【重点】【LCA】剑指offer68：二叉树最近公共祖先|235. 二叉搜索树的最近公共祖先

LCA（lowest common ancestor）问题
力扣，【二叉搜索树】
【普通二叉树】

1.二叉搜索树

思路

Python

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
        while root:
            if p.val < root.val and q.val < root.val:
                root = root.left
            elif p.val > root.val and q.val > root.val:
                root = root.right
            else:
                break
            
        return root

Java

// 迭代版
class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        while (root != null) {
            if (p.val < root.val && q.val < root.val) {
                root = root.left;
            } else if (p. val > root.val && q.val > root.val) {
                root = root.right;
            } else {
                break;
            }

        }
        return root;
    }
}

// 递归版
class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if (root == null) {
            return null;
        }
        if (root.val < p.val && root.val < q.val) {
            return lowestCommonAncestor(root.right, p, q);
        } else if (root.val > p.val && root.val > q.val) {
            return lowestCommonAncestor(root.left, p, q);
        }

        return root;
    }
}

2.普通二叉树

参考思路

Python

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    def lowestCommonAncestor(self, root: TreeNode, p: TreeNode, q: TreeNode) -> TreeNode:
        if not root or root == p or root == q:
            return root
        left_node = self.lowestCommonAncestor(root.left, p, q)
        right_node = self.lowestCommonAncestor(root.right, p, q)
        if left_node and right_node:
            return root
        elif not left_node and not right_node:
            return None
        else:
            return left_node if left_node else right_node

Java

// 版本1
class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if (root == null) {
            return null;
        }
        if (root == p || root == q) {
            return root;
        }
        TreeNode leftNode = lowestCommonAncestor(root.left, p, q);
        TreeNode rightNode = lowestCommonAncestor(root.right, p, q);
        if (leftNode != null && rightNode != null) {
            return root;
        }
        if (leftNode == null && rightNode == null) {
            return null;
        }
        return leftNode == null ? rightNode : leftNode;
    }
}

// 版本2
class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if (root == null || root == p || root == q) {
            return root;
        }
        TreeNode left = lowestCommonAncestor(root.left, p, q);
        TreeNode right = lowestCommonAncestor(root.right, p, q);
        if (left == null && right == null) {
            return null;
        } else if (left != null && right != null) {
            return root;
        }

        return left == null ? right : left;
    }
}