Least Common Ancestor : Binary Tree

Lowest Common Ancestor:

In graph theory and computer science, the lowest common ancestor (LCA) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define each node to be a descendant of itself (so if v has a direct connection from w, w is the lowest common ancestor).

The LCA of v and w in T is the shared ancestor of v and w that is located farthest from the root. Computation of lowest common ancestors may be useful, for instance, as part of a procedure for determining the distance between pairs of nodes in a tree: the distance from v to w can be computed as the distance from the root to v, plus the distance from the root to w, minus twice the distance from the root to their lowest common ancestor (Djidjev, Pantziou & Zaroliagis 1991). In ontologies, the lowest common ancestor is also known as the least common subsumer.

In a tree data structure where each node points to its parent, the lowest common ancestor can be easily determined by finding the first intersection of the paths from vand w to the root. In general, the computational time required for this algorithm is O(h) where h is the height of the tree (length of longest path from a leaf to the root). However, there exist several algorithms for processing trees so that lowest common ancestors may be found more quickly. Tarjan's off-line lowest common ancestors algorithm, for example, preprocesses a tree in linear time to provide constant-time LCA queries. In general DAGs, similar algorithms exist, but with super-linear complexity.

[SOURCE: https://en.wikipedia.org/wiki/Lowest_common_ancestor]

Problem :

Given a binary tree and two values d1& d2, find the least common ancestor of the two values in the input tree.


Example:
  Consider the following image :

Solution :
We follow a recursive approach where in we recurse through the right and left children of the parameter node .

Return value is root itself if output of each recursion is null , else the we return the value is which in non-null among the two recursive output.

Base and Edge cases are as shown in the code.

Implementation:

Binary Tree Node :

public class BinaryTreeNode {

    private int data;    private BinaryTreeNode left;    private BinaryTreeNode right;
    public int getData() {
        return data;    }

    public void setData(int data) {
        this.data = data;    }

    public BinaryTreeNode getLeft() {
        return left;    }

    public void setLeft(BinaryTreeNode left) {
        this.left = left;    }

    public BinaryTreeNode getRight() {
        return right;    }

    public void setRight(BinaryTreeNode right) {
        this.right = right;    }
}

LCA class : 

public class LCA {


    public BinaryTreeNode getLCA(BinaryTreeNode root, int data1, int data2){

    //Base case
        if (root == null){
            return  null;        }

    //edge case
        if (root.getData()==data1 || root.getData() == data2) {
            return root;        }


    BinaryTreeNode leftLCA = getLCA(root.getLeft(), data1, data2);            BinaryTreeNode rightLCA = getLCA(root.getRight(), data1, data2);

    if (leftLCA != null && rightLCA != null){
        return root;    }

    if (leftLCA == null) {
        return rightLCA;    }

    else {
        return leftLCA;    }


    }
}