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 MAX 2000000000
#define INFTY (1<<30)

void MaxHeapify(int);
void insert(int);
void increaseKey(int, int);
int HeapExtractMax(void);

int H, A[MAX];

int main(){
  int key;
  A[H] = -INFTY;
  char com[10];

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

  return 0;
}


void MaxHeapify(int i){
  int l, r, largest,keep;
  l = 2*i;
  r = 2*i+1;
  if( l <= H && A[l] > A[i] ){
    largest = l;
  }
  else {
    largest = i;
  }
  if( r <= H && A[r] > A[largest] ){
    largest = r;
  }
  if( largest != i){
    keep = A[i];
    A[i] = A[largest];
    A[largest] = keep;
    MaxHeapify(largest);
  }
}

void insert(int key){
  H++;
  A[H] = -INFTY;
  increaseKey(H, key);
}

void increaseKey(int i, int key){
  int c;
  if(key < A[i]) return;
  A[i] = key;
  while (i > 1 && A[i/2] < A[i]) {
    c = A[i/2];
    A[i/2] = A[i];
    A[i] = c;
    i = i/2;
  }
}

int HeapExtractMax(){
  int m;
  if( H < 1 ) return -INFTY;
  m = A[1];
  A[1] = A[H];
  H--;
  MaxHeapify(1);
  return m;
}