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

void maxHeapify(int);
int extract(void);
void increaseKey(int ,int);
void insert(int);

int size, A[MAX];

int main(){

  int key;
  char com[20];

  while(1){
    scanf("%s", com);
    if ( com[0] == 'i' ){
      scanf("%d", &key);
      insert(key);
    }
    else if ( strcmp(com, "extract") == 0  ){
      printf("%d\n", extract());
    }
    else break;
  }
  
  return 0;
}

void maxHeapify(int i){
  
  int l, r, largest, t;

  l = 2*i;

  r = 2*i+1;
  if ( l <= size && A[l] > A[i] ) largest = l;
  else largest = i;
  if ( r <= size && A[r] > A[largest] ) largest = r;
  if ( largest != i ){
    t = A[i]; A[i] = A[largest]; A[largest] = t;
    maxHeapify(largest);
  }
}

int extract(void){
  
  int maxv;
  
  if ( size < 1 ) return;
  maxv = A[1];
  A[1] = A[size--];
  maxHeapify(1);

  return maxv;
}

void increaseKey(int i, int key){

  int tmp;

  if ( key < A[i] ) return;

  A[i] = key;

  while ( i > 1 && A[i/2] < A[i] ){
    tmp = A[i];
    A[i] = A[i/2];
    A[i/2] = tmp;
    i = i/2;
  }
}

void insert(int key){

  size++;
  A[size] = -1000000001;
  increaseKey(size, key);
  
}