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_H 2000001
#define INF (-100)

int parent(int );
int left(int );
int right(int );
void maxHeapify(int *,int);
void insert(int,int *);
void increaseK(int *,int ,int);
int extract(int *);

int H=0;

int main(){
  int A[MAX_H];
  int i=0;
  char word[7];
  int k;
  int max=0;

  while(1){
    scanf("%s",word);
    if(word[0]=='e' && word[1]=='n') break;
    if(word[0]=='i'){
      scanf("%d",&k);
      insert(k,A);
    }
    else if(word[0]=='e'){
      max=extract(A);
      printf("%d\n",max);
    }
  }

 return 0;
}

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 *A,int i){
  int l=0;
  int r=0;
  int largest=0;
  int swap=0;
  l=left(i);
  r=right(i);

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

  if( (r<=H) && (A[r]>A[largest]) ) largest=r;

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

}

void insert(int key,int *A){
   H++;
  A[H]=INF;
  increaseK(A,H,key);
}

void increaseK(int *A,int i,int key){
  if(key<A[i]) return;
  int change=0;
  A[i]=key;
  while(i>1 && A[parent(i)] < A[i]){
    change=A[i];
    A[i]=A[parent(i)];
    A[parent(i)]=change;
    i=parent(i);
  }
}
int extract(int *A){
  int max=0;
  if(H<1) return INF;
  max=A[1];
  A[1]=A[H];
  H--;
  maxHeapify(A,1);

  return max;
}