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【数据结构】(二叉树的Java与C++实现)

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二叉树作为重要的数据结构类型,本篇二叉树内部方法的实现多采用了递归,实现了诸如(四种遍历\结点删除\结点查找\叶子数量\高度\判断是否完全二叉树\某层结点数)等方法,是值得一读的二叉树的实现 ʅ(‾◡◝)ʃ

前言

树结构的知识点比较复杂，在本篇中学习了很多Java用递归方式编写的函数体，值得一读。惰性删除是指当一个元素要被删除时，它仍被保留在树中，只是标记为删除了，这在有重复项的时候很常用，因为此时记录出现频率数的域可以减1，如果树中的实际节点数与“被删除”的节点数相同，那么树的深度预计只上升一个小的常数，因此存在一个与惰性删除相关的非常小的时间损耗，并且，如果被删除的项是重新插入的，那么久避免了分配一个新单元的开销了
IMG_6581.jpg

二叉树的Java实现

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package BinaryTree;

import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;

public class BiTree{

	private int count;
	private Node root;
	public int index;
	class Node {

		public Node lchild;
		public Node rchild;
		public int data;
		public Node(int data) {
			this.data = data;
		}
		public Node getLchild() {
			return lchild;
		}
		public void setLchild(Node lchild) {
			this.lchild = lchild;
		}
		public Node getRchild() {
			return rchild;
		}
		public void setRchild(Node rchild) {
			this.rchild = rchild;
		}
		public int getData() {
			return data;
		}
		public void setData(int data) {
			this.data = data;
		}
	}
	//二叉树的建立
	public Node CreateBTree(int[] a){
		Node root = null;
		if(a[index]!='#'){
			root = new Node(a[index]);
			index++;
			root.setLchild(CreateBTree(a));
			index++;
			root.setRchild(CreateBTree(a));		
		}
		return root;
	}
	//二叉树节点的删除
	public boolean delete(int data) {
		Node current = root;
		Node parent = root;
		boolean isleftchild = false;
		while(current.data!=data) {
			parent = current;
			if(current.data>data) {
				isleftchild = true;
				current = current.lchild;
			}else{
				isleftchild = false;
				current = current.rchild;
			}
			if(current == null) {
				return false;
			}
		}
		//被删除的节点没有子节点
		if(current.lchild==null &&current.rchild==null) {
			if(current==root) {
				root = null;
			}else if(isleftchild) {
				parent.lchild = null;
			}else {
				parent.rchild = null;
			}
			return true;
		}
		//被删除的节点有一个子节点
		if(current.lchild==null&&current.rchild!=null) {
			if(root == current) {
				root = current.rchild;
			}else if(isleftchild) {
				parent.lchild = current.rchild;
			}else {
				parent.rchild = current.rchild;
			}
		}else if(current.lchild!=null&&current.rchild==null) {
			if(root == current) {
				root = current.lchild;
			}else if(isleftchild) {
				parent.lchild = current.lchild;
			}else {
				parent.rchild = current.lchild;
		    }
	    }
		//被删除的节点有两个子节点
		if(current.lchild != null && current.rchild != null){
            //获取删除节点的后继结点
            Node successor = getSuccessor(current);
            if (root == current) {
                root = successor;
            } else if (isleftchild) {
                parent.lchild = successor;
            } else {
                parent.rchild = successor;
            }
		}
		return false;
	}
    public Node getSuccessor(Node delNode) {
        Node successorParent = delNode;
        Node successor = delNode;
        Node current = delNode.rchild;
        while (current != null) {
            successorParent = successor;
            successor = current;
            current = current.lchild;
        }
        if (successor != delNode.rchild) {
            successorParent.lchild = successor.rchild;
            successor.rchild = delNode.rchild;
        }
        return successor;
    }
    //先序遍历
    public void prevOrder(Node root) {
    	if(root == null) {
    		return;
    	}
    	System.out.print(root.getData()+" ");
    	prevOrder(root.getLchild());
    	prevOrder(root.getRchild());
    }
    //中序遍历
    public void inOrder(Node root) {
    	if(root==null) {
    		return;
    	}
    	inOrder(root.getLchild());
    	System.out.print(root.getData()+" ");
    	inOrder(root.getRchild());
    }
    //后序遍历
    public void postOrder(Node root) {
    	if(root==null) {
    		return;
    	}
    	postOrder(root.getLchild());
    	postOrder(root.getRchild());
    	System.out.print(root.getData()+" ");
    }
    //层序遍历
    public void BTreeLevelOrder(){
    	Node root = this.root;
    	Queue <Node> queue = new LinkedList<Node>();
    	LinkedList<Node> list = new LinkedList<Node>();
    	queue.offer(root);
    	while(!queue.isEmpty()){
    		Node pre = queue.poll();
    		list.add(pre);
    		if(pre.getLchild()!=null)
    			queue.offer(pre.getLchild());
    		if(pre.getRchild()!=null)
    			queue.offer(pre.getRchild());
    	}
    	Iterator<Node> it = list.iterator();
    	while(it.hasNext()){
    		Node cur = (Node)it.next();
    		System.out.print(cur.getData()+" ");
    	}	
    }
    //获得二叉树的高度
  	public int getHeight(Node root){
  		//递归获取
  		int leftHeight = 0;
  		int rightHeight = 0;
  		if(root==null){
  			return 0;
  		}else{
  			leftHeight = getHeight(root.getLchild());
  			rightHeight = getHeight(root.getRchild());
  		}
  		return leftHeight >= rightHeight ? ++leftHeight:++rightHeight; //最终高度应是左右子树高度中最大的一个
  	}
  	//获得二叉树的叶子结点
  	public int getLeaf(Node root) {
  		if(root == null) {
  			return 0;
  		}else if(root.getLchild()==null&&root.getRchild()==null) {
  			System.out.println("叶子结点："+root.getData());
  			return 1;
  		}
  		return getLeaf(root.getLchild())+getLeaf(root.getRchild());
  	}
  	//获得二叉树某一层的节点
  	public int getNum(Node root, int deep) {
  		if(deep == 1) {
  			if(root==null) {
  				return 0;
  			}else {
  				System.out.println("结点："+root.getData());
  				return 1;
  			}
  		}
  		return getNum(root.getLchild(), deep-1)+getNum(root.getRchild(), deep-1);
  	}
  	//查找某一值结点
  	public Node search(Node root, int key) {
  		if(root==null) {
  			return null;
  		}else if(root.getData()==key) {
  			return root;
  		}
  		Node left = search(root.getLchild(), key);
  		if(left!=null) {
  			return left;
  		}
  		Node right = search(root.getRchild(), key);
  		if(right!=null) {
  			return right;
  		}
  		return null;
  	}
    //判断某一结点是否存在
  	public boolean isNull(Node root) {
  		return root!=null;
  	}
    //判断一棵树是否是完全二叉树
	public boolean isCompleteBTree(){
		Node root = this.root;
		Queue <Node> queue = new LinkedList<Node>();
		queue.offer(root);
	
		while(!queue.isEmpty()){
			Node pre = queue.poll();
			if(pre==null)
				break;
			queue.offer(pre.getLchild());
			queue.offer(pre.getRchild());
			
		}
		while(!queue.isEmpty()){
			Node cur = queue.poll();
			if(cur!=null)
				return false;
		}
		return true;
     }
    public static void main(String[] args) {
		BiTree tree = new BiTree();
		int[] a = new int[]{1,2,'#',3,'#',4,'#','#',5,6,'#','#','#' };
		tree.root = tree.CreateBTree(a);
		System.out.println("先序遍历：");
		tree.prevOrder(tree.root);
		System.out.println();
		System.out.println("中序遍历：");
		tree.inOrder(tree.root);
		System.out.println();
		System.out.println("后序遍历：");
		tree.postOrder(tree.root);
		System.out.println();
		System.out.println("层序遍历：");
		tree.BTreeLevelOrder();
		System.out.println();
		System.out.println("此二叉树的高度为："+tree.getHeight(tree.root));
		System.out.println("此二叉树的叶子结点数："+tree.getLeaf(tree.root));
		System.out.println("第二层的结点树为："+tree.getNum(tree.root, 2));
		Node order =tree.search(tree.root, 6);
		System.out.println("查找值为6的结点是否存在："+tree.isNull(order));
		Node order1 = tree.search(tree.root, 7);
		System.out.println("查找值为7的结点是否存在："+tree.isNull(order1));
		System.out.println("这是一棵完全二叉树吗："+tree.isCompleteBTree());
	}
}

二叉树的C++实现

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#include <iostream>
typedef char elemtype;
using namespace std;
//二叉树的存储结构
struct bitree
{
    elemtype data;
    bitree *lchild,*rchild;
};
//建立二叉树
bitree* create()
{
    bitree *root,*s,*q[100];
    int front=1,rear=0;
    char ch;
    root=NULL;
    cout<<"请输入结点值，（‘ # ’结束）"<<endl;
    cin>>ch;
    while(ch!='#')
    {
        s=NULL;
        if(ch!=',')
        {
            s=new bitree;
            s->data=ch;
            s->lchild=NULL;
            s->rchild=NULL;
        }
        rear++;
        q[rear]=s; // 进队
        if(rear==1)
        root=s;
        else
        {
        if((s!=NULL)&&(q[front]!=NULL))
        {
            if(rear%2==0)
            q[front]->lchild=s;
        else
            q[front]->rchild=s;
        }
        if(rear%2==1)
            front++; // 出队
        }
        cin>>ch;
    }
    return root;
}
//先序遍历
void preorder(bitree *root)
{
    bitree *p;
    p=root;
    if (p!=NULL)
    {
        cout<<p->data<<" ";
        preorder(p->lchild);
        preorder(p->rchild);
    }
}
//中序遍历
void inorder(bitree *root)
{
    bitree *p;
    p=root;
    if(p!=NULL)
    {
        inorder(p->lchild);
        cout<<p->data<<" ";
        inorder(p->rchild);
    }
}
//后序遍历
void postorder(bitree *root)
{
    bitree *p;
    p=root;
    if(p!=NULL)
    {
        postorder(p->lchild);
        postorder(p->rchild);
        cout<<p->data<<" ";
    }
}
//求二叉树中叶子结点的个数
int LeafCount(bitree *T)
{
    if(!T) return 0;
    if(!T->lchild&&!T->rchild)
    {
        return 1;
    }
    else
    {
        return LeafCount(T->lchild)+LeafCount(T->rchild);
    }
}
//求树的高度
int Height(bitree *root)
{
	int L,R;
	if(root==NULL)return 0;
	else
	{
		L=Height(root->lchild);
		R=Height(root->rchild);
		return (L>R)?L+1:R+1;
	}
}
int main()
{
    bitree *root;
    int leaf;
    root=create();
    cout<<"各种遍历方式对应的遍历结果："<<endl;
    cout<<"先序遍历的结果："<<endl;
    preorder(root);
    cout<<endl;
    cout<<"中序遍历的结果："<<endl;
    inorder(root);
    cout<<endl;
    cout<<"后序遍历的结果："<<endl;
    postorder(root);
    cout<<endl;
    cout<<"树的叶子结点个数为："<<LeafCount(root)<<endl;
    cout<<"树的高度为："<<Height(root)<<endl;
}
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