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 Ruby (judge verdict: Time Limit Exceeded)

def parent(i)
  return i/2
end
def left(i)
  return i*2
end
def right(i)
  return i*2+1
end
def maxHeap(arr,i)
  l=left(i)
  r=right(i)
  if l<=@n && arr[l]>arr[i]
    largest=l
  else
    largest=i
  end
  if r<=@n && arr[r]>arr[largest]
    largest=r
  end
  if largest!=i
    arr[i],arr[largest]=arr[largest],arr[i]
    maxHeap(arr,largest)
  end
end
def buildMaxHeap(arr)
  @n.downto(1) do |i|
    maxHeap(arr,i)
  end
end
arr=Array.new()
arr << nil
loop do
  cmd,num=gets.split
  case cmd
  when 'insert'
    arr << num.to_i
    @n=arr.length-1
    buildMaxHeap(arr)
  when 'extract'
    @n=arr.length-1
    buildMaxHeap(arr)
    puts arr.delete_at(1)
  else
    break
  end
end