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 C# (judge verdict: Accepted)

using System;
using System.Collections;
using System.IO;
using System.Linq;

namespace CompetitiveProgramming
{
  class PriorityQueue<T> where T : IComparable
  {
    const int MAX_SIZE = 2000001;
    private T[] heap;
    public int Size { get; protected set; }

    public PriorityQueue()
    {
      heap = new T[MAX_SIZE];
    }

    public void Push(T x)
    {
      int i = Size++;
      
      while (i > 0)
      {
        int p = (i - 1) / 2;
        if (heap[p].CompareTo(x) >= 0)
        {
          break;
        }
        heap[i] = heap[p];
        i = p;
      }
      heap[i] = x;
    }

    public T Top()
    {
      return heap[0];
    }

    public void Pop()
    {
      T x = heap[--Size];

      int i = 0;
      while (i * 2 + 1 < Size)
      {
        int a = i * 2 + 1, b = i * 2 + 2;
        if (b < Size && heap[b].CompareTo(heap[a]) > 0)
        {
          a = b;
        }

        if (heap[a].CompareTo(x) <= 0)
        {
          break;
        }
        heap[i] = heap[a];
        i = a;
      }

      heap[i] = x;
    }

  }

  class Solve
  {
    const int INF = (int)(1e9) + 10;

    private void Main()
    {
      PriorityQueue<ulong> pq = new PriorityQueue<ulong>();

      while (true)
      {
        string[] input = Console.ReadLine().Split();
        if (input[0] == "insert")
        {
          ulong num = ulong.Parse(input[1]);
          pq.Push(num);
        }
        else if (input[0] == "extract")
        {
          Console.WriteLine(pq.Top());
          pq.Pop();
        }
        else
        {
          return;
        }
      }
      
    }

    public Solve()
    {
      Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
      Main();
      Console.Out.Flush();
    }
  }

  class Program
  {
    static void Main(string[] args)
    {
      new Solve();
    }
  }
}