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;

namespace ConsoleApp1
{

    class Program
    {
        public static int H = 0;
        static void Main()
        {
            int[] A = new int[2000000];
            while (true)
            {
                string[] command = Console.ReadLine().Split(' ');
                if (command[0].Equals("insert"))
                {
                    int i = H;
                    A[H++] = int.Parse(command[1]);
                    while (i >= 0 && A[(i - 1) / 2] < A[i]) {
                        int temp = A[i];
                        A[i] = A[(i - 1) / 2];
                        A[(i - 1) / 2] = temp;
                        i = (i - 1) / 2;
                    }
                }
                else if (command[0].Equals("extract"))
                {
                    Console.WriteLine(A[0]);
                    A[0] = A[--H];
                    Maxheapfy(A, 0);
                }
                else break;
            }
        }
        private static void Maxheapfy(int[] A, int i)
        {
            int largest = i;
            int l = (i + 1) * 2 - 1;
            int r = (i + 1) * 2;
            if (l < H && A[l] > A[i])
                largest = l;
            if (r < H && A[r] > A[largest])
                largest = r;

            if (largest != i)
            {
                int temp = A[i];
                A[i] = A[largest];
                A[largest] = temp;
                Maxheapfy(A, largest);
            }
        }
        private static void buildMaxHeap(int[] A)
        {
            for (int i = H / 2; i >= 0; i--)
            {
                Maxheapfy(A, i);
            }
        }
    }
}