235. Lowest Common Ancestor of a Binary Search Tree

Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.

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).”

        _______6______
       /              \
    ___2__          ___8__
   /      \        /      \
   0      _4       7       9
         /  \
         3   5

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

Solution:

For a given BST, we know that, all the values of left children are less than root.val and all the values of right children are greater than root.val. 

For a common ancestor of two nodes in a BST, the value of ancestor must between the values of the two nodes. 

So if root.val is greater than both of the node's values, the lowest common ancestor must be in the root's left child. If root.val is smaller then both of the nodes' values, the lowest common ancestor must be in the root's right child. 

   public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {  
     if(root.val>p.val && root.val>q.val) return lowestCommonAncestor(root.left,p,q);  
     else if(root.val<p.val && root.val < q.val) return lowestCommonAncestor(root.right,p,q);  
     return root;      
   }