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>
#include <string.h>
#define NIL -20000001
#define MAX 20000001

int S[MAX];
int heapsize = 0;

void heapIncreaseKey(int k){
  int i = heapsize;
  int tmp;
  if(k < S[i])
    printf("error\n");
  S[i] = k;
  while(i > 1 && S[i/2] < S[i]){
    tmp = S[i];
    S[i] = S[i/2];
    S[i/2] = tmp;
    i /= 2;
  }
}

void maxHeapInsert(int k){
  heapsize++;
  S[heapsize] = NIL;
  heapIncreaseKey(k);
}
void maxHeapify(int i){
  int l, r, largest, tmp;
  l = 2*i;
  r = 2*i+1;
  if(l <= heapsize && S[l] > S[i])
    largest = l;
  else
    largest = i;
  if(r <= heapsize && S[r] > S[largest])
    largest = r;

  if(largest != i){
    tmp = S[i];
    S[i] = S[largest];
    S[largest] = tmp;
    maxHeapify(largest);
  }
}


void heapExtractMax(void){
  printf("%d\n", S[1]);
  S[1] = S[heapsize];
  heapsize--;
  maxHeapify(1);
}

int main(void){
  int i, k;
  char order[10];
  int largest = 0;


  for(i = 0 ; i < MAX; i++)
    S[i] = NIL;

  while(1){

    scanf("%s", order);
    if(strcmp(order, "end") == 0)break;

    if(strcmp(order, "insert") == 0){
      scanf("%d", &k);
      maxHeapInsert(k);
    }

    if(strcmp(order, "extract") == 0){
      heapExtractMax();
    }
  }

  return 0;
}