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.
trait TreeNode {
def value: Int
def left: TreeNode
def right: TreeNode
}
object EmptyNode extends TreeNode {
def value = throw new Error("accessing empty node")
def left = throw new Error("accessing empty node")
def right = throw new Error("accessing empty node")
}
class NoneEmptyNode(var value: Int, var left: TreeNode = EmptyNode, var right: TreeNode = EmptyNode) extends TreeNode
def lowestCommonAncestor(root:TreeNode, p:TreeNode, q:TreeNode):TreeNode = {
if (root == EmptyNode || root == p || root == q) return root
val left:TreeNode = lowestCommonAncestor(root.left, p, q)
val right:TreeNode = lowestCommonAncestor(root.right, p, q)
if (left != EmptyNode && right != EmptyNode) root
else if (left != EmptyNode) right
else left
}
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