Java 数据结构-随机化队列
我目前正在从事普林斯顿算法第一部分的工作。其中一项任务是实现随机队列。这是一个关于使用不同数据结构的实现和权衡的问题 问题: 随机化队列类似于堆栈或队列,不同之处在于移除的项是从数据结构中的项中统一随机选择的。创建实现以下API的通用数据类型RandomizedQueue:Java 数据结构-随机化队列,java,random,data-structures,queue,Java,Random,Data Structures,Queue,我目前正在从事普林斯顿算法第一部分的工作。其中一项任务是实现随机队列。这是一个关于使用不同数据结构的实现和权衡的问题 问题: 随机化队列类似于堆栈或队列,不同之处在于移除的项是从数据结构中的项中统一随机选择的。创建实现以下API的通用数据类型RandomizedQueue: public class RandomizedQueue<Item> implements Iterable<Item> { public RandomizedQueue() // const
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
}
查询1.2:为了让迭代器满足随机返回元素的要求,我创建了一个包含队列所有索引的新数组,然后使用Knuth shuffle操作对数组进行洗牌,并返回队列中特定索引处的元素。但是,这需要创建一个等于队列长度的新数组。同样,我确信我错过了一个更有效的方法
2。内部类实现
第二个实现涉及一个内部节点类
public class RandomizedQueue<Item> {
private static class Node<Item> {
Item item;
Node<Item> next;
Node<Item> previous;
}
}
公共类随机化队列{
私有静态类节点{
项目;
节点下一步;
节点前向;
}
}
问题2.1。在本例中,我了解如何高效地执行出列操作:返回一个随机节点并更改相邻节点的引用
然而,我对如何返回一个迭代器感到困惑,该迭代器以随机顺序返回节点,而不必创建一个以随机顺序连接节点的全新队列
此外,除了可读性和易于实现之外,在阵列上使用这种数据结构还有什么好处
这篇文章有点长。我感谢你们花时间阅读我的问题并帮助我解决问题。谢谢 在数组实现中,查询1.1似乎是最好的方法。移除随机元素的唯一其他方法是将所有元素向上移动以填充其位置。因此,如果您有
[1,2,3,4,5]
并且删除了2
,那么您的代码将向上移动项目3、4和5,并减少计数。这将采取,平均n/2的项目移动,每次删除。所以移除是O(n)。糟糕
如果在迭代时不添加和删除项目,那么只需在现有数组上使用Fisher-Yates shuffle,并开始从前到后返回项目。没有理由复制。这取决于你的使用模式。如果您设想在迭代时从队列中添加和删除项目,那么如果您不创建副本,事情就会变得不稳定
使用链表方法,很难有效地实现随机出列操作,因为为了获得随机项,必须从前面遍历列表。因此,如果您在队列中有100个项目,并且您想要删除第85个项目,那么您必须从前面开始,在到达要删除的项目之前,遵循85个链接。由于您使用的是一个双链接列表,当要删除的项目超过中间点时,您可以通过从末尾倒数来将时间减少一半,但当队列中的项目数量很大时,这仍然是非常低效的。想象一下,从一百万个项目的队列中删除第500000个项目
对于随机迭代器,可以在开始迭代之前将链表洗牌。这需要O(n logn)时间,但只需要O(1)额外的空间。同样,在添加或删除的同时,也存在迭代的问题。如果您想要这种能力,那么您需要创建一个副本。您不需要在创建迭代器时洗牌整个数组副本,而是在使用
next()
方法访问每个元素时懒洋洋地对其进行洗牌。使用数组实现(必须是动态的/可调整大小的),以实现常量(摊销)除构建迭代器之外的所有操作的最坏情况运行时(由于无序排列,这需要线性时间)
以下是我的实现:
import java.util.Arrays;
import java.util.Iterator;
import java.util.NoSuchElementException;
import java.util.Random;
/* http://coursera.cs.princeton.edu/algs4/assignments/queues.html
*
* 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.
*/
public class RandomizedQueue<T> implements Iterable<T> {
private int queueEnd = 0; /* index of the end in the queue,
also the number of elements in the queue. */
@SuppressWarnings("unchecked")
private T[] queue = (T[]) new Object[1]; // array representing the queue
private Random rGen = new Random(); // used for generating uniformly random numbers
/**
* Changes the queue size to the specified size.
* @param newSize the new queue size.
*/
private void resize(int newSize) {
System.out.println("Resizing from " + queue.length + " to " + newSize);
T[] newArray = Arrays.copyOfRange(queue, 0, newSize);
queue = newArray;
}
public boolean isEmpty() {
return queueEnd == 0;
}
public int size() {
return queueEnd;
}
/**
* Adds an element to the queue.
* @param elem the new queue entry.
*/
public void enqueue(T elem) {
if (elem == null)
throw new NullPointerException();
if (queueEnd == queue.length)
resize(queue.length*2);
queue[queueEnd++] = elem;
}
/**
* Works in constant (amortized) time.
* @return uniformly random entry from the queue.
*/
public T dequeue() {
if (queueEnd == 0) // can't remove element from empty queue
throw new UnsupportedOperationException();
if (queueEnd <= queue.length/4) // adjusts the array size if less than a quarter of it is used
resize(queue.length/2);
int index = rGen.nextInt(queueEnd); // selects a random index
T returnValue = queue[index]; /* saves the element behind the randomly selected index
which will be returned later */
queue[index] = queue[--queueEnd]; /* fills the hole (randomly selected index is being deleted)
with the last element in the queue */
queue[queueEnd] = null; // avoids loitering
return returnValue;
}
/**
* Returns the value of a random element in the queue, doesn't modify the queue.
* @return random entry of the queue.
*/
public T sample() {
int index = rGen.nextInt(queueEnd); // selects a random index
return queue[index];
}
/*
* Every iteration will (should) return entries in a different order.
*/
private class RanQueueIterator implements Iterator<T> {
private T[] shuffledArray;
private int current = 0;
public RanQueueIterator() {
shuffledArray = queue.clone();
shuffle(shuffledArray);
}
@Override
public boolean hasNext() {
return current < queue.length;
}
@Override
public T next() {
if (!hasNext())
throw new NoSuchElementException();
return shuffledArray[current++];
}
/**
* Rearranges an array of objects in uniformly random order
* (under the assumption that {@code Math.random()} generates independent
* and uniformly distributed numbers between 0 and 1).
* @param array the array to be shuffled
*/
public void shuffle(T[] array) {
int n = array.length;
for (int i = 0; i < n; i++) {
// choose index uniformly in [i, n-1]
int r = i + (int) (Math.random() * (n - i));
T swap = array[r];
array[r] = array[i];
array[i] = swap;
}
}
}
@Override
public Iterator<T> iterator() {
return new RanQueueIterator();
}
public static void main(String[] args) {
RandomizedQueue<Integer> test = new RandomizedQueue<>();
// adding 10 elements
for (int i = 0; i < 10; i++) {
test.enqueue(i);
System.out.println("Added element: " + i);
System.out.println("Current number of elements in queue: " + test.size() + "\n");
}
System.out.print("\nIterator test:\n[");
for (Integer elem: test)
System.out.print(elem + " ");
System.out.println("]\n");
// removing 10 elements
for (int i = 0; i < 10; i++) {
System.out.println("Removed element: " + test.dequeue());
System.out.println("Current number of elements in queue: " + test.size() + "\n");
}
}
}
导入java.util.array;
导入java.util.Iterator;
导入java.util.NoSuchElementException;
导入java.util.Random;
/* http://coursera.cs.princeton.edu/algs4/assignments/queues.html
*
*随机化队列类似于堆栈或队列,不同之处在于
*删除是从数据结构中的项中随机统一选择的。
*/
公共类RandomizedQueue实现了Iterable{
private int queueEnd=0;/*队列中结束的索引,
还包括队列中的元素数*/
@抑制警告(“未选中”)
私有T[]队列=(T[])新对象[1];//表示队列的数组
private Random rGen=new Random();//用于生成一致随机数
/**
*将队列大小更改为指定的大小。
*@param newSize新队列大小。
*/
私有void resize(int newSize){
System.out.println(“从“+queue.length+”调整到“+newSize”);
T[]newArray=Arrays.copyOfRange(队列,0,新闻大小);
队列=新数组;
}
公共布尔值为空(){
返回queueEnd==0;
}
公共整数大小(){
返回队列结束;
}
/**
*将元素添加到队列中。
*@param elem创建新的队列条目。
*/
公共无效排队(T元素){
if(elem==null)
抛出新的NullPointerException();
if(queueEnd==queue.length)
调整大小(队列长度*2);
队列[queueEnd++]=elem;
}
/**
*以固定(摊销)时间工作。
*@return从队列中统一随机输入。
*/
公共T出列(){
if(queueEnd==0)//无法从空队列中删除元素
抛出新的UnsupportedOperationException();
if(queueEnd对于查询1.1:这里确实可以在固定时间内删除随机元素。
其思路如下:
- 选择要返回的随机元素
- 西南
import java.util.Arrays;
import java.util.Iterator;
import java.util.NoSuchElementException;
import java.util.Random;
/* http://coursera.cs.princeton.edu/algs4/assignments/queues.html
*
* 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.
*/
public class RandomizedQueue<T> implements Iterable<T> {
private int queueEnd = 0; /* index of the end in the queue,
also the number of elements in the queue. */
@SuppressWarnings("unchecked")
private T[] queue = (T[]) new Object[1]; // array representing the queue
private Random rGen = new Random(); // used for generating uniformly random numbers
/**
* Changes the queue size to the specified size.
* @param newSize the new queue size.
*/
private void resize(int newSize) {
System.out.println("Resizing from " + queue.length + " to " + newSize);
T[] newArray = Arrays.copyOfRange(queue, 0, newSize);
queue = newArray;
}
public boolean isEmpty() {
return queueEnd == 0;
}
public int size() {
return queueEnd;
}
/**
* Adds an element to the queue.
* @param elem the new queue entry.
*/
public void enqueue(T elem) {
if (elem == null)
throw new NullPointerException();
if (queueEnd == queue.length)
resize(queue.length*2);
queue[queueEnd++] = elem;
}
/**
* Works in constant (amortized) time.
* @return uniformly random entry from the queue.
*/
public T dequeue() {
if (queueEnd == 0) // can't remove element from empty queue
throw new UnsupportedOperationException();
if (queueEnd <= queue.length/4) // adjusts the array size if less than a quarter of it is used
resize(queue.length/2);
int index = rGen.nextInt(queueEnd); // selects a random index
T returnValue = queue[index]; /* saves the element behind the randomly selected index
which will be returned later */
queue[index] = queue[--queueEnd]; /* fills the hole (randomly selected index is being deleted)
with the last element in the queue */
queue[queueEnd] = null; // avoids loitering
return returnValue;
}
/**
* Returns the value of a random element in the queue, doesn't modify the queue.
* @return random entry of the queue.
*/
public T sample() {
int index = rGen.nextInt(queueEnd); // selects a random index
return queue[index];
}
/*
* Every iteration will (should) return entries in a different order.
*/
private class RanQueueIterator implements Iterator<T> {
private T[] shuffledArray;
private int current = 0;
public RanQueueIterator() {
shuffledArray = queue.clone();
shuffle(shuffledArray);
}
@Override
public boolean hasNext() {
return current < queue.length;
}
@Override
public T next() {
if (!hasNext())
throw new NoSuchElementException();
return shuffledArray[current++];
}
/**
* Rearranges an array of objects in uniformly random order
* (under the assumption that {@code Math.random()} generates independent
* and uniformly distributed numbers between 0 and 1).
* @param array the array to be shuffled
*/
public void shuffle(T[] array) {
int n = array.length;
for (int i = 0; i < n; i++) {
// choose index uniformly in [i, n-1]
int r = i + (int) (Math.random() * (n - i));
T swap = array[r];
array[r] = array[i];
array[i] = swap;
}
}
}
@Override
public Iterator<T> iterator() {
return new RanQueueIterator();
}
public static void main(String[] args) {
RandomizedQueue<Integer> test = new RandomizedQueue<>();
// adding 10 elements
for (int i = 0; i < 10; i++) {
test.enqueue(i);
System.out.println("Added element: " + i);
System.out.println("Current number of elements in queue: " + test.size() + "\n");
}
System.out.print("\nIterator test:\n[");
for (Integer elem: test)
System.out.print(elem + " ");
System.out.println("]\n");
// removing 10 elements
for (int i = 0; i < 10; i++) {
System.out.println("Removed element: " + test.dequeue());
System.out.println("Current number of elements in queue: " + test.size() + "\n");
}
}
}