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二叉树
本文讲解二叉树的基本操作:
  • 查找节点
  • 计算树的高度
  • 清空树
  • 递归遍历:先序遍历、中序遍历、后序遍历
  • 按层遍历
  • 前序、中序的非递归遍历
  • 树的路径
  • 树的左旋和右旋
来看一下树的结构:
class TreeNode {
String value;
TreeNode left;
TreeNode right;
public TreeNode() {
}
public TreeNode(String value) {
this.value = value;
}
}
首先,为了方便后面看到效果,先手动初始化一个有4个节点的二叉树:
Tree tree = new Tree();
TreeNode root = new TreeNode("root");
TreeNode node1 = new TreeNode("ndoe1");
TreeNode node2 = new TreeNode("ndoe2");
TreeNode node3 = new TreeNode("ndoe3");
root.left = node1;
root.right = node2;
node1.left = node3;

一、查找节点

//查找节点
public TreeNode findNode(TreeNode treeNode, String value) {
if(null == treeNode)
return null;
if(treeNode.value.equals(value))
return treeNode;
TreeNode leftNode = findNode(treeNode.left, value);//递归左子树
TreeNode rightNode = findNode(treeNode.right, value);//递归右子树
if(leftNode.value.equals(value))
return leftNode;
if(rightNode.value.equals(value))
return rightNode;
return null;
}

二、计算树的深度

//计算树的深度
//递归方法
public int deepth(TreeNode treeNode) {
if(treeNode == null)
return 0;
int left = deepth(treeNode.left);
int right = deepth(treeNode.right);
return left > right? left + 1: right + 1;
}

三、清空树

//清空二叉树
public void clearTreeNode(TreeNode treeNode) {
if(null != treeNode) {
clearTreeNode(treeNode.left);
clearTreeNode(treeNode.right);
treeNode = null;
}
}

四、递归遍历

//遍历1 先序遍历
public void showDLR(TreeNode treeNode) {
if(null != treeNode) {
showData(treeNode);
showDLR(treeNode.left);
showDLR(treeNode.right);
}
}
//遍历2 中序遍历
public void showLDR(TreeNode treeNode) {
if(null != treeNode) {
showLDR(treeNode.left);
showData(treeNode);
showLDR(treeNode.right);
}
}
//遍历3 后序遍历
public void showLRD(TreeNode treeNode) {
if(null != treeNode) {
showLRD(treeNode.left);
showLRD(treeNode.right);
showData(treeNode);
}
}

五、按层遍历

//遍历4 按层遍历 借助队列 先进先出
public void showByLevel(TreeNode treeNode) {
if(null == treeNode)
return;
LinkedList<TreeNode> list = new LinkedList<>();
TreeNode current;
list.offer(treeNode);//将根节点入队
while(!list.isEmpty()) {
current = list.poll();//队首出队
showData(current);//打印节点
if(null != current.left) {
list.offer(current.left);
}
if(null != current.right) {
list.offer(current.right);
}
}
}
运行结果:
树的深度是:3
先序遍历:
root-->ndoe1-->ndoe3-->ndoe2-->
中序遍历:
ndoe3-->ndoe1-->root-->ndoe2-->
后序遍历:
ndoe3-->ndoe1-->ndoe2-->root-->
按层遍历
root-->ndoe1-->ndoe2-->ndoe3-->

六、先序,中序遍历的非递归实现

//遍历5 前序遍历的非递归实现
public void showDLRNotRecursion(TreeNode treeNode) {
Stack<TreeNode> stack = new Stack<>();
TreeNode node = treeNode;
while(null != node || stack.size() >0) {
while(null != node) {
showData(node);
stack.push(node);
node = node.left;
}
if(stack.size() > 0) {
node = stack.pop();
node = node.right;
}
}
}
//遍历6 中序遍历的非递归实现
public void showLDRNotRecursion(TreeNode treeNode) {
Stack<TreeNode> stack = new Stack<>();
TreeNode node = treeNode;
while(null != node || stack.size() > 0) {
while(null != node) {
stack.push(node);
node = node.left;
}
if(stack.size() > 0) {
node = stack.pop();
showData(node);
node = node.right;
}
}
}

七、树的路径

public static void main(String[] args) {
TreeNode node1 = new TreeNode("1");
TreeNode node2 = new TreeNode("2");
TreeNode node3 = new TreeNode("3");
TreeNode node4 = new TreeNode("4");
TreeNode node5 = new TreeNode("5");
TreeNode node6 = new TreeNode("6");
TreeNode node7 = new TreeNode("7");
node1.left = node2;
node1.right = node3;
node2.left = node4;
node2.right = node5;
node5.left = node6;
node5.right = node7;
List<TreeNode> list = new ArrayList<>();
list.add(node1);
lujing(list, node1);
}
// 打印二叉树的所有路径
public static void lujing(List<TreeNode> list, TreeNode node) {
if (node.left == null && node.right == null) {
for (int i = 0; i < list.size(); i++) {
System.out.print(list.get(i).val + " --> ");
}
System.out.println();
return;
}
if (node.left != null) {
List<TreeNode> newList = new ArrayList<>(list);
newList.add(node.left);
lujing(newList, node.left);
}
if (node.right != null) {
List<TreeNode> newList = new ArrayList<>(list);
newList.add(node.right);
lujing(newList, node.right);
}
}

八、二叉树的左旋和右旋

  • 左旋:节点右儿子的左儿子(若存在)变为节点的右儿子,节点变为右儿子的左儿子;
  • 右旋:节点左二子的右儿子(若存在)变为节点的左二子,节点变为左二子的右儿子。
举个例子:
可以看到,如果旋转前是一个二叉排序树,那么旋转后仍然是一个二叉排序树。
// 左旋
public static void zuoxuan(TreeNode head) {
TreeNode headRight = head.right;
head.right = headRight.left;
headRight.left = head;
}
// 右旋
public static void youxuan(TreeNode head) {
TreeNode headLeft = head.left;
head.left = headLeft.right;
headLeft.right = head;
}
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On this page
一、查找节点
二、计算树的深度
三、清空树
四、递归遍历
五、按层遍历
六、先序,中序遍历的非递归实现
七、树的路径
八、二叉树的左旋和右旋