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 all 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.
C++
// C++ implementation of above implementation #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; } |
Java
// Java program of above implementation import java.util.Random; public class GFG { // This function returns k'th smallest element in arr[l..r] using // QuickSort based method. ASSUMPTION: ALL ELEMENTS IN ARR[] ARE DISTINCT static 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 Integer.MAX_VALUE; } static void swap(int[] arr, int i, int j) { int temp = arr[i]; arr[i] = arr[j]; arr[j] = 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 static 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, j); i++; } } swap(arr, i, r); return i; } static int randomPartition(int arr[], int l, int r) { int n = r - l + 1; int pivot = new Random().nextInt(1); swap(arr, l + pivot, r); return partition(arr, l, r); } // Driver program to test above methods public static void main(String args[]) { int arr[] = {12, 3, 5, 7, 4, 19, 26}; int n = arr.length, k = 3; System.out.println("K'th smallest element is " + kthSmallest(arr, 0, n - 1, k)); } } /*This code is contributed by 29AjayKumar*/ |
Python3
# Python3 implementation of above implementation # This function returns k'th smallest element # in arr[l..r] using QuickSort based method. # ASSUMPTION: ALL ELEMENTS IN ARR[] ARE DISTINCT from random import randint def randomPartition(arr, l, r): n = r - l + 1 pivot = randint(1, 100) % n arr[l + pivot], arr[r] = arr[l + pivot], arr[r] return partition(arr, l, r) def kthSmallest(arr, l, r, k): # If k is smaller than # number of elements in array if (k > 0 and k <= r - l + 1): # Partition the array around last element and # get position of pivot element in sorted array pos = randomPartition(arr, l, r) # If position is same as k if (pos - l == k - 1): return arr[pos] # If position is more, recur for left subarray if (pos - l > k - 1): 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 10**9 # 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 def partition(arr, l, r): x = arr[r] i = l for j in range(l, r): if (arr[j] <= x): arr[i], arr[j] = arr[j], arr[i] i += 1 arr[i], arr[r] = arr[r], arr[i] return i # Driver Code arr = [12, 3, 5, 7, 4, 19, 26] n = len(arr) k = 3print("K'th smallest element is", kthSmallest(arr, 0, n - 1, k)) # This code is contributed by Mohit Kumar |
C#
// C# program of above implementation using System; class GFG { // This function returns k'th smallest // element in arr[l..r] using // QuickSort based method. ASSUMPTION: // ALL ELEMENTS IN ARR[] ARE DISTINCT static 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 position is more, recur // for left subarray if (pos - l > k - 1) { 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.MaxValue; } static void swap(int[] arr, int i, int j) { int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; } // Standard partition process of QuickSort(). // It considers the last element as pivot and // oves all smaller element to left of it // and greater elements to right static 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, j); i++; } } swap(arr, i, r); return i; } static int randomPartition(int []arr, int l, int r) { int n = r - l + 1; int pivot = new Random().Next(1); swap(arr, l + pivot, r); return partition(arr, l, r); } // Driver Code public static void Main() { int []arr = {12, 3, 5, 7, 4, 19, 26}; int n = arr.Length, k = 3; Console.WriteLine("K'th smallest element is " + kthSmallest(arr, 0, n - 1, k)); } } // his code is contributed by 29AjayKumar |
Output:
K'th smallest element is 5
References:
https://www.geeksforgeeks.org/kth-smallestlargest-element-unsorted-array/
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