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 2000000

int Tree[MAX];
int n;

void maxHeapify(int i){
  int largest ,exchange, l, r;
  l = getLeft(i);
  r = getRight(i);
  
  if( ( n >= l ) && ( Tree[l] > Tree[i] ) ){
    largest = l;
  }else{
    largest = i;
  }
  if( ( n >= r ) && ( Tree[r] > Tree[largest] ) ){
    largest = r;
  }
  if (largest != i){
    exchange =  Tree[i];
    Tree[i] = Tree[largest];
    Tree[largest] = exchange;
    maxHeapify(largest);
  }  
}

void buildMaxHeap(){
  int i;
  for (i = (n/2); i >= 1; i--){
    maxHeapify(i);
  }
}

void heapIncrease(int i, int key){
  int exchange;
  if(key < Tree[i])printf("new key is smallar than current key\n");
  
  Tree[i] = key;

  while(( i > 1 ) && ( Tree[getParent(i)] <  Tree[i] )){
    exchange = Tree[i];
    Tree[i] = Tree[getParent(i)];
    Tree[getParent(i)] = exchange;
    i = getParent(i);
  }

}
void maxHeapInsert( key ){
  n = n + 1;
  Tree[n] = -2000000;
 heapIncrease(n, key);
}



int heapExtractMax(){
  int max;
  if( n < 1 )return -1;
  max = Tree[1];
  Tree[1] = Tree[n];
  --n;
  maxHeapify(1);
  return max;
}

int getParent( int i ){
  return i/2;
}

int getLeft(int i){
  return (2*i);
}

int getRight(int i){
  return (2*i + 1);
}


main()
{
  int n, i, x;
  char com[20];
  scanf("%d", &n);

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

  return 0;
}