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 2000010
#define NIL -2000000001
int k[MAX],size;

int Parent(int i){
  return i/2;
}

int Left(int i){
  return i*2;
}

int Right(int i){
  return i*2+1;
}


int maxHeapify(int i){
  int l,r,largest=NIL,e;
  l=Left(i);
  r=Right(i);
  if(l<=size && k[l]>k[i])
    largest=l;
  else largest=i;
  if(r<=size && k[r]>k[largest])
    largest=r;
  if(largest!=i){
    e=k[i];
  k[i]=k[largest];
  k[largest]=e;
  maxHeapify(largest);
  }
    }

int buildMaxHeap(){
  int i;
  for(i=size/2;i>=1;i--){
    maxHeapify(i);
  }    
}


int maxHeapInsert(int key){
  size=size+1;
  k[size]=NIL;
  heapIncreaseKey(size,key);
}

int heapIncreaseKey(int i, int key){
  int e;
  if(key<k[i]){
    return -1;
}
  k[i]=key;
  while(i>1 && k[Parent(i)]<k[i]){
    e=k[i];
  k[i]=k[Parent(i)];
  k[Parent(i)]=e;
  i=Parent(i);
  }
  
}

int heapExtractMax(){
  int max;
  if(size<1)
    return -1;
  max=k[1];
  k[1]=k[size];
  size=size-1;
  maxHeapify(1);
  return max;
}

main(){
  size=1;
  
  int i,j;
  char a[20];
  for(i=0;i<MAX;i++)
    k[i]=-(1<<29);

  while(1){

    scanf("%s", a);

    if(a[0]=='i')
      {
	scanf("%d",&j);

      maxHeapInsert(j);
      }
    else if(a[0]=='e' && a[1]=='x')
      printf("%d\n", heapExtractMax());
    else break;
  }

  return 0;
 
}