/*

 * Copyright (c) 1999, 2008, Oracle and/or its affiliates. All rights reserved.

 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.  Oracle designates this

 * particular file as subject to the "Classpath" exception as provided

 * by Oracle in the LICENSE file that accompanied this code.

 *

 * This code is distributed in the hope that it will be useful, but WITHOUT

 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

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 */

package java.util;

import java.util.Date;

import java.util.concurrent.atomic.AtomicInteger;

/**

 * A facility for threads to schedule tasks for future execution in a

 * background thread.  Tasks may be scheduled for one-time execution, or for

 * repeated execution at regular intervals.

 *

 * <p>Corresponding to each <tt>Timer</tt> object is a single background

 * thread that is used to execute all of the timer's tasks, sequentially.

 * Timer tasks should complete quickly.  If a timer task takes excessive time

 * to complete, it "hogs" the timer's task execution thread.  This can, in

 * turn, delay the execution of subsequent tasks, which may "bunch up" and

 * execute in rapid succession when (and if) the offending task finally

 * completes.

 *

 * <p>After the last live reference to a <tt>Timer</tt> object goes away

 * <i>and</i> all outstanding tasks have completed execution, the timer's task

 * execution thread terminates gracefully (and becomes subject to garbage

 * collection).  However, this can take arbitrarily long to occur.  By

 * default, the task execution thread does not run as a <i>daemon thread</i>,

 * so it is capable of keeping an application from terminating.  If a caller

 * wants to terminate a timer's task execution thread rapidly, the caller

 * should invoke the timer's <tt>cancel</tt> method.

 *

 * <p>If the timer's task execution thread terminates unexpectedly, for

 * example, because its <tt>stop</tt> method is invoked, any further

 * attempt to schedule a task on the timer will result in an

 * <tt>IllegalStateException</tt>, as if the timer's <tt>cancel</tt>

 * method had been invoked.

 *

 * <p>This class is thread-safe: multiple threads can share a single

 * <tt>Timer</tt> object without the need for external synchronization.

 *

 * <p>This class does <i>not</i> offer real-time guarantees: it schedules

 * tasks using the <tt>Object.wait(long)</tt> method.

 *

 * <p>Java 5.0 introduced the {@code java.util.concurrent} package and

 * one of the concurrency utilities therein is the {@link

 * java.util.concurrent.ScheduledThreadPoolExecutor

 * ScheduledThreadPoolExecutor} which is a thread pool for repeatedly

 * executing tasks at a given rate or delay.  It is effectively a more

 * versatile replacement for the {@code Timer}/{@code TimerTask}

 * combination, as it allows multiple service threads, accepts various

 * time units, and doesn't require subclassing {@code TimerTask} (just

 * implement {@code Runnable}).  Configuring {@code

 * ScheduledThreadPoolExecutor} with one thread makes it equivalent to

 * {@code Timer}.

 *

 * <p>Implementation note: This class scales to large numbers of concurrently

 * scheduled tasks (thousands should present no problem).  Internally,

 * it uses a binary heap to represent its task queue, so the cost to schedule

 * a task is O(log n), where n is the number of concurrently scheduled tasks.

 *

 * <p>Implementation note: All constructors start a timer thread.

 *

 * @author  Josh Bloch

 * @see     TimerTask

 * @see     Object#wait(long)

 * @since   1.3

 */

public class Timer {

    /**

     * The timer task queue.  This data structure is shared with the timer

     * thread.  The timer produces tasks, via its various schedule calls,

     * and the timer thread consumes, executing timer tasks as appropriate,

     * and removing them from the queue when they're obsolete.

     */

    private final TaskQueue queue = new TaskQueue();

    /**

     * The timer thread.

     */

    private final TimerThread thread = new TimerThread(queue);

    /**

     * This object causes the timer's task execution thread to exit

     * gracefully when there are no live references to the Timer object and no

     * tasks in the timer queue.  It is used in preference to a finalizer on

     * Timer as such a finalizer would be susceptible to a subclass's

     * finalizer forgetting to call it.

     */

    private final Object threadReaper = new Object() {

        protected void finalize() throws Throwable {

            synchronized(queue) {

                thread.newTasksMayBeScheduled = false;

                queue.notify(); // In case queue is empty.

            }

        }

    };

    /**

     * This ID is used to generate thread names.

     */

    private final static AtomicInteger nextSerialNumber = new AtomicInteger(0);

    private static int serialNumber() {

        return nextSerialNumber.getAndIncrement();

    }

    /**

     * Creates a new timer.  The associated thread does <i>not</i>

     * {@linkplain Thread#setDaemon run as a daemon}.

     */

    public Timer() {

        this("Timer-" + serialNumber());

    }

    /**

     * Creates a new timer whose associated thread may be specified to

     * {@linkplain Thread#setDaemon run as a daemon}.

     * A daemon thread is called for if the timer will be used to

     * schedule repeating "maintenance activities", which must be

     * performed as long as the application is running, but should not

     * prolong the lifetime of the application.

     *

     * @param isDaemon true if the associated thread should run as a daemon.

     */

    public Timer(boolean isDaemon) {

        this("Timer-" + serialNumber(), isDaemon);

    }

    /**

     * Creates a new timer whose associated thread has the specified name.

     * The associated thread does <i>not</i>

     * {@linkplain Thread#setDaemon run as a daemon}.

     *

     * @param name the name of the associated thread

     * @throws NullPointerException if {@code name} is null

     * @since 1.5

     */

    public Timer(String name) {

        thread.setName(name);

        thread.start();

    }

    /**

     * Creates a new timer whose associated thread has the specified name,

     * and may be specified to

     * {@linkplain Thread#setDaemon run as a daemon}.

     *

     * @param name the name of the associated thread

     * @param isDaemon true if the associated thread should run as a daemon

     * @throws NullPointerException if {@code name} is null

     * @since 1.5

     */

    public Timer(String name, boolean isDaemon) {

        thread.setName(name);

        thread.setDaemon(isDaemon);

        thread.start();

    }

    /**

     * Schedules the specified task for execution after the specified delay.

     *

     * @param task  task to be scheduled.

     * @param delay delay in milliseconds before task is to be executed.

     * @throws IllegalArgumentException if <tt>delay</tt> is negative, or

     *         <tt>delay + System.currentTimeMillis()</tt> is negative.

     * @throws IllegalStateException if task was already scheduled or

     *         cancelled, timer was cancelled, or timer thread terminated.

     * @throws NullPointerException if {@code task} is null

     */

    public void schedule(TimerTask task, long delay) {

        if (delay < 0)

            throw new IllegalArgumentException("Negative delay.");

        sched(task, System.currentTimeMillis()+delay, 0);

    }

    /**

     * Schedules the specified task for execution at the specified time.  If

     * the time is in the past, the task is scheduled for immediate execution.

     *

     * @param task task to be scheduled.

     * @param time time at which task is to be executed.

     * @throws IllegalArgumentException if <tt>time.getTime()</tt> is negative.

     * @throws IllegalStateException if task was already scheduled or

     *         cancelled, timer was cancelled, or timer thread terminated.

     * @throws NullPointerException if {@code task} or {@code time} is null

     */

    public void schedule(TimerTask task, Date time) {

        sched(task, time.getTime(), 0);

    }

    /**

     * Schedules the specified task for repeated <i>fixed-delay execution</i>,

     * beginning after the specified delay.  Subsequent executions take place

     * at approximately regular intervals separated by the specified period.

     *

     * <p>In fixed-delay execution, each execution is scheduled relative to

     * the actual execution time of the previous execution.  If an execution

     * is delayed for any reason (such as garbage collection or other

     * background activity), subsequent executions will be delayed as well.

     * In the long run, the frequency of execution will generally be slightly

     * lower than the reciprocal of the specified period (assuming the system

     * clock underlying <tt>Object.wait(long)</tt> is accurate).

     *

     * <p>Fixed-delay execution is appropriate for recurring activities

     * that require "smoothness."  In other words, it is appropriate for

     * activities where it is more important to keep the frequency accurate

     * in the short run than in the long run.  This includes most animation

     * tasks, such as blinking a cursor at regular intervals.  It also includes

     * tasks wherein regular activity is performed in response to human

     * input, such as automatically repeating a character as long as a key

     * is held down.

     *

     * @param task   task to be scheduled.

     * @param delay  delay in milliseconds before task is to be executed.

     * @param period time in milliseconds between successive task executions.

     * @throws IllegalArgumentException if {@code delay < 0}, or

     *         {@code delay + System.currentTimeMillis() < 0}, or

     *         {@code period <= 0}

     * @throws IllegalStateException if task was already scheduled or

     *         cancelled, timer was cancelled, or timer thread terminated.

     * @throws NullPointerException if {@code task} is null

     */

    public void schedule(TimerTask task, long delay, long period) {

        if (delay < 0)

            throw new IllegalArgumentException("Negative delay.");

        if (period <= 0)

            throw new IllegalArgumentException("Non-positive period.");

        sched(task, System.currentTimeMillis()+delay, -period);

    }

    /**

     * Schedules the specified task for repeated <i>fixed-delay execution</i>,

     * beginning at the specified time. Subsequent executions take place at

     * approximately regular intervals, separated by the specified period.

     *

     * <p>In fixed-delay execution, each execution is scheduled relative to

     * the actual execution time of the previous execution.  If an execution

     * is delayed for any reason (such as garbage collection or other

     * background activity), subsequent executions will be delayed as well.

     * In the long run, the frequency of execution will generally be slightly

     * lower than the reciprocal of the specified period (assuming the system

     * clock underlying <tt>Object.wait(long)</tt> is accurate).  As a

     * consequence of the above, if the scheduled first time is in the past,

     * it is scheduled for immediate execution.

     *

     * <p>Fixed-delay execution is appropriate for recurring activities

     * that require "smoothness."  In other words, it is appropriate for

     * activities where it is more important to keep the frequency accurate

     * in the short run than in the long run.  This includes most animation

     * tasks, such as blinking a cursor at regular intervals.  It also includes

     * tasks wherein regular activity is performed in response to human

     * input, such as automatically repeating a character as long as a key

     * is held down.

     *

     * @param task   task to be scheduled.

     * @param firstTime First time at which task is to be executed.

     * @param period time in milliseconds between successive task executions.

     * @throws IllegalArgumentException if {@code firstTime.getTime() < 0}, or

     *         {@code period <= 0}

     * @throws IllegalStateException if task was already scheduled or

     *         cancelled, timer was cancelled, or timer thread terminated.

     * @throws NullPointerException if {@code task} or {@code firstTime} is null

     */

    public void schedule(TimerTask task, Date firstTime, long period) {

        if (period <= 0)

            throw new IllegalArgumentException("Non-positive period.");

        sched(task, firstTime.getTime(), -period);

    }

    /**

     * Schedules the specified task for repeated <i>fixed-rate execution</i>,

     * beginning after the specified delay.  Subsequent executions take place

     * at approximately regular intervals, separated by the specified period.

     *

     * <p>In fixed-rate execution, each execution is scheduled relative to the

     * scheduled execution time of the initial execution.  If an execution is

     * delayed for any reason (such as garbage collection or other background

     * activity), two or more executions will occur in rapid succession to

     * "catch up."  In the long run, the frequency of execution will be

     * exactly the reciprocal of the specified period (assuming the system

     * clock underlying <tt>Object.wait(long)</tt> is accurate).

     *

     * <p>Fixed-rate execution is appropriate for recurring activities that

     * are sensitive to <i>absolute</i> time, such as ringing a chime every

     * hour on the hour, or running scheduled maintenance every day at a

     * particular time.  It is also appropriate for recurring activities

     * where the total time to perform a fixed number of executions is

     * important, such as a countdown timer that ticks once every second for

     * ten seconds.  Finally, fixed-rate execution is appropriate for

     * scheduling multiple repeating timer tasks that must remain synchronized

     * with respect to one another.

     *

     * @param task   task to be scheduled.

     * @param delay  delay in milliseconds before task is to be executed.

     * @param period time in milliseconds between successive task executions.

     * @throws IllegalArgumentException if {@code delay < 0}, or

     *         {@code delay + System.currentTimeMillis() < 0}, or

     *         {@code period <= 0}

     * @throws IllegalStateException if task was already scheduled or

     *         cancelled, timer was cancelled, or timer thread terminated.

     * @throws NullPointerException if {@code task} is null

     */

    public void scheduleAtFixedRate(TimerTask task, long delay, long period) {

        if (delay < 0)

            throw new IllegalArgumentException("Negative delay.");

        if (period <= 0)

            throw new IllegalArgumentException("Non-positive period.");

        sched(task, System.currentTimeMillis()+delay, period);

    }

    /**

     * Schedules the specified task for repeated <i>fixed-rate execution</i>,

     * beginning at the specified time. Subsequent executions take place at

     * approximately regular intervals, separated by the specified period.

     *

     * <p>In fixed-rate execution, each execution is scheduled relative to the

     * scheduled execution time of the initial execution.  If an execution is

     * delayed for any reason (such as garbage collection or other background

     * activity), two or more executions will occur in rapid succession to

     * "catch up."  In the long run, the frequency of execution will be

     * exactly the reciprocal of the specified period (assuming the system

     * clock underlying <tt>Object.wait(long)</tt> is accurate).  As a

     * consequence of the above, if the scheduled first time is in the past,

     * then any "missed" executions will be scheduled for immediate "catch up"

     * execution.

     *

     * <p>Fixed-rate execution is appropriate for recurring activities that

     * are sensitive to <i>absolute</i> time, such as ringing a chime every

     * hour on the hour, or running scheduled maintenance every day at a

     * particular time.  It is also appropriate for recurring activities

     * where the total time to perform a fixed number of executions is

     * important, such as a countdown timer that ticks once every second for

     * ten seconds.  Finally, fixed-rate execution is appropriate for

     * scheduling multiple repeating timer tasks that must remain synchronized

     * with respect to one another.

     *

     * @param task   task to be scheduled.

     * @param firstTime First time at which task is to be executed.

     * @param period time in milliseconds between successive task executions.

     * @throws IllegalArgumentException if {@code firstTime.getTime() < 0} or

     *         {@code period <= 0}

     * @throws IllegalStateException if task was already scheduled or

     *         cancelled, timer was cancelled, or timer thread terminated.

     * @throws NullPointerException if {@code task} or {@code firstTime} is null

     */

    public void scheduleAtFixedRate(TimerTask task, Date firstTime,

                                    long period) {

        if (period <= 0)

            throw new IllegalArgumentException("Non-positive period.");

        sched(task, firstTime.getTime(), period);

    }

    /**

     * Schedule the specified timer task for execution at the specified

     * time with the specified period, in milliseconds.  If period is

     * positive, the task is scheduled for repeated execution; if period is

     * zero, the task is scheduled for one-time execution. Time is specified

     * in Date.getTime() format.  This method checks timer state, task state,

     * and initial execution time, but not period.

     *

     * @throws IllegalArgumentException if <tt>time</tt> is negative.

     * @throws IllegalStateException if task was already scheduled or

     *         cancelled, timer was cancelled, or timer thread terminated.

     * @throws NullPointerException if {@code task} is null

     */

    private void sched(TimerTask task, long time, long period) {

        if (time < 0)

            throw new IllegalArgumentException("Illegal execution time.");

        // Constrain value of period sufficiently to prevent numeric

        // overflow while still being effectively infinitely large.

        if (Math.abs(period) > (Long.MAX_VALUE >> 1))

            period >>= 1;

        synchronized(queue) {

            if (!thread.newTasksMayBeScheduled)

                throw new IllegalStateException("Timer already cancelled.");

            synchronized(task.lock) {

                if (task.state != TimerTask.VIRGIN)

                    throw new IllegalStateException(

                        "Task already scheduled or cancelled");

                task.nextExecutionTime = time;

                task.period = period;

                task.state = TimerTask.SCHEDULED;

            }

            queue.add(task);

            if (queue.getMin() == task)

                queue.notify();

        }

    }

    /**

     * Terminates this timer, discarding any currently scheduled tasks.

     * Does not interfere with a currently executing task (if it exists).

     * Once a timer has been terminated, its execution thread terminates

     * gracefully, and no more tasks may be scheduled on it.

     *

     * <p>Note that calling this method from within the run method of a

     * timer task that was invoked by this timer absolutely guarantees that

     * the ongoing task execution is the last task execution that will ever

     * be performed by this timer.

     *

     * <p>This method may be called repeatedly; the second and subsequent

     * calls have no effect.

     */

    public void cancel() {

        synchronized(queue) {

            thread.newTasksMayBeScheduled = false;

            queue.clear();

            queue.notify();  // In case queue was already empty.

        }

    }

    /**

     * Removes all cancelled tasks from this timer's task queue.  <i>Calling

     * this method has no effect on the behavior of the timer</i>, but

     * eliminates the references to the cancelled tasks from the queue.

     * If there are no external references to these tasks, they become

     * eligible for garbage collection.

     *

     * <p>Most programs will have no need to call this method.

     * It is designed for use by the rare application that cancels a large

     * number of tasks.  Calling this method trades time for space: the

     * runtime of the method may be proportional to n + c log n, where n

     * is the number of tasks in the queue and c is the number of cancelled

     * tasks.

     *

     * <p>Note that it is permissible to call this method from within a

     * a task scheduled on this timer.

     *

     * @return the number of tasks removed from the queue.

     * @since 1.5

     */

     public int purge() {

         int result = 0;

         synchronized(queue) {

             for (int i = queue.size(); i > 0; i--) {

                 if (queue.get(i).state == TimerTask.CANCELLED) {

                     queue.quickRemove(i);

                     result++;

                 }

             }

             if (result != 0)

                 queue.heapify();

         }

         return result;

     }

}

/**

 * This "helper class" implements the timer's task execution thread, which

 * waits for tasks on the timer queue, executions them when they fire,

 * reschedules repeating tasks, and removes cancelled tasks and spent

 * non-repeating tasks from the queue.

 */

class TimerThread extends Thread {

    /**

     * This flag is set to false by the reaper to inform us that there

     * are no more live references to our Timer object.  Once this flag

     * is true and there are no more tasks in our queue, there is no

     * work left for us to do, so we terminate gracefully.  Note that

     * this field is protected by queue's monitor!

     */

    boolean newTasksMayBeScheduled = true;

    /**

     * Our Timer's queue.  We store this reference in preference to

     * a reference to the Timer so the reference graph remains acyclic.

     * Otherwise, the Timer would never be garbage-collected and this

     * thread would never go away.

     */

    private TaskQueue queue;

    TimerThread(TaskQueue queue) {

        this.queue = queue;

    }

    public void run() {

        try {

            mainLoop();

        } finally {

            // Someone killed this Thread, behave as if Timer cancelled

            synchronized(queue) {

                newTasksMayBeScheduled = false;

                queue.clear();  // Eliminate obsolete references

            }

        }

    }

    /**

     * The main timer loop.  (See class comment.)

     */

    private void mainLoop() {

        while (true) {

            try {

                TimerTask task;

                boolean taskFired;

                synchronized(queue) {

                    // Wait for queue to become non-empty

                    while (queue.isEmpty() && newTasksMayBeScheduled)

                        queue.wait();

                    if (queue.isEmpty())

                        break; // Queue is empty and will forever remain; die

                    // Queue nonempty; look at first evt and do the right thing

                    long currentTime, executionTime;

                    task = queue.getMin();

                    synchronized(task.lock) {

                        if (task.state == TimerTask.CANCELLED) {

                            queue.removeMin();

                            continue;  // No action required, poll queue again

                        }

                        currentTime = System.currentTimeMillis();

                        executionTime = task.nextExecutionTime;

                        if (taskFired = (executionTime<=currentTime)) {

                            if (task.period == 0) { // Non-repeating, remove

                                queue.removeMin();

                                task.state = TimerTask.EXECUTED;

                            } else { // Repeating task, reschedule

                                queue.rescheduleMin(

                                  task.period<0 ? currentTime   - task.period

                                                : executionTime + task.period);

                            }

                        }

                    }

                    if (!taskFired) // Task hasn't yet fired; wait

                        queue.wait(executionTime - currentTime);

                }

                if (taskFired)  // Task fired; run it, holding no locks

                    task.run();

            } catch(InterruptedException e) {

            }

        }

    }

}

/**

 * This class represents a timer task queue: a priority queue of TimerTasks,

 * ordered on nextExecutionTime.  Each Timer object has one of these, which it

 * shares with its TimerThread.  Internally this class uses a heap, which

 * offers log(n) performance for the add, removeMin and rescheduleMin

 * operations, and constant time performance for the getMin operation.

 */

class TaskQueue {

    /**

     * Priority queue represented as a balanced binary heap: the two children

     * of queue[n] are queue[2*n] and queue[2*n+1].  The priority queue is

     * ordered on the nextExecutionTime field: The TimerTask with the lowest

     * nextExecutionTime is in queue[1] (assuming the queue is nonempty).  For

     * each node n in the heap, and each descendant of n, d,

     * n.nextExecutionTime <= d.nextExecutionTime.

     */

    private TimerTask[] queue = new TimerTask[128];

    /**

     * The number of tasks in the priority queue.  (The tasks are stored in

     * queue[1] up to queue[size]).

     */

    private int size = 0;

    /**

     * Returns the number of tasks currently on the queue.

     */

    int size() {

        return size;

    }

    /**

     * Adds a new task to the priority queue.

     */

    void add(TimerTask task) {

        // Grow backing store if necessary

        if (size + 1 == queue.length)

            queue = Arrays.copyOf(queue, 2*queue.length);

        queue[++size] = task;

        fixUp(size);

    }

    /**

     * Return the "head task" of the priority queue.  (The head task is an

     * task with the lowest nextExecutionTime.)

     */

    TimerTask getMin() {

        return queue[1];

    }

    /**

     * Return the ith task in the priority queue, where i ranges from 1 (the

     * head task, which is returned by getMin) to the number of tasks on the

     * queue, inclusive.

     */

    TimerTask get(int i) {

        return queue[i];

    }

    /**

     * Remove the head task from the priority queue.

     */

    void removeMin() {

        queue[1] = queue[size];

        queue[size--] = null;  // Drop extra reference to prevent memory leak

        fixDown(1);

    }

    /**

     * Removes the ith element from queue without regard for maintaining

     * the heap invariant.  Recall that queue is one-based, so

     * 1 <= i <= size.

     */

    void quickRemove(int i) {

        assert i <= size;

        queue[i] = queue[size];

        queue[size--] = null;  // Drop extra ref to prevent memory leak

    }

    /**

     * Sets the nextExecutionTime associated with the head task to the

     * specified value, and adjusts priority queue accordingly.

     */

    void rescheduleMin(long newTime) {

        queue[1].nextExecutionTime = newTime;

        fixDown(1);

    }

    /**

     * Returns true if the priority queue contains no elements.

     */

    boolean isEmpty() {

        return size==0;

    }

    /**

     * Removes all elements from the priority queue.

     */

    void clear() {

        // Null out task references to prevent memory leak

        for (int i=1; i<=size; i++)

            queue[i] = null;

        size = 0;

    }

    /**

     * Establishes the heap invariant (described above) assuming the heap

     * satisfies the invariant except possibly for the leaf-node indexed by k

     * (which may have a nextExecutionTime less than its parent's).

     *

     * This method functions by "promoting" queue[k] up the hierarchy

     * (by swapping it with its parent) repeatedly until queue[k]'s

     * nextExecutionTime is greater than or equal to that of its parent.

     */

    private void fixUp(int k) {

        while (k > 1) {

            int j = k >> 1;

            if (queue[j].nextExecutionTime <= queue[k].nextExecutionTime)

                break;

            TimerTask tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;

            k = j;

        }

    }

    /**

     * Establishes the heap invariant (described above) in the subtree

     * rooted at k, which is assumed to satisfy the heap invariant except

     * possibly for node k itself (which may have a nextExecutionTime greater

     * than its children's).

     *

     * This method functions by "demoting" queue[k] down the hierarchy

     * (by swapping it with its smaller child) repeatedly until queue[k]'s

     * nextExecutionTime is less than or equal to those of its children.

     */

    private void fixDown(int k) {

        int j;

        while ((j = k << 1) <= size && j > 0) {

            if (j < size &&

                queue[j].nextExecutionTime > queue[j+1].nextExecutionTime)

                j++; // j indexes smallest kid

            if (queue[k].nextExecutionTime <= queue[j].nextExecutionTime)

                break;

            TimerTask tmp = queue[j];  queue[j] = queue[k]; queue[k] = tmp;

            k = j;

        }

    }

    /**

     * Establishes the heap invariant (described above) in the entire tree,

     * assuming nothing about the order of the elements prior to the call.

     */

    void heapify() {

        for (int i = size/2; i >= 1; i--)

            fixDown(i);

    }

}