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 2000010

int Tree[MAX]; // Tree

int n;

void maxHeapify(int i){
  int largest, exchange, gl, gr;
  gl = getLeft(i);
  gr = getRight(i);
  
  if((n >= gl) && (Tree[gl] > Tree[i])) largest = gl;

  else largest = i;
  
  if((n >= gr) && (Tree[gr] > Tree[largest])) largest = gr;

  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");
  
  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;
}