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 {
        List<int> _heap;
        int _size;

        public PriorityQueue() {
            _heap = new List<int>();
            _heap.Add(int.MinValue);
        }

        public void Enqueue(int num) {
            _size++;
            _heap.Add(int.MinValue);
            IncreaseKey(_size, num);
        }

        public int Dequeue() {
            if (_size < 1)
                return int.MinValue;
            int ret = _heap[1];
            _heap[1] = _heap[_size];
            _heap.RemoveAt(_size);
            _size--;
            MaxHeapify(1);
            return ret;
        }

        public int Peek() {
            return _heap[1];
        }

        public int Count {
            get {
                return _size;
            }
        }

        private void MaxHeapify(int i) {
            int l = i * 2;
            int r = i * 2 + 1;
            int largest = (l <= _size && _heap[l] > _heap[i]) ? l : i;
            if (r <= _size && _heap[r] > _heap[largest])
                largest = r;

            if (largest != i) {
                Swap(i, largest);
                MaxHeapify(largest);
            }
        }

        private void IncreaseKey(int i, int key) {
            if (key < _heap[i])
                return;
            _heap[i] = key;
            while (i > 1) {
                int j = i / 2;
                if (_heap[j] < _heap[i])
                    Swap(i, j);
                i = j;
            }
        }

        private void Swap(int a, int b) {
            int temp = _heap[a];
            _heap[a] = _heap[b];
            _heap[b] = temp;
        }
    }

    class Program {
        static void Main(string[] args) {
            PriorityQueue pq = new PriorityQueue();
            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);
        }
    }
}