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>
#define INF 100000000;

int heapExtractMax();
void maxHeapify(int);
void buildMaxHeap();
void heapIncreaseKey(int, int);
void maxHeapInsert(int);

int length = 1;
int A[2000001];
 
int main()
{
  char order[8];
  int data, i = 1;
  
  while(order[0] != 'e' || order[1] != 'n')
    {
      scanf("%s", order);
     
      if(order[0] == 'i')
	{
	  scanf("%d", &data);
	  maxHeapInsert(data);
	}
      else if(order[0] == 'e' && order[1] == 'x') printf("%d\n", heapExtractMax());
    }
  return 0;
}
 
void maxHeapify(int i)
{
  int l, r, largest, a;
  
  l = i*2;
  r = i*2+1;
 
  if(l <= length && A[l] > A[i]) largest = l;
  else largest = i;
 
  if(r <= length && A[r] > A[largest]) largest = r;
 
  if(largest != i)
    {
      a = A[i];
      A[i] = A[largest];
      A[largest] = a;
      maxHeapify(largest);
    } 
}
 
int heapExtractMax()
{
  int max;
  
  if(length < 1) return -INF;
  
  max = A[1];
  A[1] = A[length];
  length--;
  maxHeapify(1);
 
  return max;
}

void maxHeapInsert(int key)
{ 
  length++;
  A[length] =- INF;
  heapIncreaseKey(length, key);
}
 
void heapIncreaseKey(int i, int key)
{
  int a;
  
  if(key < A[i]) return;
  
  A[i] = key;
  
  while(i > 1 && A[i/2] < A[i])
    {
      a = A[i];
      A[i] = A[i/2];
      A[i/2] = a;
      i = i/2;
    }
}