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<limits.h>
#include<stdlib.h>
void maxHeapify(int *,int);
void buildMaxHeap(int *);
void heapExtractMax(int *);
void maxHeapInsert(int *,int);
void heapIncreaseKey(int *,int,int);
int H;
int main(){
  int *A;
  A=(int *)malloc(sizeof(int)*2000001);
  int i,j,x;
  char str[20];
  while(1){
    scanf("%s",str);
   
    if(str[2]=='s'){
      scanf("%d",&x);
      maxHeapInsert(A,x);
    }
    else if(str[2]=='t'){
      heapExtractMax(A);
    }
    else if(str[2]=='d')
      break;
  }

  return 0;
}
void maxHeapify(int A[],int i){
  int l,r,largest,hoge;
  l=i*2;
  r=i*2+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){
 
    hoge=A[i];
    A[i]=A[largest];
    A[largest]=hoge;
    maxHeapify(A,largest);
  }
    
  
  
}
void buildMaxHeap(int A[]){
  int i;
  for(i=H/2;i>0;i--)
    maxHeapify(A,i);

}
void heapExtractMax(int A[]){
  int max;
  if(H<1){printf("heap underflow\n"); return;}
  max = A[1];
  A[1]=A[H];
  H--;
  maxHeapify(A,1);
  printf("%d\n",max);
    

}
void maxHeapInsert(int A[],int key){
  H++;
  A[H]=INT_MIN;

  heapIncreaseKey(A,H,key);

}
void heapIncreaseKey(int A[],int i,int key){
  int p,hoge;

  if (key<A[i]){
    printf("new key is smaller than current key\n");
  return;
  }
  A[i]=key;
  p=i/2;
  while(i>1&&A[p]<A[i]){
    hoge=A[i];
    A[i]=A[p];
    A[p]=hoge;
    i=p;
    p/=2;
  }


}