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  N 2000000
#define INF -2100000000

int h,a[N+1];

void maxHeapify(int);
int extract(void);
void increasekey(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 maxHeapify(int i){
  int l,r,largest,temp;
  
  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){
    temp = a[i];
    a[i] = a[largest];
    a[largest] = temp;
    maxHeapify(largest);
  }
}

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

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

void insert(int key){
  h++;
  a[h] = INF;
  increasekey(h, key);
}