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 build_upward as, i
  p_i = (i + 1) / 2 - 1
  if p_i >= 0 && as[p_i] < as[i]
    as[p_i], as[i] = as[i], as[p_i]
    build_upward as, p_i
  end
end

def build_downward as, i
  a_len = as.length
  l_i = 2 * (i + 1) - 1
  r_i = 2 * (i + 1)
  v = as[i]
  l_v = ((a_len - 1) >= l_i) ? as[l_i] : -1
  r_v = ((a_len - 1) >= r_i) ? as[r_i] : -1

  largest_i = i
  largest_v = as[i]
  if l_v > largest_v
    largest_i = l_i
    largest_v = l_v
  end
  if r_v > largest_v
    largest_i = r_i
    largest_v = r_v
  end
  if largest_i != i
    as[i], as[largest_i] = as[largest_i], as[i]
    build_downward as, largest_i
  end
end

heap = []
res = []
while l = gets
  command, val = l.chomp.split(' ')
  case command
  when 'end'
    puts res.join("\n")
    break
  when 'insert'
    heap << val.to_i
    build_upward heap, heap.length - 1
  when 'extract'
    res << heap[0]
    if heap.length > 1
      heap[0] = heap.pop
      build_downward heap, 0
    end
  end
end