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: Accepted)

$s = 0
$heap = []

def max_heapify(i)
    l = i * 2
    r = l + 1

    if (l <= $s) && ($heap[i] < $heap[l])
        maxi = l
    else
        maxi = i
    end

    if (r <= $s) && ($heap[maxi] < $heap[r])
        maxi = r
    end

    if maxi != i
        $heap[i], $heap[maxi] = $heap[maxi], $heap[i]
        max_heapify(maxi)
    end
end

def heap_increase(v)
    $s += 1
    $heap[$s] = v
    i = $s
    while (i > 1) && ($heap[i/2] < $heap[i])
        $heap[i], $heap[i/2] = $heap[i/2], $heap[i]
        i /= 2
    end
end

def heap_extract
    max = $heap[1]
    $heap[1] = $heap[$s];
    $s -= 1
    max_heapify(1)
    max
end

while cmd = gets.chomp do
    if cmd == "end"
        break
    end

    if cmd == "extract"
        puts heap_extract
    else
        c = cmd.split[1].to_i
        heap_increase(c)
    end
end