Java数据结构——二叉树的递归与非递归遍历（DFS）

Posted 2021-02-15 橘子洲头。

二叉树的遍历分为递归遍历和非递归遍历

一、递归实现前、中、后序遍历
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、非递归实现前、中、后序遍历

import java.util.Stack;
public class BTree2 {
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;
}
//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();
}
}
}

public static void main(String[] args) {
init();
preOrder(root);
System.out.println();
inOrder(root);
System.out.println();
postOrder(root);
System.out.println();
}
}

　

三、查找最大值

// 查找最大值
public static Node maxNode() {
Node node = root;
Node maxNode = node;
while (node != null) {
maxNode = node;
node = node.getRichild();
}
return maxNode;
}

　　

四、查找最小值

// 查找最小值
public static Node minNode() {
Node node = root;
Node minNode = node;
while (node != null) {
minNode = node;
node = node.getLechild();
}
return minNode;
}

　　

五、插入节点

// 插入节点
public static boolean insert(Object data, Node parent) {
Node node = new Node(data, null, null);
if (root == null || parent == null) {
root = node;
return true;
} else if (parent.getLechild() != null && parent.getRichild() != null) {
return false;
} else {
if (parent.getLechild() != null) {
parent.setRichild(node);
} else {
parent.setLechild(node);
}
return true;
}
}

　　

六、查找节点

// 查找节点
public static void find(Node n, Object data) {
if (n != null) {
if (n.getData() == data) {
System.out.println(n);
return;
} else {
find(n.getLechild(), data);
find(n.getRichild(), data);
}
}
}