数据结构（java）二叉树的基本操作

1.二叉树的性质：

1.若规定根结点的层数为1，则一棵非空二叉树的第i层上最多有2*-1(i>0)个结点

2.若规定只有根节点的二叉树的深度为1，则深度为K的二叉树的最大结点数是2都k次方-1

3.对于任何一个二叉树，如果其叶结点个数为 nO，度为2的非叶结点个数为n2，则有n0=n2+1

4.具有n个结点的完全二叉树的深度k为log2（n+1）上取整

5.对于具有n个结点的完全二叉树，如果按照从上至下从左至右的顺序对所有节点从0开始编号，则

的结点有：

。若i>0，双亲序号：(i-1)/2；i=0，i为根结点编号、无双亲结点

。若2i+1<n，左孩子序号：2i+1，否则无左孩子

。若2i+2<n，右孩子序号：2i+2，否则无右孩子

2.二叉树的前，中，后序遍历

前序遍历：

java 复制代码

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

public class BinaryTree {
    static class TreeNode {
        public char val;
        public TreeNode left;//存储左孩子的引用
        public TreeNode right;//存储右孩子的引用

        public TreeNode(char val) {
            this.val = val;
        }
    }

    public TreeNode createTree() {
        TreeNode A = new TreeNode('A');
        TreeNode B = new TreeNode('B');
        TreeNode C = new TreeNode('C');
        TreeNode D = new TreeNode('D');
        TreeNode E = new TreeNode('E');
        TreeNode F = new TreeNode('F');
        TreeNode G = new TreeNode('G');
        TreeNode H = new TreeNode('H');

        A.left = B;
        A.right = C;
        B.left = D;
        B.right = E;
        C.left = F;
        C.right = G;
        E.right = H;
        return A;
    }

    public int i = 0;

    public TreeNode createTree(String str) {
        TreeNode root = null;
        if (str.charAt(i) != '#') {
            root = new TreeNode(str.charAt(i));
            i++;
            root.left = createTree(str);
            root.right = createTree(str);
        } else {
            i++;
        }
        return root;
    }


    // 前序遍历
    public void preOrder(TreeNode root) {
        if (root == null) return;
        System.out.print(root.val + " ");
        preOrder(root.left);
        preOrder(root.right);
    }

    public void preOrderNor(TreeNode root) {
        if (root == null) return;
        Stack<TreeNode> stack = new Stack<>();
        TreeNode cur = root;

        while (cur != null || !stack.isEmpty()) {
            while (cur != null) {
                stack.push(cur);
                System.out.print(cur.val + " ");
                cur = cur.left;
            }
            TreeNode top = stack.pop();
            cur = top.right;
        }
    }

中序遍历：

java 复制代码

public void inOrder(TreeNode root) {
        if (root == null) return;
        inOrder(root.left);
        System.out.print(root.val + " ");
        inOrder(root.right);
    }


    public void inOrderNor(TreeNode root) {
        if (root == null) return;
        Stack<TreeNode> stack = new Stack<>();
        TreeNode cur = root;

        while (cur != null || !stack.isEmpty()) {
            while (cur != null) {
                stack.push(cur);
                cur = cur.left;
            }
            TreeNode top = stack.pop();
            System.out.print(top.val + " ");

            cur = top.right;
        }
    }

后序遍历：

java 复制代码

public void postOrder(TreeNode root) {
        if (root == null) return;
        postOrder(root.left);
        postOrder(root.right);
        System.out.print(root.val + " ");
    }

    public void postOrderNor(TreeNode root) {
        if (root == null) return;
        Stack<TreeNode> stack = new Stack<>();
        TreeNode cur = root;
        TreeNode prev = null;
        while (cur != null || !stack.isEmpty()) {
            while (cur != null) {
                stack.push(cur);
                cur = cur.left;
            }
            TreeNode top = stack.peek();
            if (top.right == null || top.right == prev) {
                System.out.print(top.val + " ");
                stack.pop();
                prev = top;
            } else {
                cur = top.right;
            }

        }

获取叶子节点的个数：

java 复制代码

public static int leafSize;
    public void getLeafNodeCount(TreeNode root) {
        if(root == null) {
            return;
        }

        if(root.left == null && root.right == null) {
            leafSize++;
        }

        getLeafNodeCount(root.left);
        getLeafNodeCount(root.right);
    }

    public int getLeafNodeCount2(TreeNode root) {
       if(root == null) {
           return 0;
       }
        if(root.left == null && root.right == null) {
            return 1;
        }
       return getLeafNodeCount2(root.left) +
               getLeafNodeCount2(root.right);
    }
    public int getKLevelNodeCount(TreeNode root,int k) {
        if(root == null) {
            return 0;
        }
        if(k == 1) {
            return 1;
        }
        return getKLevelNodeCount(root.left,k-1) +
                getKLevelNodeCount(root.right,k-1);
    }