236. Lowest Common Ancestor of a Binary Tree

Posted 2020-10-23 张乐乐章

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 5and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

 

解题思路

• Divide & Conquer 的思路
• 如果root为空，则返回空
• 如果root等于其中某个node，则返回root
• 如果上述两种情况都不满足，则divide，左右子树分别调用该方法
• Divide & Conquer中治这一步要考虑清楚，本题三种情况
• 如果left和right都有结果返回，说明root是最小公共祖先
• 如果只有left有返回值，说明left的返回值是最小公共祖先
• 如果只有?right有返回值，说明?right的返回值是最小公共祖先

 1 class Solution {
 2     public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
 3         if(root ==null || p==root||q==root) return root;
 4         TreeNode lp = lowestCommonAncestor(root.left,p,q);
 5         TreeNode rp = lowestCommonAncestor(root.right,p,q);
 6         if(lp!=null&&rp!=null) return root;
 7         if(lp==null&&rp!=null) return rp;
 8         if(lp!=null&&rp==null) return lp;
 9         return null;
10     }
11 }