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 <string.h>

#define H 2000000

int  parent(int);
int  left(int);
int  right(int);
void maxHeapify(int);
int  heapExtractMax(void);
void maxHeapInsert(int);
void heapIncreaseKey(int,int);

int n=0;
int A[H];

int main(){

 int i;
 int key;
 char str[8];

 while(1){
 scanf("%s",str);
 if( strcmp(str,"end")==0 ) break;

 if( strcmp(str,"insert")==0 ){
 scanf("%d",&key); 
 maxHeapInsert(key);
 }

 if( strcmp(str,"extract")==0 ){
 printf("%d\n",heapExtractMax());
 }
}

 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 i){

  int l;
  int r;
  int tmp;
  int largest;

  l = left(i);
  r = right(i);

  if(l<=n && A[l]>A[i]){
    largest = l;
  }

  else{
    largest = i;
  }

  if(r<=n && A[r]>A[largest]){
    largest = r;
  }

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

int heapExtractMax(void){

  int max;

  if(n < 1){
    fprintf(stderr,"heap underflow\n");
    exit(1);
  }

  max = A[1];
  A[1] = A[n];
  n--;
  maxHeapify(1);
  return max;
}

void maxHeapInsert(int key){
  n = n + 1;
  A[n] = -1;
  heapIncreaseKey(n,key);
}

void heapIncreaseKey(int i, int key){

  int tmp;
  
  if(key < A[i]){
    fprintf(stderr,"new key is smaller than current key\n");
    exit(1);
  }
  A[i] = key;
  while(i>1 && A[parent(i)] < A[i]){
    tmp = A[i];
    A[i] = A[parent(i)];
    A[parent(i)] = tmp;
    i = parent(i);
  }
}