数据结构--树与二叉树

数据结构分类

集合

线性结构(一对一)

树形结构(一对多)

图结构(多对多)

数据结构三要素

1、逻辑结构

2、数据的运算

3、存储结构（物理结构）

树的概念

树的分类

满二叉树和完全二叉树

二叉排序树

平衡二叉树

二叉树分类总结

二叉树的存储结构

顺序存储

链式存储

二叉树的遍历

先序遍历

javascript 复制代码

class Node {
            constructor(value) {
                this.value = value;
                this.left = null;
                this.right = null;
            }
        }
        const tree = new Node('A');

        tree.left = new Node('B');
        tree.right = new Node('C');
        tree.left.left = new Node('D');
        tree.left.right = new Node('E');
        tree.right.left = new Node('F');
        tree.right.right = new Node('G');
        // 前序遍历
        const preorderTraversal = (root) => {
            if (root === null) return;
            console.log(root.value); // 访问根节点
            preorderTraversal(root.left); // 遍历左子树
            
            preorderTraversal(root.right); // 遍历右子树
        };

        preorderTraversal(tree);

中序遍历

javascript 复制代码

class Node {
            constructor(value) {
                this.value = value;
                this.left = null;
                this.right = null;
            }
        }
        const tree = new Node('A');

        tree.left = new Node('B');
        tree.right = new Node('C');
        tree.left.left = new Node('D');
        tree.left.right = new Node('E');
        tree.right.left = new Node('F');
        tree.right.right = new Node('G');
        // 前序遍历
        const preorderTraversal = (root) => {
            if (root === null) return;
            preorderTraversal(root.left); // 遍历左子树
            console.log(root.value); // 访问根节点
            
            preorderTraversal(root.right); // 遍历右子树
        };

        preorderTraversal(tree);

后序遍历

javascript 复制代码

class Node {
            constructor(value) {
                this.value = value;
                this.left = null;
                this.right = null;
            }
        }
        const tree = new Node('A');

        tree.left = new Node('B');
        tree.right = new Node('C');
        tree.left.left = new Node('D');
        tree.left.right = new Node('E');
        tree.right.left = new Node('F');
        tree.right.right = new Node('G');
        // 前序遍历
        const preorderTraversal = (root) => {
            if (root === null) return;
            preorderTraversal(root.left); // 遍历左子树
            
            preorderTraversal(root.right); // 遍历右子树
            console.log(root.value); // 访问根节点
        };

        preorderTraversal(tree);

遍历构造二叉树

javascript 复制代码

        const generateTreeHelper = (node, n) => {
            node.left = new TreeNode(n);
            node.right = new TreeNode(n);
            n -= 1;

            if (n > 0) {
                generateTreeHelper(node.left, n);
                generateTreeHelper(node.right, n);
            }
        };

        const generateTree = (n) => {
            let root = null;

            if (n <= 0) return root;

            root = new TreeNode(3);
            generateTreeHelper(root, n - 1);

            return root;
        };

        console.log('--------root', generateTree(3));