Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.
According to the : “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.
这道求二叉树的最小共同父节点的题是之前那道的Follow Up。跟之前那题不同的地方是,这道题是普通是二叉树,不是二叉搜索树,所以就不能利用其特有的性质,所以我们只能在二叉树中来搜索p和q,然后从路径中找到最后一个相同的节点即为父节点,我们可以用递归来实现,写法很简洁,代码如下:
class Solution {public: TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) { if (!root || p == root || q == root) return root; TreeNode *left = lowestCommonAncestor(root->left, p, q); TreeNode *right = lowestCommonAncestor(root->right, p , q); if (left && right) return root; return left ? left : right; }};
上述代码可以进行优化一下,在找完左子树的共同父节点时如果结果存在,且不是p或q,那么不用再找右子树了,直接返回这个结果即可,同理,对找完右子树的结果做同样处理,参见代码如下:
class Solution {public: TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) { if (!root || p == root || q == root) return root; TreeNode *left = lowestCommonAncestor(root->left, p, q); if (left && left != p && left != q) return left; TreeNode *right = lowestCommonAncestor(root->right, p , q); if (right && right != p && right != q) return right; if (left && right) return root; return left ? left : right; }};
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