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

int A[N+1], 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 i){

  int l, r, largest, temp;

  l = left(i);
  r = right(i);
  if(l <= n && A[l] > A[i]) largest = l;
  else largest = i;
  if(r <= n && A[r] > A[largest]) largest = r;

  if(largest != i){
    temp = A[i];
    A[i] = A[largest];
    A[largest] = temp;
    maxHeapify(largest);
  }
  
}

int heapExtractMax(){

  int max;
  
  if(n < 1) printf("heap underflow\n");
  max = A[1];
  A[1] = A[n];
  n--;
  maxHeapify(1);
  return max;
}

void heapIncreaseKey(int i, int key){

  int temp;

  if(key < A[i]) printf("new key is smaller than current key\n");
  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);
  }
}

void maxHeapInsert(int key){

  n++;
  A[n] = -1;
  heapIncreaseKey(n, key);
}

int main(){

  int key;
  char str[8];

  while(1){
    scanf("%s", str);
    if(str[0] == 'e' && str[1] == 'n') break;
    if(str[0] == 'i'){
      scanf("%d", &key);
      maxHeapInsert(key);
    } else {
      printf("%d\n", heapExtractMax());
    }
  }
  
  return 0;
}