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 N 2000000

int H=0,T[N];
void BuildMaxHeap(int*);
void MaxHeapify(int* , int );
void swap(int * ,int ,int);
void insert(int* , int);
int  extract(int*);
void HeapIncreaseKey(int* ,int,int);


int main(){

  int i,n,key;
  char com[20];
  while(1){
  scanf("%s",com);
  if(com[0]=='i'){
    scanf("%d",&key);
    insert(T,key);
  }
  else if(com[1]=='x')
    printf("%d\n",extract(T));
  else break;
  }
  
  return 0;
}

void MaxHeapify( int* T,int i){
  int l,r,largest,tmp;

  l=2*i;
  r=2*i+1;

  if(l<=H && T[i]<T[l])largest=l;
  else largest=i;

  if(r<=H && T[largest]<T[r])largest=r;

  if(largest!=i){
    swap(T,i,largest);
    MaxHeapify(T,largest);
  }
  
  
}

void BuildMaxHeap(int* T){
  int i;
  for(i=H/2;i>=1;i--)
    MaxHeapify(T,i);
 
}

void swap(int* T,int i, int j){

  int tmp;

  tmp=T[i];
  T[i]=T[j];
  T[j]=tmp;
}

void insert(int* T,int key){
  H++;
  T[H]=-1;
  HeapIncreaseKey(T,H,key);
}

void  HeapIncreaseKey(int* T, int i,int key ){
  if(key<T[i]){
    fprintf(stderr,"new key id smaller than current key");
    return ;
  }

  T[i]=key;

  while(i>1 && T[i/2]<T[i]){
    swap(T,i/2,i);
    i=i/2;
  }
}

int extract(int* T){
  int max;

  if(H<1){
    fprintf(stderr,"heap underflow");
    return 0;
  }

  max=T[1];
  T[1]=T[H];
  H--;
  MaxHeapify(T,1);

  return max;
}