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: Time Limit Exceeded)

#include <stdio.h>
#include <string.h>
 
void insert(int);
int hpEM(void);
void hpIK(int); 
void maxHp(int i);
int parentNode(int i); 
int A[2000001];
int heap_size;
 
int main(){
 
  int i, key;
  char com[8];
 
  while(scanf("%s",com), strcmp(com,"end")){
    if(com[0]=='i'){
      scanf("%d",&key);
      insert(key);
    }
    if(com[0]=='e'){
      printf("%d\n",hpEM());
    }
  }
 
  return 0;
 
}
 
void insert(int key){
 
  heap_size++;
  A[heap_size] = -1;
  hpIK(key);
 
}
 
void hpIK(int key){
 
  int i = heap_size, tmp;
 
  if(key < A[i]){
    printf("Error ???°?????????????????????¨?????????????????°???????");
    return;
  }
  A[i] = key;
  while(i > 1 && A[parentNode(i)] < A[i]){
    tmp = A[parentNode(i)];
    A[parentNode(i)] = A[i];
    A[i] = tmp;
    i = parentNode(i);
  }
 
}
 
int hpEM(void){
 
  int max;
  if(heap_size < 1){
    printf("Error ????????????¢??????????????????");
    return;
  }
  max = A[1];
  A[1] = A[heap_size];
  heap_size--;
  maxHp(1);
  return max;
 
}
  
void maxHp(int i){
    int l = i/2;
    int r = 2*i+1;
    int largest, tmp;
      
    if(l <= heap_size && A[l] > A[i]){
        largest = l;    
    }else{
        largest = i;
    }
    if(r <= heap_size && A[r] > A[largest]){
        largest = r;    
    }
    if(largest != i){
        tmp = A[i];
        A[i] = A[largest];
        A[largest] = tmp;
        maxHp(largest);
    }
}
 
int parentNode(int i){
    return (int)i/2;
}