Lowest Common Ancestor of a Binary Tree

题目描述：

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 allowa 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.

找普通二叉树的最小共同父节点。

这就是找到从root到p和q的路径，找到他们最后一个相同的节点就是他们的父节点。

代码如下：

public class Solution {    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {        List<TreeNode> list1=new ArrayList<TreeNode>();        List<TreeNode> list2=new ArrayList<TreeNode>();        List<TreeNode> path1=new ArrayList<TreeNode>();        List<TreeNode> path2=new ArrayList<TreeNode>();        findPath(root, p, list1, path1);        findPath(root, q, list2, path2);        int i=0;        for(;i<path1.size()&&i<path2.size();i++){            if(path1.get(i)!=path2.get(i))                break;        }        return path1.get(i-1);    }        public void findPath(TreeNode root, TreeNode p ,List<TreeNode> list ,List<TreeNode> result){        if(root==p){            list.add(root);            result.addAll(list);            return;        }        if(root.left!=null){            list.add(root);            findPath(root.left, p, list, result);            list.remove(list.size()-1);        }        if(root.right!=null){            list.add(root);            findPath(root.right, p, list, result);            list.remove(list.size()-1);        }    }}

之前findPath我是这么写的，这么做会超时，开销也太大。

public void findPath(TreeNode root, TreeNode p ,List<TreeNode> list ,List<TreeNode> result){if(root==p){list.add(root);result.addAll(list);return;}if(root.left!=null){List<TreeNode> newlist1=new ArrayList<TreeNode>(list);list.add(root);findPath(root.left, p, newlist1, result);}if(root.right!=null){List<TreeNode> newlist2=new ArrayList<TreeNode>(list);newlist2.add(root);findPath(root.right, p, newlist2, result);}}

我看别人还有一种递归，这种也是值得学习的：

public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {      if(root==null || p==null || q==null) return null;            List<TreeNode> pathp = new ArrayList<>();      List<TreeNode> pathq = new ArrayList<>();      pathp.add(root);      pathq.add(root);            getPath(root, p, pathp);      getPath(root, q, pathq);            TreeNode lca = null;      for(int i=0; i<pathp.size() && i<pathq.size(); i++) {          if(pathp.get(i) == pathq.get(i)) lca = pathp.get(i);          else break;      }      return lca;  }    private boolean getPath(TreeNode root, TreeNode n, List<TreeNode> path) {      if(root==n) {          return true;      }            if(root.left!=null) {          path.add(root.left);          if(getPath(root.left, n, path)) return true;          path.remove(path.size()-1);      }            if(root.right!=null) {          path.add(root.right);          if(getPath(root.right, n, path)) return true;          path.remove(path.size()-1);      }            return false;  }