# Print all array elements appearing more than N / K times

• Difficulty Level : Medium
• Last Updated : 11 Mar, 2022

Given an array arr[] of size N and an integer K, the task is to find all the array elements that appear more than (N / K) times.

Examples:

Input: arr[] = { 1, 2, 6, 6, 6, 6, 6, 10 }, K = 4
Output: 6
Explanation:
The frequency of 6 in the array is greater than N / K(= 2). Therefore, the required output is 6.

Input: arr[] = { 3, 4, 4, 5, 5, 5, 5 }, K = 4
Output: 4 5
Explanation:
The frequency of 4 in the array is greater than N / K(= 1).
The frequency of 5 in the array is greater than N / K(= 1).
Therefore, the required output is 4 5.

Naive Approach: The simplest approach to solve this problem is to traverse the array and for every distinct array element, count its frequency and check if exceeds N / K or not. If found to be true, then print the array element.

Time Complexity: O(N2)
Auxiliary Space: O(1)

Sorting-based Approach: The idea is to sort the array followed by traversal of the array to count the frequency of every distinct array element by checking if adjacent elements are equal or not. If frequency of the array element is found to be greater than N / K, then print the array element.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement``// the above approach` `#include ``using` `namespace` `std;` `// Function to print all array elements``// whose frequency is greater than N / K``void` `NDivKWithFreq(``int` `arr[], ``int` `N, ``int` `K)``{``    ``// Sort the array, arr[]``    ``sort(arr, arr + N);` `    ``// Traverse the array``    ``for` `(``int` `i = 0; i < N;) {` `        ``// Stores frequency of arr[i]``        ``int` `cnt = 1;` `        ``// Traverse array elements which``        ``// is equal to arr[i]``        ``while` `((i + 1) < N``               ``&& arr[i] == arr[i + 1]) {` `            ``// Update cnt``            ``cnt++;` `            ``// Update i``            ``i++;``        ``}` `        ``// If frequency of arr[i] is``        ``// greater than (N / K)``        ``if` `(cnt > (N / K)) {` `            ``cout << arr[i] << ``" "``;``        ``}``        ``i++;``    ``}``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 1, 2, 2, 6, 6, 6, 6, 7, 10 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);``    ``int` `K = 4;` `    ``NDivKWithFreq(arr, N, K);` `    ``return` `0;``}`

## Java

 `// Java program to implement``// the above approach``import` `java.util.*;` `class` `GFG{` `// Function to print all array elements``// whose frequency is greater than N / K``static` `void` `NDivKWithFreq(``int` `arr[], ``int` `N, ``int` `K)``{``    ``// Sort the array, arr[]``    ``Arrays.sort(arr);` `    ``// Traverse the array``    ``for` `(``int` `i = ``0``; i < N;) {` `        ``// Stores frequency of arr[i]``        ``int` `cnt = ``1``;` `        ``// Traverse array elements which``        ``// is equal to arr[i]``        ``while` `((i + ``1``) < N``               ``&& arr[i] == arr[i + ``1``]) {` `            ``// Update cnt``            ``cnt++;` `            ``// Update i``            ``i++;``        ``}` `        ``// If frequency of arr[i] is``        ``// greater than (N / K)``        ``if` `(cnt > (N / K)) {` `            ``System.out.print(arr[i]+ ``" "``);``        ``}``        ``i++;``    ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, ``2``, ``2``, ``6``, ``6``, ``6``, ``6``, ``7``, ``10` `};``    ``int` `N = arr.length;``    ``int` `K = ``4``;` `    ``NDivKWithFreq(arr, N, K);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to implement``# the above approach` `# Function to print all array elements``# whose frequency is greater than N / K``def` `NDivKWithFreq(arr, N, K):``    ` `    ``# Sort the array, arr[]``    ``arr ``=` `sorted``(arr)` `    ``# Traverse the array``    ``i ``=` `0``    ` `    ``while` `i < N:``        ` `        ``# Stores frequency of arr[i]``        ``cnt ``=` `1` `        ``# Traverse array elements which``        ``# is equal to arr[i]``        ``while` `((i ``+` `1``) < N ``and``               ``arr[i] ``=``=` `arr[i ``+` `1``]):` `            ``# Update cnt``            ``cnt ``+``=` `1` `            ``# Update i``            ``i ``+``=` `1` `        ``# If frequency of arr[i] is``        ``# greater than (N / K)``        ``if` `(cnt > (N ``/``/` `K)):``            ``print``(arr[i], end ``=` `" "``)``            ` `        ``i ``+``=` `1` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``arr ``=` `[ ``1``, ``2``, ``2``, ``6``, ``6``, ``6``, ``6``, ``7``, ``10` `]``    ``N ``=` `len``(arr)``    ``K ``=` `4` `    ``NDivKWithFreq(arr, N, K)` `# This code is contributed by mohit kumar 29`

## C#

 `// C# program to implement``// the above approach ``using` `System;``   ` `class` `GFG{``   ` `// Function to print all array elements``// whose frequency is greater than N / K``static` `void` `NDivKWithFreq(``int``[] arr, ``int` `N,``                          ``int` `K)``{``    ` `    ``// Sort the array, arr[]``    ``Array.Sort(arr);`` ` `    ``// Traverse the array``    ``for``(``int` `i = 0; i < N;)``    ``{``        ` `        ``// Stores frequency of arr[i]``        ``int` `cnt = 1;`` ` `        ``// Traverse array elements which``        ``// is equal to arr[i]``        ``while` `((i + 1) < N &&``               ``arr[i] == arr[i + 1])``        ``{``            ` `            ``// Update cnt``            ``cnt++;`` ` `            ``// Update i``            ``i++;``        ``}`` ` `        ``// If frequency of arr[i] is``        ``// greater than (N / K)``        ``if` `(cnt > (N / K))``        ``{``            ``Console.Write(arr[i] + ``" "``);``        ``}``        ``i++;``    ``}``}``   ` `// Driver Code``public` `static` `void` `Main()``{``    ``int``[] arr = { 1, 2, 2, 6, 6, 6, 6, 7, 10 };``    ``int` `N = arr.Length;``    ``int` `K = 4;`` ` `    ``NDivKWithFreq(arr, N, K);``}``}` `// This code is contributed by code_hunt`

## Javascript

 ``

Output:

`6`

Time Complexity: O(N * log2N)
Auxiliary Space: O(1)

Binary Search-Based Approach: The problem can be solved using Binary Search technique. The idea is to traverse the array and count the frequency of every distinct array element by calculating the upper bound of array elements. Finally, check if the frequency of the array element is greater than N / K or not. If found to be true, then print the array element. Follow the steps below to solve the problem:

• Sort the array, arr[].
• Traverse the array using the variable i and find the upper_bound of arr[i] say, X and check if (x – i) is greater than N / K or not. If found to be true then print the arr[i].
• Finally, update i = X.

## C++

 `// C++ program to implement``// the above approach` `#include ``using` `namespace` `std;` `// Function to+ find the upper_bound of``// an array element``int` `upperBound(``int` `arr[], ``int` `N, ``int` `K)``{` `    ``// Stores minimum index``    ``// in which K lies``    ``int` `l = 0;` `    ``// Stores maximum index``    ``// in which K lies``    ``int` `r = N;` `    ``// Calculate the upper``    ``// bound of K``    ``while` `(l < r) {` `        ``// Stores mid element``        ``// of l and r``        ``int` `mid = (l + r) / 2;` `        ``// If arr[mid] is less``        ``// than or equal to K``        ``if` `(arr[mid] <= K) {` `            ``// Right subarray``            ``l = mid + 1;``        ``}` `        ``else` `{` `            ``// Left subarray``            ``r = mid;``        ``}``    ``}``    ``return` `l;``}` `// Function to print all array elements``// whose frequency is greater than N / K``void` `NDivKWithFreq(``int` `arr[], ``int` `N, ``int` `K)``{` `    ``// Sort the array arr[]``    ``sort(arr, arr + N);` `    ``// Stores index of``    ``// an array element``    ``int` `i = 0;` `    ``// Traverse the array``    ``while` `(i < N) {` `        ``// Stores upper bound of arr[i]``        ``int` `X = upperBound(arr, N, arr[i]);` `        ``// If frequency of arr[i] is``        ``// greater than N / 4``        ``if` `((X - i) > N / 4) {` `            ``cout << arr[i] << ``" "``;``        ``}` `        ``// Update i``        ``i = X;``    ``}``}` `// Driver Code``int` `main()``{``    ``// Given array arr[]``    ``int` `arr[] = { 1, 2, 2, 6, 6, 6, 6, 7, 10 };` `    ``// Size of array``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``int` `K = 4;` `    ``// Function Call``    ``NDivKWithFreq(arr, N, K);` `    ``return` `0;``}`

## Java

 `// Java program to implement``// the above approach``import` `java.util.*;``class` `GFG{` `// Function to+ find the upper_bound of``// an array element``static` `int` `upperBound(``int` `arr[], ``int` `N, ``int` `K)``{` `    ``// Stores minimum index``    ``// in which K lies``    ``int` `l = ``0``;` `    ``// Stores maximum index``    ``// in which K lies``    ``int` `r = N;` `    ``// Calculate the upper``    ``// bound of K``    ``while` `(l < r)``    ``{` `        ``// Stores mid element``        ``// of l and r``        ``int` `mid = (l + r) / ``2``;` `        ``// If arr[mid] is less``        ``// than or equal to K``        ``if` `(arr[mid] <= K)``        ``{` `            ``// Right subarray``            ``l = mid + ``1``;``        ``}` `        ``else``        ``{` `            ``// Left subarray``            ``r = mid;``        ``}``    ``}``    ``return` `l;``}` `// Function to print all array elements``// whose frequency is greater than N / K``static` `void` `NDivKWithFreq(``int` `arr[], ``int` `N, ``int` `K)``{` `    ``// Sort the array arr[]``    ``Arrays.sort(arr);` `    ``// Stores index of``    ``// an array element``    ``int` `i = ``0``;` `    ``// Traverse the array``    ``while` `(i < N)``    ``{` `        ``// Stores upper bound of arr[i]``        ``int` `X = upperBound(arr, N, arr[i]);` `        ``// If frequency of arr[i] is``        ``// greater than N / 4``        ``if` `((X - i) > N / ``4``)``        ``{` `            ``System.out.print(arr[i] + ``" "``);``        ``}` `        ``// Update i``        ``i = X;``    ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``// Given array arr[]``    ``int` `arr[] = { ``1``, ``2``, ``2``, ``6``, ``6``, ``6``, ``6``, ``7``, ``10` `};` `    ``// Size of array``    ``int` `N = arr.length;``    ``int` `K = ``4``;` `    ``// Function Call``    ``NDivKWithFreq(arr, N, K);``}``}` `// This code is contributed by shikhasingrajput`

## Python3

 `# Python program to implement``# the above approach` `# Function to+ find the upper_bound of``# an array element``def` `upperBound(arr, N, K):` `  ``# Stores minimum index``    ``# in which K lies``    ``l ``=` `0``;` `    ``# Stores maximum index``    ``# in which K lies``    ``r ``=` `N;` `    ``# Calculate the upper``    ``# bound of K``    ``while` `(l < r):` `        ``# Stores mid element``        ``# of l and r``        ``mid ``=` `(l ``+` `r) ``/``/` `2``;` `        ``# If arr[mid] is less``        ``# than or equal to K``        ``if` `(arr[mid] <``=` `K):` `            ``# Right subarray``            ``l ``=` `mid ``+` `1``;``        ``else``:` `            ``# Left subarray``            ``r ``=` `mid;``    ``return` `l;` `# Function to print all array elements``# whose frequency is greater than N / K``def` `NDivKWithFreq(arr, N, K):``  ` `  ``# Sort the array arr``    ``arr.sort();` `    ``# Stores index of``    ``# an array element``    ``i ``=` `0``;` `    ``# Traverse the array``    ``while` `(i < N):` `        ``# Stores upper bound of arr[i]``        ``X ``=` `upperBound(arr, N, arr[i]);` `        ``# If frequency of arr[i] is``        ``# greater than N / 4``        ``if` `((X ``-` `i) > N ``/``/` `4``):``            ``print``(arr[i], end``=``"");` `        ``# Update i``        ``i ``=` `X;` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``  ` `    ``# Given array arr``    ``arr ``=` `[``1``, ``2``, ``2``, ``6``, ``6``, ``6``, ``6``, ``7``, ``10``];` `    ``# Size of array``    ``N ``=` `len``(arr);``    ``K ``=` `4``;` `    ``# Function Call``    ``NDivKWithFreq(arr, N, K);` `    ``# This code is contributed by 29AjayKumar`

## C#

 `// C# program to implement``// the above approach``using` `System;``class` `GFG``{` `  ``// Function to+ find the upper_bound of``  ``// an array element``  ``static` `int` `upperBound(``int` `[]arr, ``int` `N, ``int` `K)``  ``{` `    ``// Stores minimum index``    ``// in which K lies``    ``int` `l = 0;` `    ``// Stores maximum index``    ``// in which K lies``    ``int` `r = N;` `    ``// Calculate the upper``    ``// bound of K``    ``while` `(l < r)``    ``{` `      ``// Stores mid element``      ``// of l and r``      ``int` `mid = (l + r) / 2;` `      ``// If arr[mid] is less``      ``// than or equal to K``      ``if` `(arr[mid] <= K)``      ``{` `        ``// Right subarray``        ``l = mid + 1;``      ``}` `      ``else``      ``{` `        ``// Left subarray``        ``r = mid;``      ``}``    ``}``    ``return` `l;``  ``}` `  ``// Function to print all array elements``  ``// whose frequency is greater than N / K``  ``static` `void` `NDivKWithFreq(``int` `[]arr, ``int` `N, ``int` `K)``  ``{` `    ``// Sort the array arr[]``    ``Array.Sort(arr);` `    ``// Stores index of``    ``// an array element``    ``int` `i = 0;` `    ``// Traverse the array``    ``while` `(i < N)``    ``{` `      ``// Stores upper bound of arr[i]``      ``int` `X = upperBound(arr, N, arr[i]);` `      ``// If frequency of arr[i] is``      ``// greater than N / 4``      ``if` `((X - i) > N / 4)``      ``{` `        ``Console.Write(arr[i] + ``" "``);``      ``}` `      ``// Update i``      ``i = X;``    ``}``  ``}` `  ``// Driver Code``  ``public` `static` `void` `Main(``string``[] args)``  ``{` `    ``// Given array arr[]``    ``int` `[]arr = { 1, 2, 2, 6, 6, 6, 6, 7, 10 };` `    ``// Size of array``    ``int` `N = arr.Length;``    ``int` `K = 4;` `    ``// Function Call``    ``NDivKWithFreq(arr, N, K);``  ``}``}` `// This code is contributed by AnkThon`

## Javascript

 ``

Output:

`6`

Time Complexity: O(N * log2N)
Auxiliary Space: O(1)

#### Another Approach: Using Built-in Python functions:

• Count the frequencies of every element using Counter() function.
• Traverse the frequency array and print all the elements which occur at more than n/k times.

Below is the implementation:

## Python3

 `# Python3 implementation``from` `collections ``import` `Counter` `# Function to find the number of array``# elements with frequency more than n/k times``def` `printElements(arr, n, k):` `    ``# Calculating n/k``    ``x ``=` `n``/``/``k` `    ``# Counting frequency of every``    ``# element using Counter``    ``mp ``=` `Counter(arr)``    ` `    ``# Traverse the map and print all``    ``# the elements with occurrence atleast n/k times``    ``for` `it ``in` `mp:``        ``if` `mp[it] > x:``            ``print``(it)`  `# Driver code``arr ``=` `[``1``, ``2``, ``2``, ``6``, ``6``, ``6``, ``6``, ``7``, ``10``]` `# Size of array``n ``=` `len``(arr)``k ``=` `4` `printElements(arr, n, k)` `# This code is contributed by vikkycirus`

Output:

`6`

Time Complexity: O(N)

Auxiliary Space: O(N)

Efficient Approach: To optimize the above approach, the idea is to store the frequency of each distinct array element into a Map. Finally, traverse the map and check if its frequency is greater than (N / K) or not. If found to be true, then print the array element. Refer to this article for the discussion of this approach.

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

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