Java数据结构——二叉树的遍历（汇总）

二叉树的遍历分为深度优先遍历（DFS)和广度优先遍历（BFS)

DFS遍历主要有：

• 前序遍历
• 中序遍历
• 后序遍历

一、递归实现DFS
Node.java:

public class Node {
private Object data;
Node richild;
Node lechild;
 
public Object getData() {
return data;
}
 
public void setData(Object data) {
this.data = data;
}
 
public Node getRichild() {
return richild;
}
 
public void setRichild(Node richild) {
this.richild = richild;
}
 
public Node getLechild() {
return lechild;
}
 
public void setLechild(Node lechild) {
this.lechild = lechild;
}
 
public Node(Object data, Node lechild, Node richild) {
super();
this.data = data;
this.richild = richild;
this.lechild = lechild;
}
 
public Node() {
super();
}
 
}

递归遍历：

public class BTree {
 
private static Node root;
//构造树
public static void init() {
Node node1 = new Node("A", null, null);
Node node2 = new Node("B", node1, null);
Node node3 = new Node("C", null, null);
Node node4 = new Node("D", node2, node3);
Node node5 = new Node("E", null, null);
Node node6 = new Node("F", null, node5);
Node node7 = new Node("G", node4, node6);
root = node7;
}
//访问节点
public static void visited(Node n) {
System.out.print(n.getData() + " ");
}
//前序遍历
public static void preOrder(Node n) {
if (n != null) {
visited(n);
preOrder(n.getLechild());
preOrder(n.getRichild());
}
}
//中序遍历
public static void inOrder(Node n) {
if (n != null) {
inOrder(n.getLechild());
visited(n);
inOrder(n.getRichild());
}
}
//后序遍历
public static void postOrder(Node n) {
if (n != null) {
postOrder(n.getLechild());
postOrder(n.getRichild());
visited(n);
}
}
 
public static void main(String[] args) {
init();
System.out.print("递归前序：");
preOrder(root);
System.out.println();
System.out.print("递归中序：");
inOrder(root);
System.out.println();
System.out.print("递归后序：");
postOrder(root);
System.out.println();
}
 
}

二、非递归实现DFS（依靠栈）

//前序遍历
public static void preOrder(Node n) {
System.out.print("非递归前序：");
Stack<Node> stack = new Stack<>();
int index = 0;
while (n != null || index > 0) {
while (n != null) {
System.out.print(n.getData() + " ");
stack.push(n);
index++;
n = n.getLechild();
}
n = stack.pop();
index--;
n = n.getRichild();
}
}
//中序遍历
public static void inOrder(Node n) {
System.out.print("非递归中序：");
Stack<Node> stack = new Stack<>();
int index = 0;
while (n != null || index > 0) {
while (n != null) {
stack.push(n);
index++;
n = n.getLechild();
}
n = stack.pop();
System.out.print(n.getData() + " ");
index--;
n = n.getRichild();
}
}
//后序遍历
public static void postOrder(Node n) {
System.out.print("非递归后序：");
Stack<Node> stack = new Stack<>();
int index = 0;
Node lastVisited = null;
while (n != null || index > 0) {
while (n != null) {
stack.push(n);
index++;
n = n.getLechild();
}
n = stack.peek();
if (n.getRichild() == null || n.getRichild() == lastVisited) {
System.out.print(n.getData() + " ");
lastVisited = n;
index--;
stack.pop();
n = null;
} else {
n = n.getRichild();
}
}
}

　　

三、实现层序遍历（依靠队列）

public static void LevenOrder(Node root) {
if (root == null) {
return;
}
Queue<Node> queue = new LinkedList<>();
queue.add(root);
Node temp = null;
while (!queue.isEmpty()) {
temp = queue.poll();
visited(temp);
if (temp.getLeChild() != null) {
queue.add(temp.getLeChild());
}
if (temp.getRChild() != null) {
queue.add(temp.getChild());
}
}
}