## 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 4For 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; } } } };