**Lowest Common Ancestor of Two Nodes in a Binary Tree

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

解法一： 

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Version 1: Traditional Method

public class Solution {
    private ArrayList<TreeNode> getPath2Root(TreeNode node) {
        ArrayList<TreeNode> list = new ArrayList<TreeNode>();
        while (node != null) {
            list.add(node);
            node = node.parent;
        }
        return list;
    }
    public TreeNode lowestCommonAncestor(TreeNode node1, TreeNode node2) {
        ArrayList<TreeNode> list1 = getPath2Root(node1);
        ArrayList<TreeNode> list2 = getPath2Root(node2);
        
        int i, j;
        for (i = list1.size() - 1, j = list2.size() - 1; i >= 0 && j >= 0; i--, j--) {
            if (list1.get(i) != list2.get(j)) {
                return list1.get(i).parent;
            }
        }
        return list1.get(i+1);
    }
}

 解法二：分治法

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 (root == null){
            return null;
        }
        if (root == A || root == B){
            return root;//当找到一中一个node， 向上传递这个node
        }
        TreeNode left = lowestCommonAncestor(root.left, A, B);
        TreeNode right = lowestCommonAncestor(root.right, A, B);
        if (left != null && right != null){//check左右，如果左右分别包含两个node则这个root就是LCA， 向上传递这个node
            return root;
        } else if (left != null){//只有左边有node，向上传递此node
            return left;
        } else if (right != null){
            return right;
        } else{//左右边都没有node 传递null
            return null;
        }
    }
}

 video: http://www.bittiger.io/videos/TLfAyc3Hxfaxp2Fs9/Jj33gh5tbGcFyKCWa

reference：http://ryanleetcode.blogspot.com/2015/04/lowest-common-ancestor.html