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 <limits.h>
#include <string.h>

#define MAX 2000001


void maxHeapInsert(int *, int);
void heapIncreasekey(int *, int, int);
int heapExtractMax(int *);
void maxHeapify(int *, int);


int size = 0;


int main(){
  char o[8];
  int A[MAX];
  int c, i;
  int p;

  o[0] = NULL;

  for(i = 0; i < MAX; i++){
    A[i] = -1;
  }

  while(i){
    scanf("%s", o);

    if(o[0] == 'i'){
      scanf("%d", &c);

      maxHeapInsert(A, c);
    }
    else if(o[1] == 'x'){
      p = heapExtractMax(A);
      printf("%d\n", p);
    }
    else break;
    
  }
  
  return 0;
}


void maxHeapInsert(int *A, int key){
  size += 1;
  A[size] = INT_MIN;
  heapIncreasekey(A, size, key);
}


void heapIncreasekey(int *A, int i, int key){
  int temp;
  
  if(key < A[i]) exit(1);

  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;
  }
}


int heapExtractMax(int *A){
  int max;
  
  if(size < 1) exit(2);

  max = A[1];
  A[1] = A[size];

  size--;

  maxHeapify(A, 1);
  return max;
}


void maxHeapify(int *A, int i){
  int largest;
  int temp;
  int r, l;

  l = i*2;
  r = i*2+1;

  if(l <= size && A[l] > A[i]) largest = l;
  else largest = i;

  if(r <= size && A[r] > A[largest]) largest = r;
  
  if(largest != i){
    temp = A[i];
    A[i] = A[largest];
    A[largest] = temp;

    maxHeapify(A, largest);
  }
}