Find k most frequent in linear time

• Difficulty Level : Medium
• Last Updated : 03 Feb, 2022

Given an array of integers, we need to print k most frequent elements. If there is a tie, we need to prefer the elements whose first appearance is first.

Examples:

Input : arr[] = {10, 5, 20, 5, 10, 10, 30}, k = 2
Output : 10 5

Input : arr[] = {7, 7, 6, 6, 6, 7, 5, 4, 4, 10, 5}, k = 3
Output : 7 6 5
Explanation :
In this example, 7 and 6 have the same frequencies. We print 7 first because the first appearance of 7 is first. Similarly, 5 and 4 have the same frequencies. We prefer 5 because 5’s first appearance is first.

We have discussed two methods in the post below.
Find k numbers with most occurrences in         the given array
Let us first talk about a simple solution that prints in any order in the case of a tie. Then we will discuss the solution that takes of the order.

The idea is to use hashing with frequency indexing. We first store counts in a hash. Then we traverse through the hash and use frequencies as the index to store elements with given frequencies. The important factor here is, the maximum frequency can be n. So an array of size n+1 would be good.

C++

 `// C++ implementation to find k numbers with most``// occurrences in the given array``#include ``using` `namespace` `std;` `// function to print the k numbers with most occurrences``void` `print_N_mostFrequentNumber(``int` `arr[], ``int` `n, ``int` `k)``{``    ``// unordered_map 'um' implemented as frequency``    ``// hash table``    ``unordered_map<``int``, ``int``> um;``    ``for` `(``int` `i = 0; i < n; i++)``        ``um[arr[i]]++;` `    ``// Use frequencies as indexes and put``    ``// elements with given frequency in a``    ``// vector (related to a frequency)``    ``vector<``int``> freq[n + 1];``    ``for` `(``auto` `x : um)``        ``freq[x.second].push_back(x.first);` `    ``// Initialize count of items printed``    ``int` `count = 0;` `    ``// Traverse the frequency array from``    ``// right side as we need the most``    ``// frequent items.``    ``for` `(``int` `i = n; i >= 0; i--) {` `        ``// Print items of current frequency``        ``for` `(``int` `x : freq[i]) {``            ``cout << x << ``" "``;``            ``count++;``            ``if` `(count == k)``                ``return``;``        ``}``    ``}``}` `// Driver program to test above``int` `main()``{``    ``int` `arr[] = { 3, 1, 4, 4, 5, 2, 6, 1 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``int` `k = 2;``    ``print_N_mostFrequentNumber(arr, n, k);``    ``return` `0;``}`

Java

 `// Java implementation to find k elements with max occurrence.``import` `java.util.*;``public` `class` `KFrequentNumbers {``    ``static` `void` `print_N_mostFrequentNumber(``int``[] arr, ``int` `n, ``int` `k)``    ``{``        ``Map mp = ``new` `HashMap();` `        ``// Put count of all the distinct elements in Map``        ``// with element as the key & count as the value.``        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``// Get the count for the element if already``            ``// present in the Map or get the default value``            ``// which is 0.``            ``mp.put(arr[i], mp.getOrDefault(arr[i], ``0``) + ``1``);``        ``}` `        ``// Initialize an array list of array lists``        ``List > freq = ``new` `ArrayList >();``        ``for` `(``int` `i = ``0``; i <= n; i++)``            ``freq.add(``new` `ArrayList());` `        ``// Use frequencies as indexes and add corresponding``        ``// values to the list``        ``for` `(Map.Entry x : mp.entrySet())``            ``freq.get(x.getValue()).add(x.getKey());` `        ``// Traverse freq[] from right side.``        ``int` `count = ``0``;``        ``for` `(``int` `i = n; i >= ``0``; i--) {``            ``for` `(``int` `x : freq.get(i)) {``                ``System.out.println(x);``                ``count++;``                ``if` `(count == k)``                    ``return``;``            ``}``        ``}``    ``}` `    ``// Driver Code to test the code.``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { ``3``, ``1``, ``4``, ``4``, ``5``, ``2``, ``6``, ``1` `};``        ``int` `n = arr.length;``        ``int` `k = ``2``;``        ``print_N_mostFrequentNumber(arr, n, k);``    ``}``}`

Python3

 `# Python3 implementation to find k numbers``# with most occurrences in the given array` `# Function to print k numbers with most occurrences``def` `print_N_mostFrequentNumber(arr, n, k):``    ` `    ``# unordered_map 'um' implemented as``    ``# frequency hash table``    ``um ``=` `{}``    ``for` `i ``in` `range``(n):``        ``um[arr[i]] ``=`  `um.get(arr[i], ``0``) ``+` `1` `    ``# Use frequencies as indexes and put``    ``# elements with given frequency in a``    ``# vector (related to a frequency)``    ``freq ``=` `[[] ``for` `i ``in` `range``(n ``+` `1``)]``    ``for` `x ``in` `um:``        ``freq[um[x]].append(x)` `    ``# Initialize count of items printed``    ``count ``=` `0` `    ``# Traverse the frequency array from``    ``# right side as we need the most``    ``# frequent items.``    ``for` `i ``in` `range``(n, ``-``1``, ``-``1``):``        ` `        ``# Print items of current frequency``        ``for` `x ``in` `sorted``(freq[i])[::``-``1``]:``            ``print``(x, end ``=` `" "``)``            ``count ``+``=` `1``            ` `            ``if` `(count ``=``=` `k):``                ``return` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``arr ``=` `[ ``3``, ``1``, ``4``, ``4``, ``5``, ``2``, ``6``, ``1` `]``    ``n ``=` `len``(arr)``    ``k ``=` `2``    ` `    ``print_N_mostFrequentNumber(arr, n, k)` `# This code is contributed by mohit kumar 29`

C#

 `// C# implementation to find``// k elements with max occurrence.``using` `System;``using` `System.Collections.Generic;``class` `KFrequentNumbers{` `static` `void` `print_N_mostFrequentNumber(``int``[] arr,``                                       ``int` `n, ``int` `k)``{``  ``Dictionary<``int``,``             ``int``> mp = ``new` `Dictionary<``int``,``                                      ``int``>();` `  ``// Put count of all the``  ``// distinct elements in Map``  ``// with element as the key``  ``// & count as the value.``  ``for` `(``int` `i = 0; i < n; i++)``  ``{``    ``// Get the count for the``    ``// element if already``    ``// present in the Map``    ``// or get the default value``    ``// which is 0.``    ``if``(mp.ContainsKey(arr[i]))``    ``{``      ``mp[arr[i]] = mp[arr[i]] + 1;``    ``}``    ``else``    ``{``      ``mp.Add(arr[i], 1);``    ``}``  ``}` `  ``// Initialize an array``  ``// list of array lists``  ``List > freq =``            ``new` `List >();``  ` `  ``for` `(``int` `i = 0; i <= n; i++)``    ``freq.Add(``new` `List<``int``>());` `  ``// Use frequencies as indexes``  ``// and add corresponding``  ``// values to the list``  ``foreach` `(KeyValuePair<``int``,``                        ``int``> x ``in` `mp)``    ``freq[x.Value].Add(x.Key);` `  ``// Traverse []freq from``  ``// right side.``  ``int` `count = 0;``  ``for` `(``int` `i = n; i >= 0; i--)``  ``{``    ``foreach` `(``int` `x ``in` `freq[i])``    ``{``      ``Console.WriteLine(x);``      ``count++;``      ``if` `(count == k)``        ``return``;``    ``}``  ``}``}` `// Driver Code to test the code.``public` `static` `void` `Main(String[] args)``{``  ``int` `[]arr = {3, 1, 4, 4,``               ``5, 2, 6, 1};``  ``int` `n = arr.Length;``  ``int` `k = 2;``  ``print_N_mostFrequentNumber(arr, n, k);``}``}` `// This code is contributed by Princi Singh`

Javascript

 ``

Output:

`4 1`

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

Printing according to the first appearance. To keep the required order, we traverse the original array instead of the map. To avoid duplicates, we need to mark processed entries as -1 on the map.

C++

 `// C++ implementation to find k numbers with most``// occurrences in the given array``#include ``using` `namespace` `std;` `// function to print the k numbers with most occurrences``void` `print_N_mostFrequentNumber(``int` `arr[], ``int` `n, ``int` `k)``{``    ``// unordered_map 'um' implemented as frequency``    ``// hash table``    ``unordered_map<``int``, ``int``> um;``    ``for` `(``int` `i = 0; i < n; i++)``        ``um[arr[i]]++;` `    ``// Use frequencies as indexes and put``    ``// elements with given frequency in a``    ``// vector (related to a frequency)``    ``vector<``int``> freq[n + 1];``    ``for` `(``int` `i = 0; i < n; i++) {``        ``int` `f = um[arr[i]];``        ``if` `(f != -1) {``            ``freq[f].push_back(arr[i]);``            ``um[arr[i]] = -1;``        ``}``    ``}` `    ``// Initialize count of items printed``    ``int` `count = 0;` `    ``// Traverse the frequency array from``    ``// right side as we need the most``    ``// frequent items.``    ``for` `(``int` `i = n; i >= 0; i--) {` `        ``// Print items of current frequency``        ``for` `(``int` `x : freq[i]) {``            ``cout << x << ``" "``;``            ``count++;``            ``if` `(count == k)``                ``return``;``        ``}``    ``}``}` `// Driver program to test above``int` `main()``{``    ``int` `arr[] = { 3, 1, 4, 4, 5, 2, 6, 1 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``int` `k = 3;``    ``print_N_mostFrequentNumber(arr, n, k);``    ``return` `0;``}`

Java

 `// Java implementation to find k elements with max occurrence.``import` `java.util.*;``public` `class` `KFrequentNumbers {``    ``static` `void` `print_N_mostFrequentNumber(``int``[] arr, ``int` `n, ``int` `k)``    ``{``        ``Map mp = ``new` `HashMap();` `        ``// Put count of all the distinct elements in Map``        ``// with element as the key & count as the value.``        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``// Get the count for the element if already``            ``// present in the Map or get the default value``            ``// which is 0.``            ``mp.put(arr[i], mp.getOrDefault(arr[i], ``0``) + ``1``);``        ``}` `        ``// Initialize an array list of array lists``        ``List > freq = ``new` `ArrayList >();``        ``for` `(``int` `i = ``0``; i <= n; i++)``            ``freq.add(``new` `ArrayList());` `        ``// Use frequencies as indexes and add corresponding``        ``// values to the list``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``int` `f = mp.get(arr[i]);``            ``if` `(f != -``1``) {``                ``freq.get(f).add(arr[i]);``                ``mp.put(arr[i], -``1``);``            ``}``        ``}` `        ``// Traverse freq[] from right side.``        ``int` `count = ``0``;``        ``for` `(``int` `i = n; i >= ``0``; i--) {``            ``for` `(``int` `x : freq.get(i)) {``                ``System.out.println(x);``                ``count++;``                ``if` `(count == k)``                    ``return``;``            ``}``        ``}``    ``}` `    ``// Driver Code to test the code.``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { ``3``, ``1``, ``4``, ``4``, ``5``, ``2``, ``6``, ``1` `};``        ``int` `n = arr.length;``        ``int` `k = ``3``;``        ``print_N_mostFrequentNumber(arr, n, k);``    ``}``}`

Python3

 `# Python implementation to find k elements``# with max occurrence.``def` `print_N_mostFrequentNumber(arr, n, k):``    ``mp ``=` `{}``    ` `    ``# Put count of all the distinct``    ``# elements in Map with element``    ``# as the key & count as the value.``    ``for` `i ``in` `range``(n):``      ` `        ``# Get the count for the element``        ``# if already present in the Map``        ``# or get the default value which is 0.``        ``if` `arr[i] ``in` `mp:``            ``mp[arr[i]] ``+``=` `1``        ``else``:``            ``mp[arr[i]] ``=` `0``            ` `    ``# Initialize an array list of array lists``    ``freq ``=` `[[] ``for` `i ``in` `range``(n``+``1``)]``    ` `    ``# Use frequencies as indexes and``    ``# add corresponding values to``    ``# the list``    ``for` `i ``in` `range``(n):``        ``f ``=` `mp[arr[i]]``        ``if` `(f !``=` `-``1``):``            ``freq[f].append(arr[i])``            ``mp[arr[i]] ``=` `-``1``            ` `    ``# Traverse []freq from right side.``    ``count ``=` `0``    ``for` `i ``in` `range``(n, ``-``1``, ``-``1``):``        ``for` `x ``in` `freq[i]:``            ``print``(x ,end ``=` `" "``)``            ``count``+``=``1``            ` `            ``if` `(count ``=``=` `k):``                ``return``      ` `# Driver Code``arr ``=` `[``3``, ``1``, ``4``, ``4``, ``5``, ``2``, ``6``, ``1``]``n ``=` `len``(arr)``k ``=` `3` `print_N_mostFrequentNumber(arr, n, k)` `# This code is contributed by Shubham Singh`

C#

 `// C# implementation to find k elements``// with max occurrence.``using` `System;``using` `System.Collections.Generic;` `class` `GFG{``    ` `static` `void` `print_N_mostFrequentNumber(``int``[] arr,``                                       ``int` `n, ``int` `k)``{``    ``Dictionary<``int``,``               ``int``> mp = ``new` `Dictionary<``int``,``                                        ``int``>();` `    ``// Put count of all the distinct``    ``// elements in Map with element``    ``// as the key & count as the value.``    ``for``(``int` `i = 0; i < n; i++)``    ``{``        ` `        ``// Get the count for the element``        ``// if already present in the Map``        ``// or get the default value which is 0.``        ``if` `(mp.ContainsKey(arr[i]))``            ``mp[arr[i]]++;``        ``else``            ``mp.Add(arr[i], 0);``    ``}` `    ``// Initialize an array list of array lists``    ``List> freq = ``new` `List>();``    ``for``(``int` `i = 0; i <= n; i++)``        ``freq.Add(``new` `List<``int``>());` `    ``// Use frequencies as indexes and``    ``// add corresponding values to``    ``// the list``    ``for``(``int` `i = 0; i < n; i++)``    ``{``        ``int` `f = mp[arr[i]];``        ``if` `(f != -1)``        ``{``            ``freq[f].Add(arr[i]);` `            ``if` `(mp.ContainsKey(arr[i]))``                ``mp[arr[i]] = -1;``            ``else``                ``mp.Add(arr[i], 0);``        ``}``    ``}` `    ``// Traverse []freq from right side.``    ``int` `count = 0;``    ``for``(``int` `i = n; i >= 0; i--)``    ``{``        ``foreach``(``int` `x ``in` `freq[i])``        ``{``            ``Console.Write(x);``            ``Console.Write(``" "``);``            ``count++;``            ` `            ``if` `(count == k)``                ``return``;``        ``}``    ``}``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 3, 1, 4, 4, 5, 2, 6, 1 };``    ``int` `n = arr.Length;``    ``int` `k = 3;``    ` `    ``print_N_mostFrequentNumber(arr, n, k);``}``}` `// This code is contributed by Amit Katiyar`

Javascript

 ``

Output:

`1 4 3`

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

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