二叉树基础

一、二叉树定义

二叉树（binary tree）是指树中节点的度不大于2的有序树，它是一种最简单且最重要的树。二叉树的递归定义为：二叉树是一棵空树，或者是一棵由一个根节点和两棵互不相交的，分别称作根的左子树和右子树组成的非空树；左子树和右子树又同样都是二叉树。

   

总结：每个人最多有2个孩子，但每个孩子只能有一个爸爸。

   

二、二叉树的前序、中序、后序遍历

给定一个二叉树集合，如何换为二叉树 ？

例：List = [8,9,96,34,19,69,72,null,null,24,57,25,47,68,null]  

public class BinaryTreeTest{

public static void main(String[] args) {

        Integer targetSum = 22;

        List<Integer> binaryTreeList = Arrays.asList(8,9,96,34,19,69,72,null,null,24,57,25,47,68,null);

   

        List<TreeNode> nodes = new ArrayList<>();

        for (Integer integer : binaryTreeList) {

            nodes.add(new TreeNode(integer == null ? 0:integer));

        }

   

        //构建二叉树

        if (nodes.size() > 0) {

            for (int i = 0; i < binaryTreeList.size()/2 ; i++) {

                //左

                if (nodes.get(2*i + 1) != null) {

                    nodes.get(i).left = nodes.get(2*i + 1);

                }

   

                //右

                if (binaryTreeList.get(2*i + 2) != null) {

                    nodes.get(i).right = nodes.get(2*i + 2);

                }

            }

        }

        printBinaryTreeOfPreOrder(nodes.get(0));

        System.out.println();

        System.out.println("result:"+pathSum(nodes.get(0), targetSum));

    }

   

    //前序

    private static void printBinaryTreeOfPreOrder(TreeNode node){

        if (node != null) {

            System.out.print(node.getVal()+",");

            printBinaryTreeOfPreOrder(node.getLeft());

            printBinaryTreeOfPreOrder(node.getRight());

        }

    }}

   

@Getter

@Setter

class TreeNode {

    Integer val;

    TreeNode left;

    TreeNode right;

   

    TreeNode() {

    }

   

    TreeNode(Integer val) {

        this.val = val;

    }

   

    TreeNode(int val, TreeNode left, TreeNode right) {

        this.val = val;

        this.left = left;

        this.right = right;

    }

}

   

   

   

   

1、前序遍历 根节点-左子-右子 (代码见上)

输出：8,9,34,19,24,57,96,69,25,47,72,68

   

2、中序遍历 左子-根节点-右子

输出：34,9,24,19,57,8,25,69,47,96,68,72

    //中序

    private static void printBinaryTreeOfInfix(TreeNode node){

        if (node != null) {

            printBinaryTreeOfInfix(node.getLeft());

            System.out.print(node.val+",");

            printBinaryTreeOfInfix(node.getRight());

        }

    }

   

3、后续遍历 左子-右子-根节点

输出：34,24,57,19,9,25,47,69,68,72,96,8

//后序

    private static void printBinaryTreeOfPostOrder(TreeNode node){

        if (node != null) {

            printBinaryTreeOfPostOrder(node.getLeft());

            printBinaryTreeOfPostOrder(node.getRight());

            System.out.print(node.val+",");

        }

    }