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: Wrong Answer)

def parent(i)
  return i/2-1
end

def left(i)
  return i*2-1
end

def right(i)
  return i*2
end

def max_heapify(heap,i)
  l=left(i)
  r=right(i)

  if l < heap.length and heap[l] > heap[i-1]
    largest = l
  else
    largest = i-1
  end
  if r < heap.length and heap[r] > heap[largest]
    largest = r
  end

  if largest != i-1
    heap[i-1], heap[largest] = heap[largest], heap[i-1]
    max_heapify(heap, largest+1)
  end
end

def insert(heap, key)
  heap.push(key)
  i=heap.length
  while i > 1 and heap[parent(i)] < heap[i-1]
    heap[parent(i)], heap[i-1] = heap[i-1], heap[parent(i)]
    i = parent(i)
  end
end

def extract(heap)
  ret = heap[0]
  heap[0] = heap.pop
  max_heapify(heap, 1)
  return ret
end

inputs = STDIN.read().split("\n").map{ |line| line.split(" ")}

heap=[]

inputs.each do |line|
  case line[0]
  when 'insert' then
    insert(heap, line[1].to_i)
  when 'extract' then
    print "#{extract(heap)}\n"
  when 'end' then
    exit
  end
end