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 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.

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;  
}