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 NUM 2000000
void insert(int);
int extract();
void maxHeapify(int);
void heapIncreaseKey(int,int);

int a[NUM],heapsize=0;

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

void insert(int n){
  heapsize++;
  a[heapsize]=-1;
  heapIncreaseKey(heapsize,n);
}

int extract(){
  int max;
  if(heapsize<1){
    return -1;
  }
  max=a[1];
  a[1]=a[heapsize];
  heapsize--;
  maxHeapify(1);
  return max;
}

void maxHeapify(int i){
  int l,r,largest,a1;
  l=2*i;
  r=2*i+1;
  if(l<=heapsize&&a[l]>a[i]){
    largest=l;
  }else{
    largest=i;
  }
  if(r<=heapsize&&a[r]>a[largest]){
    largest=r;
  }
  if(largest!=i){
    a1=a[i];
    a[i]=a[largest];
    a[largest]=a1;
    maxHeapify(largest);
  }
}

void heapIncreaseKey(int i,int n){
  int a1;
  if(n<a[i]){
    return;
  }
  a[i]=n;
  while(i>1&&a[i/2]<a[i]){
    a1=a[i];
    a[i]=a[i/2];
    a[i/2]=a1;
    i=i/2;
  }
}