LeetCode----Lowest Common Ancestor of a Binary Tree

Lowest Common Ancestor of a Binary Tree

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.

分析：

此时的二叉树为普通的二叉树，无法像BST树一样可以利用BST的特性进行求解了。

思路：递归在root结点的左右子树中搜索p和q，如果两边都搜索成功，说明root即为LCA，否则，如果p和q为上下级关系时，此时只能搜索到p或者q（因为一旦搜索成功即停止搜索，递归返回了），返回后的结点p或者q即为要找的LCA。

代码：

class Solution(object):
    def lowestCommonAncestor(self, root, p, q):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
        if not root or root == p or root == q:
            return root
        l = self.lowestCommonAncestor(root.left, p, q)
        r = self.lowestCommonAncestor(root.right, p, q)
        # 如果l和r都存在，说明root是LCA；否则，返回的是只会是l或者r，表示p和q为上下级关系
        return root if l and r else (l if l else r)