# [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.

TreeNode * LCA(TreeNode * root, TreeNode * p, TreeNode * q)

• if root is null, return null
• if root == p || root == q, return root // find the target node
• else:
• left = LCA(root->left, p, q)
• right = LCA(root->right, p, q)
• if(left && right) return root; //lowest ancestor
• else return left == nullptr? right: left; //return the non null child

/**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
class Solution {
public:
//what if a node does not exist in tree
//what if p == nullptr || q == nullptr
TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
if(root == nullptr || p == nullptr || q == nullptr){
return nullptr;
}
else if(root == p || root == q){
return root;
}
else{
//search deeper
TreeNode * left = lowestCommonAncestor(root->left, p, q);
TreeNode * right = lowestCommonAncestor(root->right, p, q);
if((left && right)){
//lowest ancestor
return root;
}
else{
//below ancestor or above ancestor
return left == nullptr? right: left;
}
}
}
};

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