occurs " + freq[i] + " times");    }     // Driver Code    public static void main(String[] args)    {        int arr[] = { 1, 1, 1, 2, 3, 3, 5,                      5, 8, 8, 8, 9, 9, 10 };        int n = arr.length;         findFrequency(arr, n);    }} // This code is contributed by 29AjayKumar

Python3

 # Python 3 program to count number of occurrences of# each element in the array in less than O(n) time # A recursive function to count number of occurrences# for each element in the array without traversing# the whole arraydef findFrequencyUtil(arr, low, high, freq):         # If element at index low is equal to element    # at index high in the array    if (arr[low] == arr[high]):                 # increment the frequency of the element        # by count of elements between high and low        freq[arr[low]] += high - low + 1         else:                 # Find mid and recurse for left         # and right subarray        mid = int((low + high) / 2)        findFrequencyUtil(arr, low, mid, freq)        findFrequencyUtil(arr, mid + 1, high, freq)     # A wrapper over recursive function# findFrequencyUtil(). It print number of# occurrences of each element in the array.def findFrequency(arr, n):         # create a empty vector to store frequencies    # and initialize it by 0. Size of vector is    # maximum value (which is last value in sorted    # array) plus 1.    freq = [0 for i in range(n - 1 + 1)]         # Fill the vector with frequency    findFrequencyUtil(arr, 0, n - 1, freq)     # Print the frequencies    for i in range(0, arr[n - 1] + 1, 1):        if (freq[i] != 0):            print("Element", i, "occurs",                        freq[i], "times") # Driver Codeif __name__ == '__main__':    arr = [1, 1, 1, 2, 3, 3, 5,           5, 8, 8, 8, 9, 9, 10]    n = len(arr)    findFrequency(arr, n)     # This code is contributed by# Surendra_Gangwar

C#

 // C# program to count number of occurrences of// each element in the array in less than O(n) timeusing System; class GFG {     // A recursive function to count number of occurrences    // for each element in the array without traversing    // the whole array    static void findFrequencyUtil(int[] arr, int low,                                  int high, int[] freq)    {        // If element at index low is equal to element        // at index high in the array        if (arr[low] == arr[high]) {            // increment the frequency of the element            // by count of elements between high and low            freq[arr[low]] += high - low + 1;        }        else {            // Find mid and recurse for left and right            // subarray            int mid = (low + high) / 2;            findFrequencyUtil(arr, low, mid, freq);            findFrequencyUtil(arr, mid + 1, high, freq);        }    }     // A wrapper over recursive function    // findFrequencyUtil(). It print number of    // occurrences of each element in the array.    static void findFrequency(int[] arr, int n)    {        // create a empty vector to store frequencies        // and initialize it by 0. Size of vector is        // maximum value (which is last value in sorted        // array) plus 1.        int[] freq = new int[arr[n - 1] + 1];         // Fill the vector with frequency        findFrequencyUtil(arr, 0, n - 1, freq);         // Print the frequencies        for (int i = 0; i <= arr[n - 1]; i++)            if (freq[i] != 0)                Console.WriteLine("Element " + i + " occurs " + freq[i] + " times");    }     // Driver Code    public static void Main(String[] args)    {        int[] arr = { 1, 1, 1, 2, 3, 3, 5,                      5, 8, 8, 8, 9, 9, 10 };        int n = arr.Length;         findFrequency(arr, n);    }} // This code is contributed by Princi Singh

Javascript


Output
Element 1 occurs 3 times
Element 2 occurs 1 times
Element 3 occurs 2 times
Element 5 occurs 2 times
Element 8 occurs 3 times
Element 9 occurs 2 times
Element 10 occurs 1 times

Complexity Analysis:

• Time Complexity: O(m log n).
Where m is the number of distinct elements in the array of size n. Since m <= M (a constant) (elements are in a limited range), the time complexity of this solution is O(log n).
• Space Complexity:O(n).
To store the elements in the HashMap O(n) extra space is needed.

Method 4

C++

 // C++ program to count number of occurrences of// each element in the array #include #include using namespace std; // It prints number of// occurrences of each element in the array.void findFrequency(int input[], int n){    for (int i = 0; i < n; i++)        input[i]--;     for (int i = 0; i < n; i++)        input[input[i] % n] += n;     for (int i = 0; i < n; i++) {          if(input[i]/n)              cout<<"Element "<<(i+1)<<" occurs "<

Java

 // Java program to count number// of occurrences of each// element in the arrayimport java.io.*;import java.util.*;class GFG {     // It prints number of    // occurrences of each    // element in the array.    static void findFrequency(int[] input, int n)    {        for (int i = 0; i < n; i++)            input[i]--;         for (int i = 0; i < n; i++)            input[input[i] % n] += n;         for (int i = 0; i < n; i++) {            if ((input[i] / n)!=0)            System.out.println("Element " +(i + 1) + " occurs " + input[i] / n+ " times");            // Change the element back to original value            input[i] = input[i] % n + 1;        }    }     // Driver function    public static void main(String[] args)    {        int[] arr            = { 1, 1, 1, 2, 3, 3, 5, 5, 8, 8, 8, 9, 9, 10 };        int n = arr.length;        findFrequency(arr, n);    }} // This code is contributed by aditya kumar

https://youtu.be/B2hI-QPoisk