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# 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 p and q as the lowest node in T that has both p and q as descendants (where we allow

**a node to be a descendant of itself**).”Given binary search tree: root = [6,2,8,0,4,7,9,null,null,3,5]

**Example 1:**

Input:

root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8

Output:

6

Explanation:

The LCA of nodes 2 and 8 is 6.

**Example 2:**

Input:

root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4

Output:

2

Explanation:

The LCA of nodes 2 and 4 is 2

, since a node can be a descendant of itself according to the LCA definition.

**Note:**

- All of the nodes' values will be unique.
- p and q are different and both values will exist in the BST.

/**

* Definition for a binary tree node.

* public class TreeNode {

* int val;

* TreeNode left;

* TreeNode right;

* TreeNode(int x) { val = x; }

* }

*/

class Solution {

public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {

// Value of current node or parent node.

int parentVal = root.val;

// Value of p

int pVal = p.val;

// Value of q;

int qVal = q.val;

if (pVal > parentVal && qVal > parentVal) {

// If both p and q are greater than parent

return lowestCommonAncestor(root.right, p, q);

} else if (pVal < parentVal && qVal < parentVal) {

// If both p and q are lesser than parent

return lowestCommonAncestor(root.left, p, q);

} else {

// We have found the split point, i.e. the LCA node.

return root;

}

}

}

Iterative

public class Solution {

public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {

if(root == null || root == p || root == q) return root;

TreeNode left = lowestCommonAncestor(root.left, p, q);

TreeNode right = lowestCommonAncestor(root.right, p, q);

if(left != null && right != null) return root;

return left != null ? left : right;

}

}

Last modified 3yr ago