Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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>
#include <string.h>

int A[2000000];
int heap_size=0;

void maxHeapify(int i)
{
  int l, r, largest, max;
  l = i*2;
  r = i*2+1;

  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){
    max = A[largest];
    A[largest] = A[i];
    A[i] = max;
    maxHeapify(largest);
  }
}

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

void heapIncreaseKey(int i,int key)
{
  int max;
  if(key<A[i])
    return ;
  
  A[i] = key;
  while(i>1 && A[i/2]<A[i]){
    max = A[i/2];
    A[i/2] = A[i];
    A[i] = max;
    i = i/2;
  }
}

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

int main()
{
  char str[20];
  int i=0, key;
  while(1){
    scanf("%s",str);
    if(str[2]=='d') break;
    else if(str[0]=='e'){
      printf("%d\n",heapExtractMax());
    }
    else{
      scanf("%d",&key);
      maxHeapInsert(key);
    }
  }

  return 0;
}