Massive Algorithms: Princeton Programming Assignment 2 Checklist: Randomized Queues and Dequeues

Princeton Programming Assignment 2 Checklist: Randomized Queues and Dequeues

https://www.cnblogs.com/evasean/p/7204843.html

二、随机队列Randomized Queue

设计要求：A randomized queue is similar to a stack or queue, except that the item removed is chosen uniformly at random from items in the data structure.

异常处理：The order of two or more iterators to the same randomized queue must be mutually independent; each iterator must maintain its own random order. Throw a java.lang.IllegalArgumentException if the client attempts to add a null item; throw a java.util.NoSuchElementException if the client attempts to sample or dequeue an item from an empty randomized queue; throw a java.lang.UnsupportedOperationException if the client calls the remove() method in the iterator; throw a java.util.NoSuchElementException if the client calls the next() method in the iterator and there are no more items to return.

性能要求： Your randomized queue implementation must support each randomized queue operation (besides creating an iterator) in constant amortized time. That is, any sequence of m randomized queue operations (starting from an empty queue) should take at most cm steps in the worst case, for some constant c. A randomized queue containing nitems must use at most 48n + 192 bytes of memory. Additionally, your iterator implementation must support operations next() and hasNext() in constant worst-case time; and construction in linear time; you may (and will need to) use a linear amount of extra memory per iterator.

分析：

该队列每次移除的元素是随机的，性能要求提到迭代器的next方法必须是常数时间，很容易发现链表不容易满足该需求，需要用数组，代码如下：

 60     private void resize(int cap) {
 61         Item[] temp = (Item[]) new Object[cap];
 62         for (int i = 0; i < size; i++)
 63             temp[i] = rqArrays[i];
 64         rqArrays = temp;
 65     }
 66 
 67     public void enqueue(Item item) {
 68         // add the item
 69         valivate(item);
 70         rqArrays[size++] = item;
 71         if (size == rqArrays.length)
 72             resize(2 * rqArrays.length);
 73     }
 74 
 75     public Item dequeue() {
 76         // remove and return a random item
 77         // 随机选取一个位置，将这个位置的元素与队列末尾的元素交换位置
 78         // dequeue末尾元素时就达到随机remove元素的目的
 79         if (size == 0)
 80             throw new NoSuchElementException("the RandomizeQueue is empty!");
 81         int r = StdRandom.uniform(0, size);
 82         size--;
 83         Item delItem = rqArrays[r];
 84         rqArrays[r] = rqArrays[size];
 85         rqArrays[size] = null;
 86         if (size > 0 && size == rqArrays.length / 4)
 87             resize(rqArrays.length / 2);
 88         return delItem;
 89     }

http://coursera.cs.princeton.edu/algs4/assignments/queues.html
Dequeue. A double-ended queue or deque (pronounced "deck") is a generalization of a stack and a queue that supports adding and removing items from either the front or the back of the data structure. Create a generic data type Deque that implements the following API:

public class Deque<Item> implements Iterable<Item> {
   public Deque()                           // construct an empty deque
   public boolean isEmpty()                 // is the deque empty?
   public int size()                        // return the number of items on the deque
   public void addFirst(Item item)          // add the item to the front
   public void addLast(Item item)           // add the item to the end
   public Item removeFirst()                // remove and return the item from the front
   public Item removeLast()                 // remove and return the item from the end
   public Iterator<Item> iterator()         // return an iterator over items in order from front to end
   public static void main(String[] args)   // unit testing
}

Randomized queue. A randomized queue is similar to a stack or queue, except that the item removed is chosen uniformly at random from items in the data structure. Create a generic data type RandomizedQueue that implements the following API:

public class RandomizedQueue<Item> implements Iterable<Item> {
   public RandomizedQueue()                 // construct an empty randomized queue
   public boolean isEmpty()                 // is the queue empty?
   public int size()                        // return the number of items on the queue
   public void enqueue(Item item)           // add the item
   public Item dequeue()                    // remove and return a random item
   public Item sample()                     // return (but do not remove) a random item
   public Iterator<Item> iterator()         // return an independent iterator over items in random order
   public static void main(String[] args)   // unit testing
}

Corner cases. The order of two or more iterators to the same randomized queue must be mutually independent; each iterator must maintain its own random order. Throw a java.lang.NullPointerException if the client attempts to add a null item; throw a java.util.NoSuchElementException if the client attempts to sample or dequeue an item from an empty randomized queue; throw a java.lang.UnsupportedOperationException if the client calls the remove() method in the iterator; throw a java.util.NoSuchElementException if the client calls the next() method in the iterator and there are no more items to return.
Performance requirements. Your randomized queue implementation must support each randomized queue operation (besides creating an iterator) in constant amortized time. That is, any sequence of M randomized queue operations (starting from an empty queue) should take at most cM steps in the worst case, for some constant c. A randomized queue containing N items must use at most 48N + 192 bytes of memory. Additionally, your iterator implementation must support operations next() and hasNext() in constant worst-case time; and construction in linear time; you may (and will need to) use a linear amount of extra memory per iterator.
Subset client. Write a client program Subset.java that takes a command-line integer k; reads in a sequence of N strings from standard input using StdIn.readString(); and prints out exactly k of them, uniformly at random. Each item from the sequence can be printed out at most once. You may assume that 0 ≤ k ≤ N, where N is the number of string on standard input.

% echo A B C D E F G H I | java Subset 3       % echo AA BB BB BB BB BB CC CC | java Subset 8
C                                              BB
G                                              AA
A                                              BB
                                               CC
% echo A B C D E F G H I | java Subset 3       BB
E                                              BB
F                                              CC
G                                              BB

The running time of Subset must be linear in the size of the input. You may use only a constant amount of memory plus either one Deque or RandomizedQueue object of maximum size at most N, where N is the number of strings on standard input. (For an extra challenge, use only one Deque or RandomizedQueue object of maximum size at most k.) It should have the following API.

public class Subset {
   public static void main(String[] args)
}

http://coursera.cs.princeton.edu/algs4/checklists/queues.html

It is very important that you carefully plan your implementation before you begin. In particular, for each data structure that you're implementing (RandomizedQueue and Deque), you must decide whether to use a linked list, an array, or something else. If you make the wrong choice, you will not achieve the performance requirements and you will have to abandon your code and start over.
Make sure that your memory use is linear in the current number of items, as opposed to the greatest number of items that has ever been in the data structure since its instantiation. If you're using a resizing array, you must resize the array when it becomes sufficiently empty. You must also take care to avoid loitering anytime you remove an item.
Make sure to test what happens when your data structures are emptied. One very common bug is for something to go wrong when your data structure goes from non-empty to empty and then back to non-empty. Make sure to include this in your tests.
Make sure to test that multiple iterators can be used simultaneously. You can test this with a nested foreach loop. The iterators should operate independently of one another.
Don't rely on our automated tests for debugging. You don't have access to the source code of our testing suite, so the Assessment Details may be hard to utilize for debugging. As suggested above, write your own unit tests; it's good practice.
If you use a linked list, consider using a sentinel node (or nodes). Sentinel nodes can simplify your code and prevent bugs. However, they are not required (and we have not provided examples that use sentinel nodes).

http://www.jyuan92.com/blog/coursera-algorithmprinceton-hw2-queues/

public class Deque<Item> implements Iterable<Item> {

    private int N;

    private Node front;

    private Node end;

    private class Node {

        private Item item;

        private Node next;

        private Node prev;

}

/**

     * Initializes an empty Deque.

*/

    public Deque() {                          // construct an empty deque

        N = 0;

        front = null;

        end = null;

}

/**

*

     * @return whether the Deque is empty

*/

    public boolean isEmpty() {                // is the deque empty?

        // cannot use front == null to check whether the Deque is Empty.

        // Because when the Deque is empty and you add the first item into it. before the if statement

        // you have already let front.item = item. So it's not empty now.

        // return front == null;

        return N == 0;

}

/**

     * return the number of items in the Deque

*

     * @return the number of items in the Deque

*/

    public int size() {                       // return the number of items on the deque

        return N;

}

/**

     * add item into the front of the Deque

*

     * @param item

     * @throws NullPointerException if the input item is null

*/

    public void addFirst(Item item) {         // insert the item at the front

        if (item == null)

            throw new NullPointerException();

        Node newFront = front;

        front = new Node();

        front.prev = null;

        front.item = item;

        if (isEmpty()) {

            front.next = null;

            end = front;

        } else {

            front.next = newFront;

            newFront.prev = front;

}

        N++;

}

    public void addLast(Item item) {           // insert the item at the end

        if (item == null)

            throw new NullPointerException();

        Node newEnd = end;

        end = new Node();

        end.next = null;

        end.item = item;

        if (isEmpty()) {

            end.prev = null;

            front = end;

        } else {

            newEnd.next = end;

            end.prev = newEnd;

}

        N++;

}

    public Item removeFirst() {               // delete and return the item at the front

        if (isEmpty())

            throw new NoSuchElementException();

        Item item = front.item;

        // Should consider if there are just one node in the Linkedlist

        if(N == 1){

            front = null;

            end = null;

        }else{

            front = front.next;

            front.prev = null;

}

        N--;

        return item;

}

    public Item removeLast() {                // delete and return the item at the end

        if (isEmpty())

            throw new NoSuchElementException();

        Item item = end.item;

        if(N == 1){

            front = null;

            end = null;

        }else{

            end = end.prev;

            end.next = null;

}

        N--;

        return item;

}

/**

     * Returns an iterator to this stack that iterates through the items in LIFO order.

*

     * @return an iterator to this stack that iterates through the items in LIFO order.

*/

    public Iterator<Item> iterator() {        // return an iterator over items in order from front to end

        return new ListIterator();

}

    // an iterator, doesn't implement remove() since it's optional

    private class ListIterator implements Iterator<Item> {

        private Node current = front;

        public boolean hasNext() {

            return current != null;

}

        public Item next() {

            // check whether the current is null, not current->next is null!

            if (current == null)

                throw new NoSuchElementException();

            Item item = current.item;

            current = current.next;

            return item;

}

//

        public void remove() {

            throw new UnsupportedOperationException();

}

}

In the isEmpty() method，you cannot directly use “front == null” to check whether the Deque is or not empty, because when the Deque is empty and you add the first item into it. before the if statement you have already let front.item = item. So it’s not empty now.
Don’t forget to throw exception when necessary, such as if the insert item is null, or when you want to remove from an empty Deque, you should throw NoSuchElementException()
No matter which method{addFirst(), addLast(), removeFirst(), removeLast()}, you should always consider: what if the Deque is empty?

public class RandomizedQueue<Item> implements Iterable<Item> {

    private int length;

    private Item items[];

    public RandomizedQueue() {                // construct an empty randomized queue

        // java cannot create a generic array, so we should use cast to implements this

        items = (Item[]) new Object[2];

        length = 0;

}

    public boolean isEmpty() {                // is the queue empty?

        return length == 0;

}

    public int size() {                       // return the number of items on the queue

        return length;

}

    private void resize(int n) {

        Item newItems[] = (Item[]) new Object[n];

        for (int i = 0; i < length; i++) {

            newItems[i] = items[i];

}

        items = newItems;

}

    public void enqueue(Item item) {          // add the item

        if (item == null)

            throw new NullPointerException();

        if (length == items.length)

            resize(items.length * 2);

        items[length] = item;

        length++;

}

    public Item dequeue() {                   // delete and return a random item

        if (isEmpty())

            throw new NoSuchElementException();

        int random = StdRandom.uniform(length);

        Item item = items[random];

        if (random != length - 1)

            items[random] = items[length - 1];

        // don't forget to put the newArray[newLength] to be null to avoid Loitering

        // Loitering: Holding a reference to an object when it is no longer needed.

        items[length - 1] = null;

        length--;

        if (length > 0 && length == items.length / 4)

            resize(items.length / 2);

        return item;

}

    public Item sample() {                    // return (but do not delete) a random item

        if (isEmpty())

            throw new NoSuchElementException();

        int random = StdRandom.uniform(length);

        Item item = items[random];

        return item;

}

    public Iterator<Item> iterator() {        // return an independent iterator over items in random order

        return new QueueIterator();

}

    private class QueueIterator implements Iterator<Item> {

        // Must copy the item in items[] into a new Array

        // Because when create two independent iterators to same randomized queue, the original one

        // has been changed and the second one will lead to false result.

        private int index = 0;

        private int newLength = length;

        private Item newArray[] = (Item[]) new Object[length];

        private QueueIterator() {

            for (int i = 0; i < newLength; i++) {

                newArray[i] = items[i];

}

}

        public boolean hasNext() {

            return index <= newLength - 1;

}

        public Item next() {

            if (newArray[index] == null)

                throw new NoSuchElementException();

//            Item item = items[index];

//            index++;

//            return item;

            int random = StdRandom.uniform(newLength);

            Item item = newArray[random];

            if (random != newLength - 1)

                newArray[random] = newArray[newLength - 1];

            newLength--;

            newArray[newLength] = null;

//            if (newLength > 0 && newLength == newArray.length / 4)

//                resize(newArray.length / 2);

            return item;

}

        public void remove() {

            throw new UnsupportedOperationException();

}

}

Because the output of it is randomized, so when we implement those method, we do not need to use front and end pointers, just use tail pointers direct to the array.length when execute enqueue() method.
Everytime when you do a dequeue(), the item in that index should delete, what should we do next?: put the item in array[length-1] position to the item you delete. And don’t forget!!! put the array[length-1] to be null to avoid Loitering(Holding a reference to an object when it is no longer needed)
Java don’t support generic array, so we must use cast to implements this, like items = (Item[]) new Object[2]
Don’t forget to check the really array size, and use resize() method to release space. That’s very important when doing an interview.
When implements the Iterator, you must create a new array and copy the item from the original array. Because when create two independent iterators to same randomized queue, the original one has been changed and the second one will lead to false result.

根据指定的性能和API要求，选择适当的实现方式（动态数组、单、双向链表），实现Randomized Queue和Deque，主要训练基本的算法分析和编程严谨性（完善处理corner-case），但并无特别的难点。有两个小技巧可以提出：链表可使用sentinel node(s)使代码更简洁（checklist已提），写client时可先shuffle再插入(bonus)。

 * Write a client program Subset.java that takes a command-line integer k; reads in a sequence of

 * N strings from standard input using StdIn.readString(); and prints out exactly k of them,

 * uniformly at random. Each item from the sequence can be printed out at most once. You may assume

 * that 0 ≤ k ≤ N, where N is the number of string on standard input.

*/

public class Subset {

    public static void main(String[] args) {

        RandomizedQueue<String> randomizedQueue = new RandomizedQueue<String>();

        int k = Integer.parseInt(args[0]);

        int count = 0;

        while (!StdIn.isEmpty()) {

            randomizedQueue.enqueue(StdIn.readString());

            count++;

}

        while (count - k > 0) {

            randomizedQueue.dequeue();

            count--;

}

        for (int i = 0; i < k; i++)

            StdOut.println(randomizedQueue.dequeue());

}

https://github.com/vgoodvin/princeton-algs4/blob/master/Randomized%20Queues%20and%20Deques/RandomizedQueue.java
public class RandomizedQueue<Item> implements Iterable<Item> {

private List<Item> list;

/**
* Construct an empty randomized queue
*/
public RandomizedQueue() {
list = new ArrayList<Item>();
}

/**
* Is the queue empty?
* @return boolean
*/
public boolean isEmpty() {
return list.isEmpty();
}

/**
* return the number of items on the queue
* @return integer
*/
public int size() {
return list.size();
}

/**
* Add the item
* @param item
*/
public void enqueue(Item item) {
if (item == null) {
throw new java.lang.NullPointerException();
}
list.add(item);
}

/**
* delete and return a random item
* @return
*/
public Item dequeue() {
if (isEmpty()) {
throw new java.util.NoSuchElementException();
}
int index = StdRandom.uniform(size());
return (Item) list.remove(index);
}

/**
* return (but do not delete) a random item
* @return
*/
public Item sample() {
if (isEmpty()) {
throw new java.util.NoSuchElementException();
}
int index = StdRandom.uniform(size());
return (Item) list.get(index);
}

private class RandomizedQueueIterator<E> implements Iterator<E> {
public boolean hasNext() {
return size() > 0;
}
public E next() {
if (isEmpty()) {
throw new java.util.NoSuchElementException();
}
return (E) dequeue(); //not good
}
public void remove() {
throw new java.lang.UnsupportedOperationException();
}
}

/**
* return an independent iterator over items in random order
* @return
*/
public Iterator<Item> iterator() {
return new RandomizedQueueIterator<Item>();
}
}
https://github.com/zhichaoh/Coursera-Algorithms/blob/master/src/RandomizedQueue.java
public class RandomizedQueue<Item> implements Iterable<Item> {

private List<Item> queue;

private int count = 0;

public RandomizedQueue() { // construct an empty randomized queue
queue = new ArrayList<Item>();
count = 0;
}

public boolean isEmpty() { // is the queue empty?
return count == 0;
}

public int size() { // return the number of items on the queue
return count;
}

public void enqueue(Item item) { // add the item
if(item==null) throw new java.lang.NullPointerException();
queue.add(item);
queue.set(count, item);
count ++;
}

public Item dequeue() { // delete and return a random item
if(isEmpty()) throw new java.util.NoSuchElementException();
int pt = (int)(Math.random()*count);
Item current = queue.get(pt);
queue.set(pt, queue.get(count-1));
count--;
queue.remove(count);
return current;
}

public Item sample() { // return (but do not delete) a random item
if(isEmpty()) throw new java.util.NoSuchElementException();
int pt = (int)(Math.random()*count);
return queue.get(pt);
}

public Iterator<Item> iterator() { // return an independent iterator over items in random order
return new RandomizedQueueIterator();
}

private class RandomizedQueueIterator implements Iterator<Item> {

List<Item> rQ = null;

int pt;

public RandomizedQueueIterator(){
rQ = new ArrayList<Item>();
for(int i=0;i<count;i++)
rQ.add(queue.get(i));
Collections.shuffle(rQ);
pt = 0;
}

@Override
public boolean hasNext() {
return pt<count;
}

@Override
public Item next() {
if(!hasNext()) throw new java.util.NoSuchElementException();
Item current = rQ.get(pt);
pt ++;
return current;
}

@Override
public void remove() {
throw new UnsupportedOperationException();
}

}
http://blog.csdn.net/liuweiran900217/article/details/18906209

Princeton Programming Assignment 2 Checklist: Randomized Queues and Dequeues

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