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.Generic;
using System.Linq;
using System.Text;

namespace Practice
{
    class Program
    {

        static void Main(string[] args)
        {
            SolveA(args);
            //SolveB(args);
            //SolveC(args);
            //SolveD(args);


        }
        static void SolveA(string[] args)
        {

            List<long> a = new List<long>(2000000 + 1);
            a.Add(0);// dummy
           
            while(true)
            {
                string[] szarr = Console.ReadLine().Split(' ');
                string cmd = szarr[0];
                if(cmd == "insert")
                {
                    long key = long.Parse(szarr[1]);
                    Insert(a, key);
                }else if(cmd == "extract")
                {
                    Console.WriteLine(HeapExtractMax(a));
                }
                else
                {
                    // end
                    break;
                }
            }
        }
        static long HeapExtractMax(List<long> a)
        {
            if( a.Count < 1)
            {
                return 0;
            }
            long max = a[1];
            a[1] = a[a.Count - 1];
            a.RemoveAt(a.Count - 1);
            MaxHeapify(a, 1);
            return max;
        }
        static void Insert(List<long> a, long key)
        {
            a.Add(long.MinValue);
            HeapIncreaseKey(a, a.Count-1, key);
        }
        static void HeapIncreaseKey(List<long> a, int i, long key)
        {
            if( key < a[i])
            {
                // error
                return;
            }

            a[i] = key;
            while(i > 1 && a[Parent(i)] < a[i])
            {
                long tmp = a[i];
                a[i] = a[Parent(i)];
                a[Parent(i)] = tmp;
                i = Parent(i);
            }
        }
        static int Parent(int i) { return i / 2; }
        static int Left(int i) { return 2 * i; }
        static int Right(int i) { return 2 * i + 1; }
        static void MaxHeapify(List<long> a, int i)
        {
            int l = i * 2;
            int r = i * 2 + 1;
            int largest = 0;
            if( l < a.Count && a[l] > a[i])
            {
                largest = l;
            }else
            {
                largest = i;
            }
            if( r < a.Count && a[r] > a[largest])
            {
                largest = r;
            }

            if( largest != i)
            {
                long tmp = a[i];
                a[i] = a[largest];
                a[largest] = tmp;
                MaxHeapify(a, largest);
            }
        }
        static void BuildMaxHeap(List<long> a)
        {
            for(int i=a.Count / 2; i >= 1; --i)
            {
                MaxHeapify(a, i);
            }
        }
    }

}