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 INFTY (1<<30)

int i, H, A[2000000];

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

void maxHeapify(int *A, int i){
  int largest, tmp;
  int 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){
    tmp = A[i];
    A[i] = A[largest];
    A[largest] = tmp;
    maxHeapify(A, largest);
  }
}

int extract(){
  int maxv;
  if(H<1)return -INFTY;
  maxv=A[1];
  A[1]=A[H--];
  maxHeapify(A,1);
  return maxv;
}

void increaseKey(int i, int key){
  int tmp;
  if(key<A[i])return;
  A[i]=key;
  while(1){
    if(i<=1 || A[i/2]>=A[i])break;
    tmp=A[i];
    A[i]=A[i/2];
    A[i/2]=tmp;
    i=i/2;
  }
}

void insert(int key){
  A[++H]=-INFTY;
  increaseKey(H, key);
}



int main(){
  int key;
  char C[8];
  
  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;
}