给定一个由N 个整数和一个整数K组成的数组arr[] ,任务是使用 Priority Queue 找到数组中的第K个最小元素。
例子:
Input: arr[] = {5, 20, 10, 7, 1}, N = 5, K = 2
Output: 5
Explanation: In the given array, the 2nd smallest element is 5. Therefore, the required output is 5.
Input: arr[] = {5, 20, 10, 7, 1}, N = 5, K = 5
Output: 20
Explanation: In the given array, the 5th smallest element is 20. Therefore, the required output is 20.
做法:思路是利用Java的PriorityQueue Collection或者priority_queue STL库来实现Max_Heap ,找到第K个最小的数组元素。请按照以下步骤解决问题:
- 使用 priority_queue 实现最大堆。
- 将前K 个数组元素推入priority_queue 。
- 从那以后,每次插入数组元素后,弹出priority_queue 顶部的元素。
- 完成数组遍历后,打印优先级队列顶部的元素作为所需答案。
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
using namespace std;
// Function to find kth smallest array element
void kthSmallest(vector& v, int N, int K)
{
// Implement Max Heap using
// a Priority Queue
priority_queue heap1;
for (int i = 0; i < N; ++i) {
// Insert elements into
// the priority queue
heap1.push(v[i]);
// If size of the priority
// queue exceeds k
if (heap1.size() > K) {
heap1.pop();
}
}
// Print the k-th smallest element
cout << heap1.top() << endl;
}
// Driver code
int main()
{
// Given array
vector vec = { 5, 20, 10, 7, 1 };
// Size of array
int N = vec.size();
// Given K
int K = 2;
// Function Call
kthSmallest(vec, N, K % N);
return 0;
}
Java
// Java program for the above approach
import java.util.*;
class CustomComparator implements Comparator {
@Override
public int compare(Integer number1, Integer number2) {
int value = number1.compareTo(number2);
// elements are sorted in reverse order
if (value > 0) {
return -1;
}
else if (value < 0) {
return 1;
}
else {
return 0;
}
}
}
class GFG{
// Function to find kth smallest array element
static void kthSmallest(int []v, int N, int K)
{
// Implement Max Heap using
// a Priority Queue
PriorityQueue heap1 = new PriorityQueue(new CustomComparator());
for (int i = 0; i < N; ++i) {
// Insert elements into
// the priority queue
heap1.add(v[i]);
// If size of the priority
// queue exceeds k
if (heap1.size() > K) {
heap1.remove();
}
}
// Print the k-th smallest element
System.out.print(heap1.peek() +"\n");
}
// Driver code
public static void main(String[] args)
{
// Given array
int []vec = { 5, 20, 10, 7, 1 };
// Size of array
int N = vec.length;
// Given K
int K = 2;
// Function Call
kthSmallest(vec, N, K % N);
}
}
// This code is contributed by Amit Katiyar
Python3
# Python3 program for the above approach
# Function to find kth smallest array element
def kthSmallest(v, N, K):
# Implement Max Heap using
# a Priority Queue
heap1 = []
for i in range(N):
# Insert elements into
# the priority queue
heap1.append(v[i])
# If size of the priority
# queue exceeds k
if (len(heap1) > K):
heap1.sort()
heap1.reverse()
del heap1[0]
# Print the k-th smallest element
heap1.sort()
heap1.reverse()
print(heap1[0])
# Driver code
# Given array
vec = [ 5, 20, 10, 7, 1 ]
# Size of array
N = len(vec)
# Given K
K = 2
# Function Call
kthSmallest(vec, N, K % N)
# This code is contributed by divyeshrabadiya07
C#
// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG
{
// Function to find kth smallest array element
static void kthSmallest(int []v, int N, int K)
{
// Implement Max Heap using
// a Priority Queue
List heap1 = new List();
for (int i = 0; i < N; ++i) {
// Insert elements into
// the priority queue
heap1.Add(v[i]);
// If size of the priority
// queue exceeds k
if (heap1.Count > K) {
heap1.Sort();
heap1.Reverse();
heap1.RemoveAt(0);
}
}
heap1.Sort();
heap1.Reverse();
// Print the k-th smallest element
Console.WriteLine(heap1[0]);
}
// Driver code
public static void Main(String[] args)
{
// Given array
int []vec = { 5, 20, 10, 7, 1 };
// Size of array
int N = vec.Length;
// Given K
int K = 2;
// Function Call
kthSmallest(vec, N, K % N);
}
}
// This code is contributed by gauravrajput1
Javascript
输出:
5
时间复杂度: O(N LogK)
辅助空间: O(K),因为优先级队列随时保持在最大 k 个元素上。
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