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 C (judge verdict: Accepted)

#include<stdio.h>

#define MAX 2000000

int size, a[MAX+1];

void maxHeapify(int i){

  int l,r,large,t;
  
  l = 2*i;

  r = 2*i+1;

  if((l <= size) && (a[l] > a[i])){
    large = l;
  }
  
  else{
    large = i;
  }
  
  if((r <= size) && (a[r] > a[large])){
    large = r;
  }
  
  if(large != i){
    t = a[i];
    a[i] = a[large];
    a[large] = t;
    
    maxHeapify(large);
    
  }
  
}

int extract(){

  int maxv;

  if(size < 1){
    return;
  }
  
  maxv = a[1];
  
  a[1] = a[size--];
  
  maxHeapify(1);

  return maxv;

}

void increaseKey(int i, int key){

  int x;

  if(key < a[i]){
    return;
  }
  
  a[i] = key;
  
  while((i > 1) && (a[i/2] < a[i])){

    x = a[i];
    a[i] = a[i/2];
    a[i/2] = x;
    
    i = i/2;

  }
}

void insert(int key){

  size++;
  a[size] = -1000000001;

  increaseKey(size,key);
  
}

int main(){

  int key;
  char c[20];

  while(1){

    scanf("%s",c);
    if(c[0] == 'i'){

      scanf("%d",&key);
      

      insert(key);
    }

    else if(strcmp(c,"extract") == 0){
      printf("%d\n",extract());
    }

    else{
      break;
    }
    
  }

  return 0;

}