二叉树

1. 树的概念

1.1 满二叉树、完全二叉树、二叉搜索树

 满二叉树：高度为h，由2^h-1个节点构成的二叉树称为满二叉树；

 完全二叉树：完全二叉树是由满二叉树而引出来的，若设二叉树的深度为h，除第 h 层外，其它各层 (1～h-1) 的结点数都达到最大个数(即1~h-1层为一个满二叉树)，第 h 层所有的结点都连续集中在最左边，堆一般都是用完全二叉树实现的；

 二叉搜索树：若它的左子树不空，则左子树上所有结点的值均小于它的根结点的值； 若它的右子树不空，则右子树上所有结点的值均大于它的根结点的值；

1.2 前驱节点、后继节点

 前驱节点：对一棵二叉树进行中序遍历，遍历后的顺序，当前节点的前一个节点为该节点的前驱节点；

 后继节点：对一棵二叉树进行中序遍历，遍历后的顺序，当前节点的后一个节点为该节点的后继节点；

1.3 二叉树性质

2. 二叉树遍历

2.1 前序遍历

    //递归
    private void preOrderR(TreeNode head) {
        if (head == null) {
            return;
        }
        System.out.print(head.val + " ");
        preOrderR(head.left);
        preOrderR(head.right);
    }

    // 先入栈右子节点 再入栈左子节点
    private void preOrder(TreeNode head) {
        Deque<TreeNode> stack = new LinkedList<>();
        stack.push(head);
        while (!stack.isEmpty()) {
            System.out.print(head.val + " ");
            TreeNode node = stack.pop();
            if (node.right != null) {
                stack.push(node.right);
            }
            if (node.left != null) {
                stack.push(node.left);
            }
        }
        System.out.println();
    }

2.2 中序遍历

    //递归
    private void inOrderR(TreeNode head) {
        if (head == null) {
            return;
        }
        preOrderR(head.left);
　　　　 System.out.print(head.val + " ");
        preOrderR(head.right);
    }

    private void inOrder(TreeNode head) {
        System.out.println("===in-order===");
        if (head == null) {
            return;
        }
        Deque<TreeNode> stack = new LinkedList<>();
        TreeNode node = head;

        while (!stack.isEmpty() || node != null) {
            if (node != null) {
                // 压入二叉树左斜边
                stack.push(node);
                node = node.left;
            } else {
                node = stack.pop();
                System.out.println(node.val + " ");
                node = node.right;
            }
        }

        System.out.println();
    }            

2.3 后序遍历

    //递归
    private void postOrderR(TreeNode head) {
        if (head == null) {
            return;
        }
        preOrderR(head.left);
        preOrderR(head.right);
　　　　 System.out.print(head.val + " ");
    }
    
    private void postOrder(TreeNode head) {
        System.out.println("===post-order===");
        if (head == null) {
            return;
        }
        Deque<TreeNode> stack = new LinkedList<>();
        Deque<TreeNode> stack2 = new LinkedList<>();
        stack.push(head);
        TreeNode node;
        while (!stack.isEmpty()) {
            // pop and stack store
            node = stack.pop();
            stack2.push(node);

            // push left node
            if (node.left != null) {
                stack.push(node.left);
            }

            if (node.right != null) {
                stack.push(node.right);
            }
        }
        while (!stack2.isEmpty()) {
            System.out.print(stack2.pop().val + " ");
        }
    }

2.4 广度遍历

public void level(TreeNode head) {
        if (head == null) {
            return;
        }
        Deque<TreeNode> queue = new LinkedList<>();
        queue.offer(head);
        while (!queue.isEmpty()) {
            TreeNode cur = queue.poll();
            System.out.println(cur.val + " ");
            if (cur.left != null) {
                queue.offer(cur.left);
            }
            if (cur.right != null) {
                queue.offer(cur.right);
            }
        }
    }

　基于上述的按层遍历二叉树代码，现有如下题目：求二叉树最大宽度 https://leetcode-cn.com/problems/maximum-width-of-binary-tree/