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<limits.h>

int H,A[2000000];

void maxH(int);
int extract(void);
void increaseK(int,int);
void insert(int);

int main(){
	int key;
	char C[10];
	while(1){
		scanf("%s",&C);
		if(C[0]=='e' && C[1]=='n')break;
		if(C[0]=='i'){
			scanf("%d",&key);
			insert(key);
		}
		else{
			printf("%d\n",extract());
		}
	}
	return 0;
}

void maxH(int i){
  int l,r,a,largest;
  l=2*i;
  r=2*i+1;
  if(l<=H && A[l]>A[i])largest=l;
  else largest=i;
  if(r<=H && A[r]>A[largest])largest=r;
  if(largest!=i){
    a=A[largest];
    A[largest]=A[i];
    A[i]=a;
    maxH(largest);
  }
}

int extract(void){
	int max;
	if(H<1)return -INT_MAX;
	max=A[1];
	A[1]=A[H--];
	maxH(1);
	return max;
}

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

void insert(int key){
	H++;
	A[H]=-INT_MAX;
	increaseK(H,key);
}