Find top k (or most frequent) numbers in a stream
Given an array of n numbers. Your task is to read numbers from the array and keep at-most K numbers at the top (According to their decreasing frequency) every time a new number is read. We basically need to print top k numbers sorted by frequency when input stream has included k distinct elements, else need to print all distinct elements sorted by frequency.
Examples:
Input : arr[] = {5, 2, 1, 3, 2}
k = 4
Output : 5 2 5 1 2 5 1 2 3 5 2 1 3 5Explanation:
- After reading 5, there is only one element 5 whose frequency is max till now.
so print 5.- After reading 2, we will have two elements 2 and 5 with the same frequency.
As 2, is smaller than 5 but their frequency is the same so we will print 2 5.- After reading 1, we will have 3 elements 1, 2 and 5 with the same frequency,
so print 1 2 5.- Similarly after reading 3, print 1 2 3 5
- After reading last element 2 since 2 has already occurred so we have now a
frequency of 2 as 2. So we keep 2 at the top and then rest of the element
with the same frequency in sorted order. So print, 2 1 3 5.Input : arr[] = {5, 2, 1, 3, 4}
k = 4
Output : 5 2 5 1 2 5 1 2 3 5 1 2 3 4Explanation:
- After reading 5, there is only one element 5 whose frequency is max till now.
so print 5.- After reading 2, we will have two elements 2 and 5 with the same frequency.
As 2, is smaller than 5 but their frequency is the same so we will print 2 5.- After reading 1, we will have 3 elements 1, 2 and 5 with the same frequency,
so print 1 2 5.
Similarly after reading 3, print 1 2 3 5- After reading last element 4, All the elements have same frequency
So print, 1 2 3 4
Approach: The idea is to store the top k elements with maximum frequency. To store them a vector or an array can be used. To keep the track of frequencies of elements creates a HashMap to store element-frequency pairs. Given a stream of numbers, when a new element appears in the stream update the frequency of that element in HashMap and put that element at the end of the list of K numbers (total k+1 elements) now compare adjacent elements of the list and swap if higher frequency element is stored next to it.
Algorithm:
- Create a Hashmap hm, and an array of k + 1 length.
- Traverse the input array from start to end.
- Insert the element at k+1 th position of the array, and update the frequency of that element in HashMap.
- Now, iterate from the position of element to zero.
- For very element, compare the frequency and swap if a higher frequency element is stored next to it, if the frequency is the same then the swap is the next element is greater.
- print the top k element in each traversal of the original array.
Implementation:
C++
// C++ program to find top k elements in a stream #include <bits/stdc++.h> using namespace std; // Function to print top k numbers void kTop( int a[], int n, int k) { // vector of size k+1 to store elements vector< int > top(k + 1); // array to keep track of frequency unordered_map< int , int > freq; // iterate till the end of stream for ( int m = 0; m < n; m++) { // increase the frequency freq[a[m]]++; // store that element in top vector top[k] = a[m]; // search in top vector for same element auto it = find(top.begin(), top.end() - 1, a[m]); // iterate from the position of element to zero for ( int i = distance(top.begin(), it) - 1; i >= 0; --i) { // compare the frequency and swap if higher // frequency element is stored next to it if (freq[top[i]] < freq[top[i + 1]]) swap(top[i], top[i + 1]); // if frequency is same compare the elements // and swap if next element is high else if ((freq[top[i]] == freq[top[i + 1]]) && (top[i] > top[i + 1])) swap(top[i], top[i + 1]); else break ; } // print top k elements for ( int i = 0; i < k && top[i] != 0; ++i) cout << top[i] << ' ' ; } cout << endl; } // Driver program to test above function int main() { int k = 4; int arr[] = { 5, 2, 1, 3, 2 }; int n = sizeof (arr) / sizeof (arr[0]); kTop(arr, n, k); return 0; } |
Java
import java.io.*; import java.util.*; class GFG { // function to search in top vector for element static int find( int [] arr, int ele) { for ( int i = 0 ; i < arr.length; i++) if (arr[i] == ele) return i; return - 1 ; } // Function to print top k numbers static void kTop( int [] a, int n, int k) { // vector of size k+1 to store elements int [] top = new int [k + 1 ]; // array to keep track of frequency HashMap<Integer, Integer> freq = new HashMap<>(); for ( int i = 0 ; i < k + 1 ; i++) freq.put(i, 0 ); // iterate till the end of stream for ( int m = 0 ; m < n; m++) { // increase the frequency if (freq.containsKey(a[m])) freq.put(a[m], freq.get(a[m]) + 1 ); else freq.put(a[m], 1 ); // store that element in top vector top[k] = a[m]; // search in top vector for same element int i = find(top, a[m]); i -= 1 ; // iterate from the position of element to zero while (i >= 0 ) { // compare the frequency and swap if higher // frequency element is stored next to it if (freq.get(top[i]) < freq.get(top[i + 1 ])) { int temp = top[i]; top[i] = top[i + 1 ]; top[i + 1 ] = temp; } // if frequency is same compare the elements // and swap if next element is high else if ((freq.get(top[i]) == freq.get(top[i + 1 ])) && (top[i] > top[i + 1 ])) { int temp = top[i]; top[i] = top[i + 1 ]; top[i + 1 ] = temp; } else break ; i -= 1 ; } // print top k elements for ( int j = 0 ; j < k && top[j] != 0 ; ++j) System.out.print(top[j] + " " ); } System.out.println(); } // Driver program to test above function public static void main(String args[]) { int k = 4 ; int [] arr = { 5 , 2 , 1 , 3 , 2 }; int n = arr.length; kTop(arr, n, k); } } // This code is contributed by rachana soma |
Python3
# Python program to find top k elements in a stream # Function to print top k numbers def kTop(a, n, k): # list of size k + 1 to store elements top = [ 0 for i in range (k + 1 )] # dictionary to keep track of frequency freq = {i: 0 for i in range (k + 1 )} # iterate till the end of stream for m in range (n): # increase the frequency if a[m] in freq.keys(): freq[a[m]] + = 1 else : freq[a[m]] = 1 # store that element in top vector top[k] = a[m] i = top.index(a[m]) i - = 1 while i > = 0 : # compare the frequency and swap if higher # frequency element is stored next to it if (freq[top[i]] < freq[top[i + 1 ]]): t = top[i] top[i] = top[i + 1 ] top[i + 1 ] = t # if frequency is same compare the elements # and swap if next element is high else if ((freq[top[i]] = = freq[top[i + 1 ]]) and (top[i] > top[i + 1 ])): t = top[i] top[i] = top[i + 1 ] top[i + 1 ] = t else : break i - = 1 # print top k elements i = 0 while i < k and top[i] ! = 0 : print (top[i],end = " " ) i + = 1 print () # Driver program to test above function k = 4 arr = [ 5 , 2 , 1 , 3 , 2 ] n = len (arr) kTop(arr, n, k) # This code is contributed by Sachin Bisht |
C#
// C# program to find top k elements in a stream using System; using System.Collections.Generic; class GFG { // function to search in top vector for element static int find( int [] arr, int ele) { for ( int i = 0; i < arr.Length; i++) if (arr[i] == ele) return i; return -1; } // Function to print top k numbers static void kTop( int [] a, int n, int k) { // vector of size k+1 to store elements int [] top = new int [k + 1]; // array to keep track of frequency Dictionary< int , int > freq = new Dictionary< int , int >(); for ( int i = 0; i < k + 1; i++) freq.Add(i, 0); // iterate till the end of stream for ( int m = 0; m < n; m++) { // increase the frequency if (freq.ContainsKey(a[m])) freq[a[m]]++; else freq.Add(a[m], 1); // store that element in top vector top[k] = a[m]; // search in top vector for same element int i = find(top, a[m]); i--; // iterate from the position of element to zero while (i >= 0) { // compare the frequency and swap if higher // frequency element is stored next to it if (freq[top[i]] < freq[top[i + 1]]) { int temp = top[i]; top[i] = top[i + 1]; top[i + 1] = temp; } // if frequency is same compare the elements // and swap if next element is high else if (freq[top[i]] == freq[top[i + 1]] && top[i] > top[i + 1]) { int temp = top[i]; top[i] = top[i + 1]; top[i + 1] = temp; } else break ; i--; } // print top k elements for ( int j = 0; j < k && top[j] != 0; ++j) Console.Write(top[j] + " " ); } Console.WriteLine(); } // Driver Code public static void Main(String[] args) { int k = 4; int [] arr = { 5, 2, 1, 3, 2 }; int n = arr.Length; kTop(arr, n, k); } } // This code is contributed by // sanjeev2552 |
Javascript
<script> // JavaScript program to find top k elements in a stream // function to search in top vector for element function find(arr, ele) { for ( var i = 0; i < arr.length; i++) if (arr[i] === ele) return i; return -1; } // Function to print top k numbers function kTop(a, n, k) { // vector of size k+1 to store elements var top = new Array(k + 1).fill(0); // array to keep track of frequency var freq = {}; for ( var i = 0; i < k + 1; i++) freq[i] = 0; // iterate till the end of stream for ( var m = 0; m < n; m++) { // increase the frequency if (freq.hasOwnProperty(a[m])) freq[a[m]]++; else freq[a[m]] = 1; // store that element in top vector top[k] = a[m]; // search in top vector for same element var i = find(top, a[m]); i--; // iterate from the position of element to zero while (i >= 0) { // compare the frequency and swap if higher // frequency element is stored next to it if (freq[top[i]] < freq[top[i + 1]]) { var temp = top[i]; top[i] = top[i + 1]; top[i + 1] = temp; } // if frequency is same compare the elements // and swap if next element is high else if (freq[top[i]] === freq[top[i + 1]] && top[i] > top[i + 1]) { var temp = top[i]; top[i] = top[i + 1]; top[i + 1] = temp; } else break ; i--; } // print top k elements for ( var j = 0; j < k && top[j] !== 0; ++j) document.write(top[j] + " " ); } document.write( "<br>" ); } // Driver Code var k = 4; var arr = [5, 2, 1, 3, 2]; var n = arr.length; kTop(arr, n, k); </script> |
5 2 5 1 2 5 1 2 3 5 2 1 3 5
Complexity Analysis:
- Time Complexity: O( n * k ).
In each traversal the temp array of size k is traversed, So the time Complexity is O( n * k ). - Space Complexity: O(n).
To store the elements in HashMap O(n) space is required.
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