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.Text;

namespace ALDS1_9_C {
    class PriorityQueue<T> where T : IComparable {
        List<T> heap;
        int size;

        public PriorityQueue() {
            heap = new List<T>();
        }

        public void Enqueue(T x) {
            heap.Add(x);
            int i = size++;

            while (i > 0) {
                int p = (i - 1) / 2;
                if (Compare(heap[p], x) <= 0)
                    break;
                heap[i] = heap[p];
                i = p;
            }
            heap[i] = x;
        }

        public T Dequeue() {
            T ret = heap[0];
            T x = heap[--size];

            int i = 0;
            while (i * 2 + 1 < size) {
                int a = i * 2 + 1;
                int b = i * 2 + 2;
                if (b < size && Compare(heap[b], heap[a]) < 0)
                    a = b;
                if (Compare(heap[a], x) >= 0)
                    break;
                heap[i] = heap[a];
                i = a;
            }
            heap[i] = x;
            heap.RemoveAt(size);
            return ret;
        }

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

        public int Count() {
            return size;
        }

        private int Compare(T x, T y) {
            return y.CompareTo(x);
        }
    }

    class Program {
        static void Main(string[] args) {
            PriorityQueue<int> pq = new PriorityQueue<int>();
            StringBuilder sb = new StringBuilder();
            bool inputEnd = false;
            while (!inputEnd) {
                string[] input = Console.ReadLine().Split(' ');
                switch (input[0]) {
                    case "insert":
                        pq.Enqueue(int.Parse(input[1]));
                        break;
                    case "extract":
                        sb.AppendLine(pq.Dequeue().ToString());
                        break;
                    case "end":
                        inputEnd = true;
                        break;
                }
            }
            Console.Write(sb);
        }
    }
}