K'th Smallest/Largest Element in Unsorted Array | Set 2 (Expected Linear Time)

We recommend to read following post as a prerequisite of this post.

K’th Smallest/Largest Element in Unsorted Array | Set 1

Given an array and a number k where k is smaller than size of array, we need to find the k’th largest element in the given array. It is given that ll array elements are distinct.

Examples:

Input: arr[] = {7, 10, 4, 3, 20, 15}
       k = 3
Output: 7

Input: arr[] = {7, 10, 4, 3, 20, 15}
       k = 4
Output: 10

We have discussed three different solutions here.

In this post method 4 is discussed which is mainly an extension of method 3 (QuickSelect) discussed in the previous post.

#include<iostream> 
#include<climits> 
#include<cstdlib> 
using namespace std; 
  
int randomPartition(int arr[], int l, int r); 
  
// This function returns k'th smallest element in arr[l..r] using 
// QuickSort based method.  ASSUMPTION: ALL ELEMENTS IN ARR[] ARE DISTINCT 
int kthSmallest(int arr[], int l, int r, int k) 
{ 
    // If k is smaller than number of elements in array 
    if (k > 0 && k <= r - l + 1) 
    { 
        // Partition the array around last element and get 
        // position of pivot element in sorted array 
        int pos = randomPartition(arr, l, r); 
  
        // If position is same as k 
        if (pos-l == k-1) 
            return arr[pos]; 
        if (pos-l > k-1)  // If position is more, recur for left subarray 
            return kthSmallest(arr, l, pos-1, k); 
  
        // Else recur for right subarray 
        return kthSmallest(arr, pos+1, r, k-pos+l-1); 
    } 
  
    // If k is more than number of elements in array 
    return INT_MAX; 
} 
  
void swap(int *a, int *b) 
{ 
    int temp = *a; 
    *a = *b; 
    *b = temp; 
} 
  
// Standard partition process of QuickSort().  It considers the last 
// element as pivot and moves all smaller element to left of it 
// and greater elements to right 
int partition(int arr[], int l, int r) 
{ 
    int x = arr[r], i = l; 
    for (int j = l; j <= r - 1; j++) 
    { 
        if (arr[j] <= x) 
        { 
            swap(&arr[i], &arr[j]); 
            i++; 
        } 
    } 
    swap(&arr[i], &arr[r]); 
    return i; 
} 
  
int randomPartition(int arr[], int l, int r) 
{ 
    int n = r-l+1; 
    int pivot = rand() % n; 
    swap(&arr[l + pivot], &arr[r]); 
    return partition(arr, l, r); 
} 
  
// Driver program to test above methods 
int main() 
{ 
    int arr[] = {12, 3, 5, 7, 4, 19, 26}; 
    int n = sizeof(arr)/sizeof(arr[0]), k = 3; 
    cout << "K'th smallest element is " << kthSmallest(arr, 0, n-1, k); 
    return 0; 
}