day13|二叉树理论

一、二叉树的定义

//定义一个二叉树：使用链式存储
public class TreeNode {

	int val; // 节点的值
	TreeNode left; // 左子节点
	TreeNode right; // 右子节点
	
	public TreeNode() {
	}
	
	// 构造函数，初始化节点值
	public TreeNode(int val){
	    this.val=val;
	}
	
	// 构造函数，初始化节点值、左子节点和右子节点
	public TreeNode(int val, TreeNode left, TreeNode right) {
	    this.val = val;
	    this.left = left;
	    this.right = right;
	}

}

二、前序遍历

package com.thirteenday.tree;

import java.util.ArrayList;
import java.util.List;


//前序遍历
/**
 * 递归三部曲：
 *  1、确定递归函数的参数和返回值
 *  2、确定递归终止条件
 *  3、确定单层递归的逻辑
 */
public class PreorderTraversal {
    /**
     * 1、确定递归函数的参数和返回值
     * @param root  树的根节点
     * @param result  将遍历的结果放在集合中
     */
    private static void preorder(TreeNode root , List<Integer> result){

        //2、确定递归终止条件
        if (root == null){
            return;
        }
        //3、确定单层递归的逻辑：前序遍历：根左右
        result.add(root.val); //根
        preorder(root.left,result);//左
        preorder(root.right,result); //右

    }
    public static List<Integer> preorderTraversal(TreeNode root){
        ArrayList<Integer> result = new ArrayList<>();
        preorder(root,result);
        return result;
    }

    public static void main(String[] args) {
        TreeNode root = new TreeNode(1, new TreeNode(2, new TreeNode(4), new TreeNode(5)), new TreeNode(3, new TreeNode(6), new TreeNode(7)));
        List<Integer> list = preorderTraversal(root);
        list.stream().forEach( e -> System.out.println(e+" "));
    }

}

三、中序遍历

package com.thirteenday.tree;

import java.util.ArrayList;
import java.util.List;

//中序遍历
public class InorderTraversal {


    /**
     * 1、确定递归函数的参数和返回值
     * @param root  树的根节点
     * @param result  将遍历的结果放在集合中
     */
    private static void preorder(TreeNode root , List<Integer> result){

        //2、确定递归终止条件
        if (root == null){
            return;
        }
        //3、确定单层递归的逻辑：中序遍历：左根右

        preorder(root.left,result);//左
        result.add(root.val); //根
        preorder(root.right,result); //右

    }

    public static List<Integer> inorderTraversal(TreeNode root){
        ArrayList<Integer> result = new ArrayList<>();
        preorder(root,result);
        return result;
    }


    public static void main(String[] args) {
        TreeNode root = new TreeNode(1, new TreeNode(2, new TreeNode(4), new TreeNode(5)), new TreeNode(3, new TreeNode(6), new TreeNode(7)));
        List<Integer> list = inorderTraversal(root);
        list.stream().forEach( e -> System.out.println(e+" "));
    }
}

四、后序遍历

//后序遍历
public class PostorderTraversal {
    /**
     * 1、确定递归函数的参数和返回值
     * @param root  树的根节点
     * @param result  将遍历的结果放在集合中
     */
    private static void preorder(TreeNode root , List<Integer> result){

        //2、确定递归终止条件
        if (root == null){
            return;
        }
        //3、确定单层递归的逻辑：后序遍历：左右根

        preorder(root.left,result);//左
        preorder(root.right,result); //右
        result.add(root.val); //根

    }

    public static List<Integer> postorderTraversal(TreeNode root){
        ArrayList<Integer> result = new ArrayList<>();
        preorder(root,result);
        return result;
    }


    public static void main(String[] args) {
        TreeNode root = new TreeNode(1, new TreeNode(2, new TreeNode(4), new TreeNode(5)), new TreeNode(3, new TreeNode(6), new TreeNode(7)));
        List<Integer> list = postorderTraversal(root);
        list.stream().forEach( e -> System.out.println(e+" "));
    }
}