236. Lowest Common Ancestor of a Binary Tree - jiejackyzhang/leetcode-note GitHub Wiki

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

        _______3______
       /              \
    ___5__          ___1__
   /      \        /      \
   6      _2       0       8
         /  \
         7   4

For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

这道题与"235. Lowest Common Ancestor of a Binary Search Tree"的区别在于这是general binary tree，没有BST的特性。

因此这里我们需要采用BFS的思想，一层一层地遍历。

1. base cases是root == null或者root == p或者root == q，则返回root；
2. left和right是对左右子树递归调用的返回值；
3. 如果left != null && right != null，说明p，q在root两边，则LCA是root，返回root；
4. 否则返回left和right中不为null的那个值。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public 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) {
            return right;
        } else if(right == null) {
            return left;
        } else {
            return root;
        }
    }
}