二叉树

本文讲解二叉树的基本操作：

• 查找节点

• 计算树的高度

• 清空树

• 递归遍历：先序遍历、中序遍历、后序遍历

• 按层遍历

• 前序、中序的非递归遍历

• 树的路径

• 树的左旋和右旋

来看一下树的结构：

class TreeNode {
    String value;
    TreeNode left;
    TreeNode right;
    public TreeNode() {

    }
    public TreeNode(String value) {
        this.value = value;
    }
}

首先，为了方便后面看到效果，先手动初始化一个有4个节点的二叉树：

Tree tree = new Tree();
TreeNode root = new TreeNode("root");
TreeNode node1 = new TreeNode("ndoe1");
TreeNode node2 = new TreeNode("ndoe2");
TreeNode node3 = new TreeNode("ndoe3");
root.left = node1;
root.right = node2;
node1.left = node3;

一、查找节点

//查找节点
public TreeNode findNode(TreeNode treeNode, String value) {
  if(null == treeNode)
    return null;

  if(treeNode.value.equals(value))
    return treeNode;

  TreeNode leftNode = findNode(treeNode.left, value);//递归左子树
  TreeNode rightNode = findNode(treeNode.right, value);//递归右子树
  if(leftNode.value.equals(value))
    return leftNode;
  if(rightNode.value.equals(value))
    return rightNode;

  return null;
}

二、计算树的深度

//计算树的深度
//递归方法
public int deepth(TreeNode treeNode) {
  if(treeNode == null)
    return 0;
  int left = deepth(treeNode.left);
  int right = deepth(treeNode.right);
  return left > right? left + 1: right + 1;
}

三、清空树

//清空二叉树
public void clearTreeNode(TreeNode treeNode) {
  if(null != treeNode) {
    clearTreeNode(treeNode.left);
    clearTreeNode(treeNode.right);
    treeNode = null;
  }
}

四、递归遍历

//遍历1 先序遍历
public void showDLR(TreeNode treeNode) {
  if(null != treeNode) {
    showData(treeNode);
    showDLR(treeNode.left);
    showDLR(treeNode.right);
  }
}
//遍历2 中序遍历
public void showLDR(TreeNode treeNode) {
  if(null != treeNode) {
    showLDR(treeNode.left);
    showData(treeNode);
    showLDR(treeNode.right);
  }
}
//遍历3 后序遍历
public void showLRD(TreeNode treeNode) {
  if(null != treeNode) {
    showLRD(treeNode.left);
    showLRD(treeNode.right);
    showData(treeNode);
  }
}

五、按层遍历

//遍历4 按层遍历 借助队列 先进先出
public void showByLevel(TreeNode treeNode) {
  if(null == treeNode)
    return;

  LinkedList<TreeNode> list = new LinkedList<>();
  TreeNode current;
  list.offer(treeNode);//将根节点入队

  while(!list.isEmpty()) {
    current = list.poll();//队首出队
    showData(current);//打印节点
    if(null != current.left) {
      list.offer(current.left);
    }
    if(null != current.right) {
      list.offer(current.right);
    }
  }
}

运行结果：

树的深度是：3
先序遍历：
root-->ndoe1-->ndoe3-->ndoe2-->
中序遍历：
ndoe3-->ndoe1-->root-->ndoe2-->
后序遍历：
ndoe3-->ndoe1-->ndoe2-->root-->
按层遍历
root-->ndoe1-->ndoe2-->ndoe3-->

六、先序，中序遍历的非递归实现

//遍历5 前序遍历的非递归实现
public void showDLRNotRecursion(TreeNode treeNode) {
  Stack<TreeNode> stack = new Stack<>();
  TreeNode node = treeNode;
  while(null != node || stack.size() >0) {
    while(null != node) {
      showData(node);
      stack.push(node);
      node = node.left;
    }
    if(stack.size() > 0) {
      node = stack.pop();
      node = node.right;
    }
  }
}
//遍历6  中序遍历的非递归实现
public void showLDRNotRecursion(TreeNode treeNode) {
  Stack<TreeNode> stack = new Stack<>();
  TreeNode node = treeNode;
  while(null != node || stack.size() > 0) {
    while(null != node) {
      stack.push(node);
      node = node.left;
    }
    if(stack.size() > 0) {
      node = stack.pop();
      showData(node);
      node = node.right;
    }
  }
}

七、树的路径

public static void main(String[] args) {
    TreeNode node1 = new TreeNode("1");
    TreeNode node2 = new TreeNode("2");
    TreeNode node3 = new TreeNode("3");
    TreeNode node4 = new TreeNode("4");
    TreeNode node5 = new TreeNode("5");
    TreeNode node6 = new TreeNode("6");
    TreeNode node7 = new TreeNode("7");
    node1.left = node2;
    node1.right = node3;
    node2.left = node4;
    node2.right = node5;
    node5.left = node6;
    node5.right = node7;

    List<TreeNode> list = new ArrayList<>();
    list.add(node1);
    lujing(list, node1);
}
// 打印二叉树的所有路径
public static void lujing(List<TreeNode> list, TreeNode node) {
        if (node.left == null && node.right == null) {
            for (int i = 0; i < list.size(); i++) {
                System.out.print(list.get(i).val + " --> ");
            }
            System.out.println();
            return;
        }

        if (node.left != null) {
            List<TreeNode> newList = new ArrayList<>(list);
            newList.add(node.left);
            lujing(newList, node.left);
        }

        if (node.right != null) {
            List<TreeNode> newList = new ArrayList<>(list);
            newList.add(node.right);
            lujing(newList, node.right);
        }
    }

八、二叉树的左旋和右旋

• 左旋：节点右儿子的左儿子（若存在）变为节点的右儿子，节点变为右儿子的左儿子；

• 右旋：节点左二子的右儿子（若存在）变为节点的左二子，节点变为左二子的右儿子。

举个例子：

可以看到，如果旋转前是一个二叉排序树，那么旋转后仍然是一个二叉排序树。

// 左旋
public static void zuoxuan(TreeNode head) {
    TreeNode headRight = head.right;
    head.right = headRight.left;
    headRight.left = head;
}

// 右旋
public static void youxuan(TreeNode head) {
    TreeNode headLeft = head.left;
    head.left = headLeft.right;
    headLeft.right = head;
}