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: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<limits.h>
#define MAX 500001

int size;
void  heapIncreaceKey();

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 id){
  int l = Left(id);
  int r = Right(id);
  int largest,temp;

  if(l<=size && A[l]>A[id]) largest = l;
  else largest = id;

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

  if(largest!=id){
    temp = A[id];
    A[id] = A[largest];
    A[largest] = temp;
    maxHeapify(A,largest);
  }
}

void builtMaxHeap(int A[]){
  int i;
  for(i=size/2 ; i>0 ; i--){
    maxHeapify(A,i);
  }
}

void maxHeapInsert(int A[],int key){
  size = size+1;
  A[size] = INT_MIN;
  heapIncreaceKey(A,size,key);
}

void heapIncreaceKey(int A[],int i,int key){
  int temp;
  if(key < A[i]) 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);
  }
}

int heapExtractMax(int A[]){
  int max;

  if(size<1) return printf("heap underflow\n");

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


main(){
  int heap[MAX],key;
  char com[10];

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