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 ALDS_1_9_C
{
    class Program
    {
        static int H;
        static int[] A;
        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 Main(string[] args)
        {
            A = new int[2000001];
            while (true)
            {
                var a = Console.ReadLine().Split(' ');
                if (a[0][0] == 'i') insert(int.Parse(a[1]));
                else if (a[0] == "extract")
                    Console.WriteLine(extract());
                else break;
            }
        }
        static int extract()
        {
            int maxv;
            if (H < 1) return int.MinValue;
            maxv = A[1];
            A[1] = A[H--];
            maxheapify(1);
            return  maxv;

        }
        static void increasekey(int i,int key)
        {
            if (key < A[i]) return;
            A[i] = key;
            while (i>1 && A[i/2]<A[i])
            {
                int temp = A[i];
                A[i] = A[i / 2];
                A[i / 2] = temp;
                i /= 2;
            }
        }
        static void insert(int key)
        {
            H++;
            A[H] = int.MinValue;
            increasekey(H, key);
        }
        static void maxheapify(int i)
        {
            int l = left(i);
            int r = right(i);
            //????????????????????????????????§?????§????????????
            int largest;
            if (l <= H && A[l] > A[i]) largest = l;
            else largest = i;
            if (r <= H && A[r] > A[largest]) largest = r;

            if (largest != i)
            {
                int tmp = A[i];
                A[i] = A[largest];
                A[largest] = tmp;
                maxheapify(largest);
            }
        }
    }
}