How does one use an priority queue to solve this type of question? In this task, you need to use 2 priority queues to print out the kth largest and jth smallest number in 2new different random vectors, vector3 and vector4. Write a function called intkthLargestPQ(vector& vec, int k), and a function called int jthSmallestPQ(vector& vec,int k).Here is an example:Original vector3: 9 8 9 2 3 7 9 577Input K for Kth largest: 3The largest number: 9Original vector4: 9 6 5 6 7 7 6 16 2Input J for Jth smallest: 3The 3 smallest number: 5Hint:Using priority queue.This problem can be solved in two ways.1.For the kthLargestPQ, we can maintain a small heap (small priority queue, smallest element in thetop) with only k elements in size. After traversing all the elements, the top element in the PQ is what wewant.The jthSmallestPQ vice versa.2. To get the kth largest element, you can construct a large priority queue using all the elements, popthe top element k-1 times, then the top element is what we want. To get the jth smallest element, you 2. To get the kth largest element, you can construct a large priority queue using all the elements, popthe top element k-1 times, then the top element is what we want. To get the jth smallest element, youcan construct a small priority queue using all the elements, pop the top element j-1 times, then the topelement is what we want.

Algorithm:Initialize an empty min-heap.Iterate through the input vector.Push each element onto the min-heap.If the size of the min-heap exceeds k, pop the smallest element.The top element of the min-heap is the kth largest number.Initialize an empty max-heap.Iterate through the input vector.Push each element onto the max-heap.If the size of the max-heap exceeds j, pop the largest element.The top element of the max-heap is the jth smallest number.Read the original vectors and user inputs for k and j.Call kthLargestPQ and jthSmallestPQ functions.Display the results.Source Code: C++ Programming:1#include <iostream> 2#include <vector> 3#include <queue> 4 5using namespace std; 6 7int kthLargestPQ(vector<int>& vec, int k) { 8 priority_queue<int, vector<int>, greater<int>> minHeap; 9 10 for (int num : vec) { 11 minHeap.push(num); 12 if (minHeap.size() > k) { 13 minHeap.pop(); 14 } 15 } 16 17 return minHeap.top(); 18} 19 20int jthSmallestPQ(vector<int>& vec, int j) { 21 priority_queue<int> maxHeap; 22 23 for (int num : vec) { 24 maxHeap.push(num); 25 if (maxHeap.size() > j) { 26 maxHeap.pop(); 27 } 28 } 29 30 return maxHeap.top(); 31} 32 33int main() { 34 vector<int> vector3 = {989, 2, 3, 7, 9, 5, 7, 7}; 35 vector<int> vector4 = {96, 56, 7, 7, 6, 1, 6, 2}; 36 37 int k; 38 cout << "Original vector3: "; 39 for (int num : vector3) { 40 cout << num << " "; 41 } 42 cout << "\nInput K for Kth largest: "; 43 cin >> k; 44 45 int kthLargest = kthLargestPQ(vector3, k); 46 cout << "The " << k << " largest number: " << kthLargest << "\n"; 47 48 int j; 49 cout << "\nOriginal vector4: "; 50 for (int num : vector4) { 51 cout << num << " "; 52 } 53 cout << "\nInput J for Jth smallest: "; 54 cin >> j; 55 56 int jthSmallest = jthSmallestPQ(vector4, j); 57 cout << "The " << j << " smallest number: " << jthSmallest << "\n"; 58 59 return 0; 60}Explanation:The program defines two functions, kthLargestPQ and jthSmallestPQ, which use min-heap and max-heap, respectively, to find the kth largest and jth smallest elements in a vector. The main function reads vectors and user inputs, calls these functions, and outputs the results. The use of priority queues efficiently handles the task of finding the kth largest and jth smallest elements without sorting the entire vector.Output: