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>

void maxHeapify(int *,int);
void heapIncreaseKey(int *,int,int);

int H=0;

int parent(int i){
  return i/2;
}
int left(int i){
  return 2*i;
}
int right(int i){
  return 2*i+1;
}


int main(){
  int i;
  int *A;
  int key;
  char order[7];


  A=(int *)malloc(sizeof(int)*10000000);
  while(1){
    scanf("%s",order);
    if(order[0]=='i'){
      H++;
      scanf("%d",&key);
      heapIncreaseKey(A,H,key);
    }
    else if(order[1]=='x'){
      printf("%d\n",A[1]);
      A[1]=A[H];
      H--;
      maxHeapify(A,1);
    }
    else break;
    
  }
  
return 0;
}
void maxHeapify(int *A,int i){
  int l;
  int r;
  int largest;
  int temp;
  l=left(i);
  r=right(i);
  if(l<=H&&A[l]>A[i]) largest=l;
  else largest=i;
  
  if(r<=H&&A[r]>A[largest]) largest=r;

  if(largest!=i){
    temp=A[i];
    A[i]=A[largest];
    A[largest]=temp;
    maxHeapify(A,largest);
  }
  return;
}
    
void heapIncreaseKey(int *A,int i,int key){
  int temp;
  A[i]=key;
  while(i>1&&A[parent(i)]<A[i]){
    temp=A[i];
    A[i]=A[parent(i)];
    A[parent(i)]=temp;
    i=parent(i);
  }
}