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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

#define MAX 20000003

int A[MAX];
int heap_size=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,r,largest;
  int temp;
  
  l = Left(i);
  r = Right(i);
  
  
  if((l <= heap_size) && (A[l] > A[i])){
    largest = l;
  }
  else {
    largest = i;
  }
  
  if((r <= heap_size) && (A[r] > A[largest])){
    largest = r;
  } 
  
  if(largest != i){
    temp = A[i];
    A[i] = A[largest];
    A[largest] = temp;
    
    maxHeapify(largest);
  } 
}

int heapExtractMax(void){
  int max,j;
  if(heap_size < 1){
    return -20;
  }
  max = A[1];
  A[1] = A[heap_size];
  heap_size = heap_size-1;

  maxHeapify(1);
  
  return max;
}

void heapIncreaseKey(int i,int key){
  int temp;
  if(key < A[i]){
    printf("error\n");
    exit(1);
  }
  
  A[i] = key;
  
  while((i > 1) && (A[Parent(i)] < A[i])){
    temp = A[i];
    A[i] = A[Parent(i)];
    A[Parent(i)] = temp;

    i = Parent(i);
  }
}

void maxHeapInsert(int key){
  heap_size = heap_size+1;
  A[heap_size] = -1000000000;
  heapIncreaseKey(heap_size,key);
}

int main(void){
  int i=1,j=0,max,a;
  char com[20];
  
  while(1){
    scanf("%s",com);  
    if(com[0] == 'i'){
      scanf("%d",&a);
      maxHeapInsert(a);
  
      heap_size++;
    }
    
    else if(com[0] == 'e' && com[1] == 'x'){
      max = heapExtractMax();
      if(max == -20){
	exit(0);
      }
      printf("%d\n",max);
    }
    else {
      break;
    }
  }
  
  return 0;
}