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 C# (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
public static class P
{
    public static void Main()
    {
        PriorityQueue<int> pqueue = new PriorityQueue<int>(true);
        while (true)
        {
            var query = Console.ReadLine().Split();
            if (query[0] == "extract") Console.WriteLine(pqueue.Pop());
            else if (query[0] == "insert") pqueue.Push(int.Parse(query[1]));
            else break;
        }
    }
}

class PriorityQueue<T> where T : IComparable<T>
{
    public int Count { get; private set; }
    private bool Descendance;
    private T[] data = new T[65536];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public PriorityQueue(bool descendance = false) { Descendance = descendance; }
    public T Top
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        get { ValidateNonEmpty(); return data[1]; }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Pop()
    {
        var top = Top;
        var elem = data[Count--];
        int index = 1;
        while (true)
        {
            if ((index << 1) >= Count)
            {
                if (index << 1 > Count) break;
                if (elem.CompareTo(data[index << 1]) > 0 ^ Descendance) data[index] = data[index <<= 1];
                else break;
            }
            else
            {
                var nextIndex = data[index << 1].CompareTo(data[(index << 1) + 1]) <= 0 ^ Descendance ? (index << 1) : (index << 1) + 1;
                if (elem.CompareTo(data[nextIndex]) > 0 ^ Descendance) data[index] = data[index = nextIndex];
                else break;
            }
        }
        data[index] = elem;
        return top;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public void Push(T value)
    {
        int index = ++Count;
        if (data.Length == Count) Extend(data.Length * 2);
        while ((index >> 1) != 0)
        {
            if (data[index >> 1].CompareTo(value) > 0 ^ Descendance) data[index] = data[index >>= 1];
            else break;
        }
        data[index] = value;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private void Extend(int newSize)
    {
        T[] newDatas = new T[newSize];
        data.CopyTo(newDatas, 0);
        data = newDatas;
    }
    private void ValidateNonEmpty() { if (Count == 0) throw new Exception(); }
}