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<stdlib.h>
#define INF 100000000;
int heapExtractMax();
void maxHeapify(int);
void buildMaxHeap();
void heapIncreaseKey(int,int);
void maxHeapInsert(int);
int length=1;
int A[2000001];

int main(){
  char order[8];
  int data,i=1;
  while(order[0]!='e'||order[1]!='n'){
    scanf("%s",order);
    
    if(order[0]=='i'){
      
      scanf("%d",&data);
      maxHeapInsert(data);
      
      
    }
    else if(order[0]=='e'&&order[1]=='x')printf("%d\n",heapExtractMax());
    
  }



  return 0;
}

void maxHeapify(int i){
  int l,r,largest,a;
  l=i*2;
  r=i*2+1;

  if(l<=length && A[l]>A[i]) largest=l;
  else largest=i;

  if(r<=length && A[r]>A[largest]) largest=r;

  if(largest!=i){
    a=A[i];
    A[i]=A[largest];
    A[largest]=a;
    maxHeapify(largest);
  } 

}

int heapExtractMax(){
  int max;
  if(length<1){ return -INF;
      }
  max=A[1];
 
  A[1]=A[length];
  length--;
  maxHeapify(1);

  return max;
}
void maxHeapInsert(int key){

  length++;
  A[length]=-INF;
  heapIncreaseKey(length,key);

}

void heapIncreaseKey(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;
  }
  
}