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 JAVA (judge verdict: Memory Limit Exceeded)


import java.util.Scanner;
public class Main {
	public static void main(String[] args){
		Scanner scr = new Scanner(System.in);
		BinaryTree<String> bt = new BinaryTree<String>();
		bt.insert(0, "zero");
		int exed = 0;
		while(true){
			String str = scr.nextLine();
			if(str.equals("extract")) {
				System.out.println(bt.extractMax().value);
				exed++;
			}
			else if(str.equals("end")) break;
			else bt.insert(Integer.parseInt(str.split(" ")[1]), str.split(" ")[1]);
			if(exed > 100) {
				System.gc();
				exed = 0;
			}
		}
		scr.close();
	}

}

class BinaryTree<T> {
	public int key;
	public T value;
	public BinaryTree<T> left;
	public BinaryTree<T> right;
	public BinaryTree<T> parent;

	BinaryTree(){
		this.value = null;
		this.key = 0;
		this.left = null;
		this.right = null;
		this.parent = null;
	}
	BinaryTree(int key, T value, BinaryTree<T> p){
		this.value = value;
		this.key = key;
		this.left = null;
		this.right = null;
		this.parent = p;
	}
	
	public void insert(int key, T value){
		if(this.parent == null && this.value == null){
			this.value = value;
			this.key = key;
			return;
		}else if(this.key >= key){ //?°???????????????????key?????´??????????????????
			if(this.left == null) this.left = new BinaryTree<T>(key, value, this);
			else this.left.insert(key, value);
		}else if(this.key < key){ //??§??????key?????´??????????????????
			if(this.right == null) this.right = new BinaryTree<T>(key, value, this);
			else this.right.insert(key, value);
		}else{
			this.value = value;
		}
		return;
	}
	public BinaryTree<T> extractMax(){
		if(this.parent == null) { //???????????¨????????????
			if(this.right == null) {
				if(this.left == null) {
					System.err.println("This tree is enpty");
					return null;
				}else return this.left.extractMax();
			}else return this.right.extractMax();
		}
		if(this.right == null){
			if(this.left == null){ //???????????´????????????????????¨??????????????¢???
				if(this.parent.left == this) this.parent.left = null;
				else/* if(this.parent.right == this) */this.parent.right = null;
			}else{
				if(this.parent.right == this) this.parent.right = this.left;
				else/* if(this.parent.left == this) */this.parent.left = this.left;
				this.left.parent = this.parent;
			}
			return this;
		}else{
			return this.right.extractMax();
		}
	}

}