[Lintcode]Lowest Common Ancestor 最近公共祖先

Given the root and two nodes in a Binary Tree. Find the lowest common ancestor(LCA) of the two nodes.

The lowest common ancestor is the node with largest depth which is the ancestor of both nodes.

Example

For the following binary tree:

  4
 / \
3   7
   / \
  5   6

LCA(3, 5) = 4

LCA(5, 6) = 7

LCA(6, 7) = 7

分析：递归。不论哪种情况（A，B处于root两侧或者同一侧）只需要在遇到A或B时，马上返回即可。同一侧时，遇到A（B）马上返回，不需要继续向下找B。因为A就是LCA。两侧时，遇到A（B）马上返回，在递归最外层返回root即为LCA。

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */
public class Solution {
    /**
     * @param root: The root of the binary search tree.
     * @param A and B: two nodes in a Binary.
     * @return: Return the least common ancestor(LCA) of the two nodes.
     */
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode A, TreeNode B) {
        if(A == root) return A;
        if(B == root) return B;
        
        TreeNode left = null, right = null;
        if(root.left != null) left = lowestCommonAncestor(root.left, A, B);
        if(root.right != null) right = lowestCommonAncestor(root.right, A, B);
        
        if(left != null && right != null) return root;
        else if(left != null) return left;
        else return right;
    }
}