Question

94. 二叉树的中序遍历

English Version

题目描述

给定一个二叉树的根节点 root ，返回 _它的 中序 遍历_ 。

 

示例 1：

输入：root = [1,null,2,3]
输出：[1,3,2]

示例 2：

输入：root = []
输出：[]

示例 3：

输入：root = [1]
输出：[1]

 

提示：

• 树中节点数目在范围 [0, 100] 内
• -100 <= Node.val <= 100

 

进阶: 递归算法很简单，你可以通过迭代算法完成吗？

解法

方法一：递归遍历

我们先递归左子树，再访问根节点，接着递归右子树。

时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 是二叉树的节点数，空间复杂度主要取决于递归调用的栈空间。

# Definition for a binary tree node.
# class TreeNode:
#   def __init__(self, val=0, left=None, right=None):
#     self.val = val
#     self.left = left
#     self.right = right
class Solution:
  def inorderTraversal(self, root: Optional[TreeNode]) -> List[int]:
    def dfs(root):
      if root is None:
        return
      dfs(root.left)
      ans.append(root.val)
      dfs(root.right)

    ans = []
    dfs(root)
    return ans

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *   int val;
 *   TreeNode left;
 *   TreeNode right;
 *   TreeNode() {}
 *   TreeNode(int val) { this.val = val; }
 *   TreeNode(int val, TreeNode left, TreeNode right) {
 *     this.val = val;
 *     this.left = left;
 *     this.right = right;
 *   }
 * }
 */
class Solution {
  private List<Integer> ans = new ArrayList<>();

  public List<Integer> inorderTraversal(TreeNode root) {
    dfs(root);
    return ans;
  }

  private void dfs(TreeNode root) {
    if (root == null) {
      return;
    }
    dfs(root.left);
    ans.add(root.val);
    dfs(root.right);
  }
}

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *   int val;
 *   TreeNode *left;
 *   TreeNode *right;
 *   TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *   TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *   TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
  vector<int> inorderTraversal(TreeNode* root) {
    vector<int> ans;
    function<void(TreeNode*)> dfs = [&](TreeNode* root) {
      if (!root) {
        return;
      }
      dfs(root->left);
      ans.push_back(root->val);
      dfs(root->right);
    };
    dfs(root);
    return ans;
  }
};

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *   Val int
 *   Left *TreeNode
 *   Right *TreeNode
 * }
 */
func inorderTraversal(root *TreeNode) (ans []int) {
  var dfs func(*TreeNode)
  dfs = func(root *TreeNode) {
    if root == nil {
      return
    }
    dfs(root.Left)
    ans = append(ans, root.Val)
    dfs(root.Right)
  }
  dfs(root)
  return
}

/**
 * Definition for a binary tree node.
 * class TreeNode {
 *   val: number
 *   left: TreeNode | null
 *   right: TreeNode | null
 *   constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 *   }
 * }
 */

function inorderTraversal(root: TreeNode | null): number[] {
  const ans: number[] = [];
  const dfs = (root: TreeNode | null) => {
    if (!root) {
      return;
    }
    dfs(root.left);
    ans.push(root.val);
    dfs(root.right);
  };
  dfs(root);
  return ans;
}

// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//   TreeNode {
//     val,
//     left: None,
//     right: None
//   }
//   }
// }
use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
  fn dfs(root: &Option<Rc<RefCell<TreeNode>>>, ans: &mut Vec<i32>) {
    if root.is_none() {
      return;
    }
    let node = root.as_ref().unwrap().borrow();
    Self::dfs(&node.left, ans);
    ans.push(node.val);
    Self::dfs(&node.right, ans);
  }

  pub fn inorder_traversal(root: Option<Rc<RefCell<TreeNode>>>) -> Vec<i32> {
    let mut ans = vec![];
    Self::dfs(&root, &mut ans);
    ans
  }
}

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *   this.val = (val===undefined ? 0 : val)
 *   this.left = (left===undefined ? null : left)
 *   this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number[]}
 */
var inorderTraversal = function (root) {
  const ans = [];
  const dfs = root => {
    if (!root) {
      return;
    }
    dfs(root.left);
    ans.push(root.val);
    dfs(root.right);
  };
  dfs(root);
  return ans;
};

方法二：栈实现非递归遍历

非递归的思路如下：

1. 定义一个栈 $stk$
2. 将树的左节点依次入栈
3. 左节点为空时，弹出栈顶元素并处理
4. 重复 2-3 的操作

时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 是二叉树的节点数，空间复杂度主要取决于栈空间。

# Definition for a binary tree node.
# class TreeNode:
#   def __init__(self, val=0, left=None, right=None):
#     self.val = val
#     self.left = left
#     self.right = right
class Solution:
  def inorderTraversal(self, root: Optional[TreeNode]) -> List[int]:
    ans, stk = [], []
    while root or stk:
      if root:
        stk.append(root)
        root = root.left
      else:
        root = stk.pop()
        ans.append(root.val)
        root = root.right
    return ans

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *   int val;
 *   TreeNode left;
 *   TreeNode right;
 *   TreeNode() {}
 *   TreeNode(int val) { this.val = val; }
 *   TreeNode(int val, TreeNode left, TreeNode right) {
 *     this.val = val;
 *     this.left = left;
 *     this.right = right;
 *   }
 * }
 */
class Solution {
  public List<Integer> inorderTraversal(TreeNode root) {
    List<Integer> ans = new ArrayList<>();
    Deque<TreeNode> stk = new ArrayDeque<>();
    while (root != null || !stk.isEmpty()) {
      if (root != null) {
        stk.push(root);
        root = root.left;
      } else {
        root = stk.pop();
        ans.add(root.val);
        root = root.right;
      }
    }
    return ans;
  }
}

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *   int val;
 *   TreeNode *left;
 *   TreeNode *right;
 *   TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *   TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *   TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
  vector<int> inorderTraversal(TreeNode* root) {
    vector<int> ans;
    stack<TreeNode*> stk;
    while (root || stk.size()) {
      if (root) {
        stk.push(root);
        root = root->left;
      } else {
        root = stk.top();
        stk.pop();
        ans.push_back(root->val);
        root = root->right;
      }
    }
    return ans;
  }
};

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *   Val int
 *   Left *TreeNode
 *   Right *TreeNode
 * }
 */
func inorderTraversal(root *TreeNode) (ans []int) {
  stk := []*TreeNode{}
  for root != nil || len(stk) > 0 {
    if root != nil {
      stk = append(stk, root)
      root = root.Left
    } else {
      root = stk[len(stk)-1]
      stk = stk[:len(stk)-1]
      ans = append(ans, root.Val)
      root = root.Right
    }
  }
  return
}

/**
 * Definition for a binary tree node.
 * class TreeNode {
 *   val: number
 *   left: TreeNode | null
 *   right: TreeNode | null
 *   constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 *   }
 * }
 */

function inorderTraversal(root: TreeNode | null): number[] {
  const stk: TreeNode[] = [];
  const ans: number[] = [];
  while (root || stk.length > 0) {
    if (root) {
      stk.push(root);
      root = root.left;
    } else {
      root = stk.pop();
      ans.push(root.val);
      root = root.right;
    }
  }
  return ans;
}

// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//   TreeNode {
//     val,
//     left: None,
//     right: None
//   }
//   }
// }
use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
  pub fn inorder_traversal(mut root: Option<Rc<RefCell<TreeNode>>>) -> Vec<i32> {
    let mut ans = vec![];
    let mut stk = vec![];
    while root.is_some() || !stk.is_empty() {
      if root.is_some() {
        let next = root.as_mut().unwrap().borrow_mut().left.take();
        stk.push(root);
        root = next;
      } else {
        let mut node = stk.pop().unwrap();
        let mut node = node.as_mut().unwrap().borrow_mut();
        ans.push(node.val);
        root = node.right.take();
      }
    }
    ans
  }
}

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *   this.val = (val===undefined ? 0 : val)
 *   this.left = (left===undefined ? null : left)
 *   this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number[]}
 */
var inorderTraversal = function (root) {
  const stk = [];
  const ans = [];
  while (root || stk.length > 0) {
    if (root) {
      stk.push(root);
      root = root.left;
    } else {
      root = stk.pop();
      ans.push(root.val);
      root = root.right;
    }
  }
  return ans;
};

方法三：Morris 实现中序遍历

Morris 遍历无需使用栈，空间复杂度为 $O(1)$。核心思想是：

遍历二叉树节点，

1. 若当前节点 root 的左子树为空，将当前节点值添加至结果列表 ans 中，并将当前节点更新为 root.right
2. 若当前节点 root 的左子树不为空，找到左子树的最右节点 prev（也即是 root 节点在中序遍历下的前驱节点）：
   • 若前驱节点 prev 的右子树为空，将前驱节点的右子树指向当前节点 root，并将当前节点更新为 root.left。
   • 若前驱节点 prev 的右子树不为空，将当前节点值添加至结果列表 ans 中，然后将前驱节点右子树指向空（即解除 prev 与 root 的指向关系），并将当前节点更新为 root.right。
3. 循环以上步骤，直至二叉树节点为空，遍历结束。

时间复杂度 $O(n)$，空间复杂度 $O(1)$。其中 $n$ 是二叉树的节点数。

# Definition for a binary tree node.
# class TreeNode:
#   def __init__(self, val=0, left=None, right=None):
#     self.val = val
#     self.left = left
#     self.right = right
class Solution:
  def inorderTraversal(self, root: Optional[TreeNode]) -> List[int]:
    ans = []
    while root:
      if root.left is None:
        ans.append(root.val)
        root = root.right
      else:
        prev = root.left
        while prev.right and prev.right != root:
          prev = prev.right
        if prev.right is None:
          prev.right = root
          root = root.left
        else:
          ans.append(root.val)
          prev.right = None
          root = root.right
    return ans

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *   int val;
 *   TreeNode left;
 *   TreeNode right;
 *   TreeNode() {}
 *   TreeNode(int val) { this.val = val; }
 *   TreeNode(int val, TreeNode left, TreeNode right) {
 *     this.val = val;
 *     this.left = left;
 *     this.right = right;
 *   }
 * }
 */
class Solution {
  public List<Integer> inorderTraversal(TreeNode root) {
    List<Integer> ans = new ArrayList<>();
    while (root != null) {
      if (root.left == null) {
        ans.add(root.val);
        root = root.right;
      } else {
        TreeNode prev = root.left;
        while (prev.right != null && prev.right != root) {
          prev = prev.right;
        }
        if (prev.right == null) {
          prev.right = root;
          root = root.left;
        } else {
          ans.add(root.val);
          prev.right = null;
          root = root.right;
        }
      }
    }
    return ans;
  }
}

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *   int val;
 *   TreeNode *left;
 *   TreeNode *right;
 *   TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *   TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *   TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
  vector<int> inorderTraversal(TreeNode* root) {
    vector<int> ans;
    while (root) {
      if (!root->left) {
        ans.push_back(root->val);
        root = root->right;
      } else {
        TreeNode* prev = root->left;
        while (prev->right && prev->right != root) {
          prev = prev->right;
        }
        if (!prev->right) {
          prev->right = root;
          root = root->left;
        } else {
          ans.push_back(root->val);
          prev->right = nullptr;
          root = root->right;
        }
      }
    }
    return ans;
  }
};

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *   Val int
 *   Left *TreeNode
 *   Right *TreeNode
 * }
 */
func inorderTraversal(root *TreeNode) (ans []int) {
  for root != nil {
    if root.Left == nil {
      ans = append(ans, root.Val)
      root = root.Right
    } else {
      prev := root.Left
      for prev.Right != nil && prev.Right != root {
        prev = prev.Right
      }
      if prev.Right == nil {
        prev.Right = root
        root = root.Left
      } else {
        ans = append(ans, root.Val)
        prev.Right = nil
        root = root.Right
      }
    }
  }
  return
}

/**
 * Definition for a binary tree node.
 * class TreeNode {
 *   val: number
 *   left: TreeNode | null
 *   right: TreeNode | null
 *   constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 *   }
 * }
 */

function inorderTraversal(root: TreeNode | null): number[] {
  const ans: number[] = [];
  while (root) {
    if (!root.left) {
      ans.push(root.val);
      root = root.right;
    } else {
      let prev = root.left;
      while (prev.right && prev.right != root) {
        prev = prev.right;
      }
      if (!prev.right) {
        prev.right = root;
        root = root.left;
      } else {
        ans.push(root.val);
        prev.right = null;
        root = root.right;
      }
    }
  }
  return ans;
}

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *   this.val = (val===undefined ? 0 : val)
 *   this.left = (left===undefined ? null : left)
 *   this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number[]}
 */
var inorderTraversal = function (root) {
  const ans = [];
  while (root) {
    if (!root.left) {
      ans.push(root.val);
      root = root.right;
    } else {
      let prev = root.left;
      while (prev.right && prev.right != root) {
        prev = prev.right;
      }
      if (!prev.right) {
        prev.right = root;
        root = root.left;
      } else {
        ans.push(root.val);
        prev.right = null;
        root = root.right;
      }
    }
  }
  return ans;
};