Problem:
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Priority Queue

A priority queue is a data structure which maintains a set $S$ of elements, each of with an associated value (key), and supports the following operations:

$insert(S, k)$: insert an element $k$ into the set $S$

$extractMax(S)$: remove and return the element of $S$ with the largest key

Write a program which performs the $insert(S, k)$ and $extractMax(S)$ operations to a priority queue $S$.
The priority queue manages a set of integers, which are also keys for the priority.

Input

Multiple operations to the priority queue $S$ are given. Each operation is given by "insert $k$", "extract" or "end" in a line. Here, $k$ represents an integer element to be inserted to the priority queue.

The input ends with "end" operation.

Output

For each "extract" operation, print the element extracted from the priority queue $S$ in a line.

Constraints

The number of operations $\leq 2,000,000$

$0 \leq k \leq 2,000,000,000$

Sample Input 1

insert 8
insert 2
extract
insert 10
extract
insert 11
extract
extract
end

Sample Output 1

8
10
11
2

Solution in JAVA (judge verdict: Accepted)

import java.util.*;
import java.io.*;

class Main{
  static int A[] = new int[2000000];
  static int H = 0;
  public static void main(String args[])throws Exception{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    String [] s = new String[2];
    while(true){
      s = br.readLine().split("\\s+");
      if(s[0].charAt(0) == 'i'){
        insert(Integer.parseInt(s[1]));
      }else if(s[0].charAt(1) == 'x'){
        System.out.println(heapExtractMax(A));
      }else{
        break;
      }
    }
  }

  static void insert(int key){
    H++;
    A[H] = (int)Double.NEGATIVE_INFINITY;
    heapIncreaseKey(A, H, key);
  }

  static void heapIncreaseKey(int A[], int i, int key){
    int tmp = 0;
    if(key<A[i]){
      return;
    }
    A[i] = key;
    while(i >1 && A[parent(i)]< A[i]){
      tmp = A[i];
      A[i] = A[parent(i)];
      A[parent(i)] = tmp;
      i = parent(i);
    }
  }

  static int heapExtractMax(int A[]){
    if(H<1){
      System.out.println("under flow");
      return (int)Double.NEGATIVE_INFINITY;
    }
    int max = A[1];
    A[1] = A[H--];
    maxHeapify(A, 1);

    return max;
  }

  static void maxHeapify(int A[], int i ){
    int l =i*2;
    int r = i*2+1;
    int largest = 0;
    int tmp;

    if(l<=H && A[l] > A[i]) largest = l;
    else largest = i;

    if(r<=H && A[r] > A[largest] ) largest = r;

    if(largest != i){
      tmp = A[i];
      A[i] = A[largest];
      A[largest] = tmp;
      maxHeapify(A, largest);
    }
  }
  static int parent(int i){
    return i/2;
  }

}