数据结构(Java)——堆的应用

生活总是会有大喜大悲，人生总是会有大起大落！不以物喜，不以己悲~

1.优先级队列的实现

优先级队列是遵循两个排序规则的集合。首先，具有更高优先级的项目在先。第二，具有相同优先级的项目使用先进先出的方法确定其排序。

首先我们创建一个PrioritizedObject对象，它存储的是将被放置在队列中的元素，该元素的优先级以及该元素放进队列的顺序。然后我们需要为它定义一个compareTo方法。

package ds.java.ch12;
/**
 * PrioritizedObject represents a node in a priority queue containing a
 * comparable object, arrival order, and a priority value.
 * 
 * @author Lewis and Chase
 * @version 4.0
 */
public class PrioritizedObject<T> implements Comparable<PrioritizedObject>
{
    private static int nextOrder = 0;
    private int priority;
    private int arrivalOrder;
    private T element;

    /**
     * Creates a new PrioritizedObject with the specified data.
     *
     * @param element the element of the new priority queue node
     * @param priority the priority of the new queue node
     */
    public PrioritizedObject(T element, int priority) 
    {
        this.element = element;
        this.priority = priority;
        arrivalOrder = nextOrder;
        nextOrder++;
    }

    /**
     * Returns the element in this node.
     *
     * @return the element contained within the node
     */
    public T getElement() 
    {
        return element;
    }

    /**
     * Returns the priority value for this node.
     *
     * @return the integer priority for this node
     */
    public int getPriority() 
    {
        return priority;
    }

    /**
     * Returns the arrival order for this node.
     *
     * @return the integer arrival order for this node
     */
    public int getArrivalOrder() 
    {
        return arrivalOrder;
    }

    /**
     * Returns a string representation for this node.
     *
     */
    public String toString() 
    {
        return (element + "  " + priority + "  " + arrivalOrder);
    }

    /**
     * Returns 1 if the this object has higher priority than 
     * the given object and -1 otherwise.
     *
     * @param obj the object to compare to this node
     * @return the result of the comparison of the given object and 
     *         this one
     */
    public int compareTo(PrioritizedObject obj) 
    {
      int result;

      if (priority > obj.getPriority())
          result = 1;
      else if (priority < obj.getPriority())
          result = -1;
      else if (arrivalOrder > obj.getArrivalOrder())
          result = 1;
      else
          result = -1;

      return result;
    }
}

优先级队列的实现

package ds.java.ch12;
import ds.java.ch12.heapImpl.ArrayHeap;

/**
 * PriorityQueue implements a priority queue using a heap.
 * 
 * @author Lewis and Chase
 * @version 4.0
 */
public class PriorityQueue<T> extends ArrayHeap<PrioritizedObject<T>>
{
    /**
     * Creates an empty priority queue.
     */
    public PriorityQueue() 
    {
        super();
    }

    /**
     * Adds the given element to this PriorityQueue.
     *
     * @param object the element to be added to the priority queue
     * @param priority the integer priority of the element to be added
     */
    public void addElement(T object, int priority) 
    {
        PrioritizedObject<T> obj = new PrioritizedObject<T>(object, priority);
        super.addElement(obj);
    }

    /**
     * Removes the next highest priority element from this priority 
     * queue and returns a reference to it.
     *
     * @return a reference to the next highest priority element in this queue
     */
    public T removeNext() 
    {
        PrioritizedObject<T> obj = (PrioritizedObject<T>)super.removeMin();
        return obj.getElement();
    }
}

2.堆排序的实现

package ds.java.ch12;

import ds.java.ch12.heapImpl.ArrayHeap;

/**
 * HeapSort sorts a given array of Comparable objects using a heap.
 * 
 * @author Lewis and Chase
 * @version 4.0
 */
public class HeapSort<T> {
    /**
     * Sorts the specified array using a Heap
     * 
     * @param data
     *            the data to be added to the heapsort
     */
    public void HeapSort(T[] data) {
        ArrayHeap<T> temp = new ArrayHeap<T>();

        // copy the array into a heap
        for (int i = 0; i < data.length; i++)
            temp.addElement(data[i]);

        // place the sorted elements back into the array
        int count = 0;
        while (!(temp.isEmpty())) {
            data[count] = temp.removeMin();
            count++;
        }
    }

    public static void main(String[] args) {
        Integer[] data = {3,1,2,5,8,7,6,9,0,4};
        HeapSort hs = new HeapSort<Integer>();
        hs.HeapSort(data);
        for(int i=0;i<data.length;i++){
            System.out.println(data[i]);
        }

    }

}

３.堆一些知识点总结

• 如果一个堆是平衡的，即所有的叶子都位于层h或h-1，其中h为log2n且n是树中的元素数目，以及所有层h中的叶子都位于树的左边，那么该堆就是完全的。
• 一个完全堆是平衡的并且添加删除算法保持了该堆的平衡性。
• add操作必须确定插入点的双亲，这样能够将该结点的某一个孩子指针设定为指向新结点。数组实现不一定需要确定新结点的双亲，因为数组实现是拥有count位置来定位的。
• 数组实现的堆的插入和删除都是更高效的。