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: Time Limit Exceeded)

#include <stdio.h>

#define N 2000001
#define SENTINEL -1

int count = 0;
int A[N];

int parent(int i){
  return i / 2;
}

int left(int i){
  return 2 * i;
}

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

void maxHeapify(int A[], int i){
  int l, r, largest, buf;
  
  l = left(i);
  r = right(i);
  
  if(l <= count && A[l] > A[i]) largest = l;
  else largest = i;
  
  if(r <= count && A[r] > A[largest]) largest = r;
  
  if(largest != i){
    buf = A[i];
    A[i] = A[largest];
    A[largest] = buf;
    maxHeapify(A, largest);
  }
}

void heapIncreaseKey(int A[], int i, int key){
  int buf;
  
  if(key < A[i]) return;  
  
  A[i] = key;
  while(i > 1 && A[parent(i)] < A[i]){
    buf = A[i];
    A[i] = A[count / 2];
    A[count / 2] = buf;
    i = count / 2;    
  }
}

void maxHeapInsert(int A[], int key){
  count++;
  
  A[count] = SENTINEL;
  
  heapIncreaseKey(A, count, key);
}

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

int main(){
  int key;
  char c[7];
  
  for(;;){
    scanf("%s", c);
    if(c[0] == 'i'){
      scanf("%d", &key);
      maxHeapInsert(A, key);
    }
    else if(c[0] == 'e' && c[1] == 'x'){
      printf("%d\n",heapExtractMax(A));
    }
    else break;
  }
  return 0;
}