k largest(or smallest) elements in an array | added Min Heap method

Question: Write an efficient program for printing k largest elements in an array. Elements in array can be in any order.

For example, if given array is [1, 23, 12, 9, 30, 2, 50] and you are asked for the largest 3 elements i.e., k = 3 then your program should print 50, 30 and 23.

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Method 1 (Use Bubble k times)
Thanks to Shailendra for suggesting this approach.
1) Modify Bubble Sort to run the outer loop at most k times.
2) Print the last k elements of the array obtained in step 1.

Time Complexity: O(nk)

Like Bubble sort, other sorting algorithms like Selection Sort can also be modified to get the k largest elements.

Method 2 (Use temporary array)
K largest elements from arr[0..n-1]

1) Store the first k elements in a temporary array temp[0..k-1].
2) Find the smallest element in temp[], let the smallest element be min.
3-a) For each element x in arr[k] to arr[n-1]. O(n-k)
If x is greater than the min then remove min from temp[] and insert x.
3-b)Then, determine the new min from temp[]. O(k)
4) Print final k elements of temp[]

Time Complexity: O((n-k)*k). If we want the output sorted then O((n-k)*k + klogk)

Thanks to nesamani1822 for suggesting this method.

Method 3(Use Sorting)
1) Sort the elements in descending order in O(nLogn)
2) Print the first k numbers of the sorted array O(k).
Following is the implementation of above.

C++

// C++ code for k largest elements in an array 
#include <bits/stdc++.h> 
using namespace std; 
  
void kLargest(int arr[], int n, int k) 
{ 
    // Sort the given array arr in reverse 
    // order. 
    sort(arr, arr + n, greater<int>()); 
  
    // Print the first kth largest elements 
    for (int i = 0; i < k; i++) 
        cout << arr[i] << " "; 
} 
  
// driver program 
int main() 
{ 
    int arr[] = { 1, 23, 12, 9, 30, 2, 50 }; 
    int n = sizeof(arr) / sizeof(arr[0]); 
    int k = 3; 
    kLargest(arr, n, k); 
} 
  
// This article is contributed by Chhavi 

Java

// Java code for k largest elements in an array 
import java.util.Arrays; 
import java.util.Collections; 
  
class GFG { 
    public static void kLargest(Integer[] arr, int k) 
    { 
        // Sort the given array arr in reverse order 
        // This method doesn't work with primitive data 
        // types. So, instead of int, Integer type 
        // array will be used 
        Arrays.sort(arr, Collections.reverseOrder()); 
  
        // Print the first kth largest elements 
        for (int i = 0; i < k; i++) 
            System.out.print(arr[i] + " "); 
    } 
  
    public static void main(String[] args) 
    { 
        Integer arr[] = new Integer[] { 1, 23, 12, 9, 
                                        30, 2, 50 }; 
        int k = 3; 
        kLargest(arr, k); 
    } 
} 
// This code is contributed by Kamal Rawal 

Python

''' Python3 code for k largest elements in an array'''
  
def kLargest(arr, k): 
    # Sort the given array arr in reverse  
    # order. 
    arr.sort(reverse = True) 
    # Print the first kth largest elements 
    for i in range(k): 
        print (arr[i], end =" ")  
  
# Driver program 
arr = [1, 23, 12, 9, 30, 2, 50] 
# n = len(arr) 
k = 3
kLargest(arr, k) 
  
# This code is contributed by shreyanshi_arun. 

C#

// C# code for k largest elements in an array 
using System; 
  
class GFG { 
    public static void kLargest(int[] arr, int k) 
    { 
        // Sort the given array arr in reverse order 
        // This method doesn't work with primitive data 
        // types. So, instead of int, Integer type 
        // array will be used 
        Array.Sort(arr); 
        Array.Reverse(arr); 
  
        // Print the first kth largest elements 
        for (int i = 0; i < k; i++) 
            Console.Write(arr[i] + " "); 
    } 
  
    // Driver code 
    public static void Main(String[] args) 
    { 
        int[] arr = new int[] { 1, 23, 12, 9, 
                                30, 2, 50 }; 
        int k = 3; 
        kLargest(arr, k); 
    } 
} 
  
// This code contributed by Rajput-Ji 

PHP

<?php  
// PHP code for k largest  
// elements in an array 
  
function kLargest(&$arr, $n, $k) 
{ 
    // Sort the given array arr  
    // in reverse order. 
    rsort($arr); 
  
    // Print the first kth  
    // largest elements 
    for ($i = 0; $i < $k; $i++) 
        echo $arr[$i] . " "; 
} 
  
// Driver Code 
$arr = array(1, 23, 12, 9,  
                30, 2, 50); 
$n = sizeof($arr); 
$k = 3; 
kLargest($arr, $n, $k); 
  
// This code is contributed  
// by ChitraNayal 
?> 

Output:

50 30 23

Time complexity: O(nlogn)

Method 4 (Use Max Heap)
1) Build a Max Heap tree in O(n)
2) Use Extract Max k times to get k maximum elements from the Max Heap O(klogn)

Time complexity: O(n + klogn)

Method 5(Use Oder Statistics)
1) Use order statistic algorithm to find the kth largest element. Please see the topic selection in worst-case linear time O(n)
2) Use QuickSort Partition algorithm to partition around the kth largest number O(n).
3) Sort the k-1 elements (elements greater than the kth largest element) O(kLogk). This step is needed only if sorted output is required.

Time complexity: O(n) if we don’t need the sorted output, otherwise O(n+kLogk)

Thanks to Shilpi for suggesting the first two approaches.

Method 6 (Use Min Heap)
This method is mainly an optimization of method 1. Instead of using temp[] array, use Min Heap.

1) Build a Min Heap MH of the first k elements (arr[0] to arr[k-1]) of the given array. O(k)

2) For each element, after the kth element (arr[k] to arr[n-1]), compare it with root of MH.
……a) If the element is greater than the root then make it root and call heapify for MH
……b) Else ignore it.
// The step 2 is O((n-k)*logk)

3) Finally, MH has k largest elements and root of the MH is the kth largest element.

Time Complexity: O(k + (n-k)Logk) without sorted output. If sorted output is needed then O(k + (n-k)Logk + kLogk)

All of the above methods can also be used to find the kth largest (or smallest) element.

C++

#include <iostream> 
using namespace std; 
  
// Swap function to interchange 
// the value of variables x and y 
int swap(int& x, int& y) 
{ 
    int temp = x; 
    x = y; 
    y = temp; 
} 
  
// Min Heap Class 
// arr holds reference to an integer  
// array size indicate the number of 
// elements in Min Heap 
class MinHeap { 
  
    int size; 
    int* arr; 
  
public: 
    // Constructor to initialize the size and arr 
    MinHeap(int size, int input[]); 
  
    // Min Heapify function, that assumes that 
    // 2*i+1 and 2*i+2 are min heap and fix the 
    // heap property for i. 
    void heapify(int i); 
  
    // Build the min heap, by calling heapify 
    // for all non-leaf nodes. 
    void buildHeap(); 
}; 
  
// Constructor to initialize data 
// members and creating mean heap 
MinHeap::MinHeap(int size, int input[]) 
{ 
    // Initializing arr and size 
  
    this->size = size; 
    this->arr = input; 
  
    // Building the Min Heap 
    buildHeap(); 
} 
  
// Min Heapify function, that assumes 
// 2*i+1 and 2*i+2 are min heap and  
// fix min heap property for i 
  
void MinHeap::heapify(int i) 
{ 
    // If Leaf Node, Simply return 
    if (i >= size / 2) 
        return; 
  
    // variable to store the smallest element 
    // index out of i, 2*i+1 and 2*i+2 
    int smallest; 
  
    // Index of left node 
    int left = 2 * i + 1; 
  
    // Index of right node 
    int right = 2 * i + 2; 
  
    // Select minimum from left node and  
    // current node i, and store the minimum 
    // index in smallest variable 
    smallest = arr[left] < arr[i] ? left : i; 
  
    // If right child exist, compare and 
    // update the smallest variable 
    if (right < size) 
        smallest = arr[right] < arr[smallest] 
                             ? right : smallest; 
  
    // If Node i violates the min heap  
    // property, swap  current node i with 
    // smallest to fix the min-heap property  
    // and recursively call heapify for node smallest. 
    if (smallest != i) { 
        swap(arr[i], arr[smallest]); 
        heapify(smallest); 
    } 
} 
  
// Build Min Heap 
void MinHeap::buildHeap() 
{ 
    // Calling Heapify for all non leaf nodes 
    for (int i = size / 2 - 1; i >= 0; i--) { 
        heapify(i); 
    } 
} 
  
void FirstKelements(int arr[],int size,int k){ 
    // Creating Min Heap for given 
    // array with only k elements 
    MinHeap* m = new MinHeap(k, arr); 
  
    // Loop For each element in array 
    // after the kth element 
    for (int i = k; i < size; i++) { 
  
        // if current element is smaller  
        // than minimum element, do nothing  
        // and continue to next element 
        if (arr[0] > arr[i]) 
            continue; 
  
        // Otherwise Change minimum element to  
        // current element, and call heapify to 
        // restore the heap property 
        else { 
            arr[0] = arr[i]; 
            m->heapify(0); 
        } 
    } 
    // Now min heap contains k maximum 
    // elements, Iterate and print 
    for (int i = 0; i < k; i++) { 
        cout << arr[i] << " "; 
    } 
} 
// Driver Program 
int main() 
{ 
  
    int arr[] = { 11, 3, 2, 1, 15, 5, 4, 
                           45, 88, 96, 50, 45 }; 
  
    int size = sizeof(arr) / sizeof(arr[0]); 
  
    // Size of Min Heap 
    int k = 3; 
  
    FirstKelements(arr,size,k); 
  
    return 0; 
} 
// This code is contributed by Ankur Goel 

Output:

50 88 96

Please write comments if you find any of the above explanations/algorithms incorrect, or find better ways to solve the same problem.

References:
http://en.wikipedia.org/wiki/Selection_algorithm

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