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>
#include<string.h>
#define N 2000000
#define INF -1

int parent(int);
int left(int);
int right(int);
void Insert(int);
int ExtraMax(void);
void Maxheap(int);
void Increasekey(int,int);

int H=0,S[N];

int main(){
  int key;
  char ch[20];
  while(1){
    scanf("%s",ch);
    if(ch[0]=='i'){
      scanf("%d",&key);
      Insert(key);
    }
    else if(ch[0]=='e' && ch[1]=='x'){
      printf("%d\n",ExtraMax());
    }
    else
      break;
  }
  return 0;
}
int parent(int i){
  return i/2;
}
int left(int i){
  return 2*i;
}
int right(int i){
  return 2*i+1;
}
void Insert(int key){
  H++;
  S[H]=INF;
  Increasekey(H,key);
}
int ExtraMax(){
  int max;
  max=S[1];
  S[1]=S[H];
  H--;
  Maxheap(1);
  return max;
}
void Maxheap(int i){
  int l,r,large,tmp;
  l=left(i);
  r=right(i);
  if(l<=H && S[l]>S[i])
    large=l;
  else large=i;
  if(r<=H && S[r]>S[large])
    large=r;

  if(large!=i){
    tmp=S[i];
    S[i]=S[large];
    S[large]=tmp;
    Maxheap(large);
  }
}
void Increasekey(int i,int key){
  int tmp;
  S[i]=key;
  while(i>1 && S[parent(i)]<S[i]){
    tmp=S[parent(i)];
    S[parent(i)]=S[i];
    S[i]=tmp;
    i=parent(i);
  }
}