07/16/2016 Tree

## Question

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.

## Solution

Result: Accepted Time: 16 ms

Here should be some explanations.

/**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     struct TreeNode *left;
*     struct TreeNode *right;
* };
*/
struct TreeNode* lowestCommonAncestor(struct TreeNode* root, struct TreeNode* p, struct TreeNode* q) {
if(!root || root == p || root == q)
return root;
struct TreeNode* left = lowestCommonAncestor(root->left, p, q);
struct TreeNode* right = lowestCommonAncestor(root->right, p, q);
if(left)
return right?root:left;
return right;
}


Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$