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


class A
{
    static int n;
   
    public static void Main() {
        int[] nodes = new int[2000001];
        StringBuilder output = new StringBuilder();
        while (true) {
            string[] input = Console.ReadLine().Split(' ');
            if (input[0] == "end") {
                break;
            }
            if (input[0] == "insert") {
                Insert(nodes, int.Parse(input[1]));
            } else {
                output.AppendLine(HeapExtractMax(nodes).ToString());
            }
        }
        Console.Write(output);
    }
    public static void Insert(int[] nodes,int key) {
        n++;
        nodes[n] = int.MinValue;
        HeapIncreaseKey(nodes, n, key);
    }

    public static void HeapIncreaseKey(int[] nodes, int n, int key) {
        if (key < nodes[n]) {
            return;
        }
        nodes[n] = key;
        while (n > 1 && nodes[n / 2] < nodes[n]) {
            int temp = nodes[n];
            nodes[n] = nodes[n / 2];
            nodes[n / 2] = temp;
            n = n / 2;
        }
    }
    public static int HeapExtractMax(int[] nodes) {
        if (n < 1) {
            Console.WriteLine("HeapUnderFlow");
            return int.MinValue;
        }
        int max = nodes[1];
        nodes[1] = nodes[n];
        n--;
        Maxheapify(nodes, 1);
        return max;
    }
    public static void Maxheapify(int[] nodes, int i) {
        int left = i * 2;
        int right = i * 2 + 1;
        int largest = (left <= n && nodes[left] > nodes[i]) ? left : i;
        if (right <= n && nodes[right] > nodes[largest]) {
            largest = right;
        }
        if (largest != i) {
            int temp = nodes[i];
            nodes[i] = nodes[largest];
            nodes[largest] = temp;
            Maxheapify(nodes, largest);
        }
    }
}