236 Lowest Common Ancestor of a Binary Tree

Total Accepted: 46265 Total Submissions: 160631 Difficulty: Medium
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.

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package tree;

public class LowestCommonAncestor {
 public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
  
  /* https://leetcode.com/discuss/45399/my-java-solution-which-is-easy-to-understand
   *     ___ 1_____
   *   /           \
   *  __2 ___       __ 3 ___
   * /    \     /        \
   * 4        5    6        7
   */

  // p, q in the same subtree, q is the child of p,  e.g  (p,q) is (2, 5) or (3, 7)
  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;   // p, q are in the different subtree of root  e.g. (p,q) is (4, 6)
  }
  return left != null ? left : right;
  
 }

 public TreeNode dfs_failed(TreeNode root, TreeNode p, TreeNode q) {
  
  TreeNode node = root;

  if (node == null)
   return null;

  if (node == p || node == q) {
   return node;
  }

  if (node.left != null) {

   node = dfs_failed(node.left, p, q);
  }
  if (node.right != null) {
   node = dfs_failed(node.right, p, q);
  }

  return node;

 }

 public static void main(String[] args) {
  // TODO Auto-generated method stub
  int[] inorder = { 4, 2, 5, 1, 6, 3, 7 };
  int[] preorder = { 1, 2, 4, 5, 3, 6, 7 };
  int[] output = { 1, 2, 3, 4, 5, 6, 7 };
  ConstructBinaryTreeFromArray cbt = new ConstructBinaryTreeFromArray();
  TreeNode root = cbt.buildTree(inorder, preorder);
   
  LowestCommonAncestor lca = new LowestCommonAncestor();
  TreeNode commonAncesor = lca.lowestCommonAncestor(root, root.left , root.left.right);  // (p,q) = (2, 5)
  
  String res = commonAncesor == null ?  "Null" : String.valueOf(commonAncesor.val);  // 2
   System.out.println(res);
 }

}