The Lowest Common Ancestor (LCA) of two nodes in a binary tree is the lowest (deepest) node in the tree that has both of the given nodes as descendants. In other words, it's the shared ancestor that is located farthest from the root.
Here are the key points about the LCA:
- Shared Ancestor: The LCA is a node that is common to both nodes whose LCA we're trying to find.
- Lowest in Depth: It's the lowest node in terms of depth in the tree.
- Deepest Common Ancestor: It's the common ancestor located farthest from the root.
For example, consider the binary tree:
3
/ \
5 1
/ \ / \
6 2 0 8
/ \
7 4
The LCA of nodes 5 and 1 is the node with value 3. Similarly, the LCA of nodes 5 and 4 is the node with value 5.
It's important to note that a node can be considered a descendant of itself, so if one of the given nodes is an ancestor of the other, that node itself is the lowest common ancestor.
The LCA problem is a common problem in computer science and has various applications, such as in determining relationships in genealogical trees, finding the nearest common ancestor in version control systems, and in solving various tree-related algorithmic problems.
