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 Ruby (judge verdict: Accepted)

def parent(i)
  i/2
end

def left(i)
  i*2
end

def right(i)
  i*2 + 1
end

def extract(i)
  l = left(i)
  r = right(i)
  h = A.length

  # printf "extract %d\n",i
  # p A
  # printf "l %d  r %d  h %d\n",l,r,h

  if l < h && A[l] > A[i]
    @largest = l
  else
    @largest = i
  end

  if r < h && A[r] > A[@largest]
    @largest = r
  end

  if @largest != i
    A[i], A[@largest] = A[@largest], A[i]
    extract(@largest)
  end
end

def insert(i)
  @parent = parent(i)
  if @parent == 0
    return
  end

  if A[i] > A[@parent]
    A[i], A[@parent] = A[@parent], A[i]
    insert(@parent)
  end
end

A = Array.new
A << 0

until (str=gets.chomp) == "end"
  # p A
  if str == "extract"
    puts A[1]
    A[1] = A.pop
    extract(1)
  else
    str = str.split(" ")
    A << str[1].to_i
    insert(A.length-1)
  end
end