堆排序和优先级队列

堆排序代码

package chap6;

public class Heap {//堆存在数组中
	private int heapsize;
	public void maxHeapify(int A[],int i)//使i为根的子树成为大顶堆
	{
		int l=2*i;//左子树
		int r=2*i+1;//右子树
		int largest;
		if (l<=heapsize && A[l-1]>A[i-1]) {//树的下标从1开始，数组下标从0开始,所以取元素的时候-1
			largest=l;//左子树比跟大，左子树标记为largest
		}else {
			largest=i;//否则默认根为largest
		}
		if (r<=heapsize && A[r-1]>A[largest-1]) {
			largest=r;//在左根右中，右最大，标记为largest
		}
		if (largest!=i) {//根与左右子树中较大元素交换
			int tmp=A[i-1];
			A[i-1]=A[largest-1];
			A[largest-1]=tmp;
			maxHeapify(A, largest);//再递归调整largest为根的子树
		}
	}
	
	public void buildMaxHeap(int A[])//构建大顶堆
	{
		for(int i=A.length/2; i>0 ; i--)//从size/2下标开始往根方向调整，因为后面的都是叶子结点，没有子树
		{
			maxHeapify(A, i);
		}
	}
	
	public void heapSort(int A[]) {//将根与最后元素交换，然后heapsize-1
		heapsize=A.length;
		buildMaxHeap(A);
		for(int i=A.length;i>1;i--)
		{
			A[0]=A[0]^A[i-1];
			A[i-1]=A[0]^A[i-1];
			A[0]=A[0]^A[i-1];
			heapsize--;
			maxHeapify(A, 1);//将剩下的继续调整
		}
	}
	public int getHeapsize() {
		return heapsize;
	}
	public void setHeapsize(int heapsize) {
		this.heapsize = heapsize;
	}
	public static void main(String[] args) {
		int A[]={20,9,30,15,1,12,0,-1,100,20};
		Heap h = new Heap();
		h.heapSort(A);
		for (int i : A) {
			System.out.println(i);
		}
	}
}

 

优先队列代码，其中使用到堆

package chap6;

public class PriorityQueue {
	private static Heap h=new Heap();
	public int heapMaximum(int A[])
	{
		return A[0];
	}
	public int heapExtractMax(int A[]) {
		if(h.getHeapsize()<1)
		{
			System.out.println("堆溢出！");
		}
		int max=A[0];
		A[0]=A[h.getHeapsize()-1];
		h.setHeapsize(h.getHeapsize()-1);
		h.maxHeapify(A, 1);
		return max;
	}
	public void heapIncreaseKey(int A[],int i,int key)
	{
		if (key<A[i-1]) {
			System.out.println("new key is smaller than current key!");
		}
		A[i-1]=key;
		while (i>1 && A[i/2-1]<A[i-1]) {//与父节点相比，不断上移，使其满足大顶堆性质
			A[i-1]=A[i/2-1]^A[i-1];
			A[i/2-1]=A[i/2-1]^A[i-1];
			A[i-1]=A[i/2-1]^A[i-1];
			i=i/2;//i往上移动
		}
	}
	
	public void maxHeapInsert(int A[],int key)
	{
		h.setHeapsize(h.getHeapsize()+1);
		heapIncreaseKey(A, h.getHeapsize(), key);
	}
	public static void main(String[] args) {
		int A[]=new int[100];
		h.setHeapsize(0);
		PriorityQueue p=new PriorityQueue();
		p.maxHeapInsert(A, 10);
		p.maxHeapInsert(A, 20);
		p.maxHeapInsert(A, 21);
		p.maxHeapInsert(A, 2);
		p.maxHeapInsert(A, 18);
		System.out.println(p.heapMaximum(A));
		System.out.println(p.heapExtractMax(A));
		System.out.println(p.heapMaximum(A));
		p.heapIncreaseKey(A, 5, 22);
		p.maxHeapInsert(A, 180);
		System.out.println(p.heapMaximum(A));
	}
}