Common Ancestor

Author: mengli

LowestCommonAncestorOfBinaryTree.java

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+/**
+ * Given a binary tree, find the lowest common ancestor of two given nodes in the tree.
+ *
+ *
+ *       _______3______
+ *      /              \
+ *   ___5__          ___1__
+ *  /      \        /      \
+ *  6      _2       0       8
+ *        /  \
+ *        7   4
+ * If you are not so sure about the definition of lowest common ancestor (LCA), please refer to my previous 
+ * post: Lowest Common Ancestor of a Binary Search Tree (BST) or the definition of LCA here. Using the tree 
+ * above as an example, the LCA of nodes 5 and 1 is 3. Please note that LCA for nodes 5 and 4 is 5.
+ *
+ * Hint:
+ * Top-down or bottom-up? Consider both approaches and see which one is more efficient.
+ */
+public class LowestCommonAncestorOfBinaryTree {
+	public TreeNode LCA(TreeNode root, TreeNode p, TreeNode q) {
+		if (root == null)
+			return null;
+		if (root == p || root == q)
+			return root;
+		TreeNode left = LCA(root.left, p, q);
+		TreeNode right = LCA(root.right, p, q);
+		if (left != null && right != null)
+			return root;
+		return left != null ? left : right;
+	}
+}

LowestCommonAncestorOfaBinarySearchTree.java

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+/**
+ * Lowest Common Ancestor of a Binary Search Tree (BST)
+ *
+ * Given a binary search tree (BST), find the lowest common ancestor of two given nodes in the BST.
+ *
+ *
+ *       _______6______
+ *      /              \
+ *   ___2__          ___8__
+ *  /      \        /      \
+ *  0      _4       7       9
+ *        /  \
+ *        3   5
+ * Using the above tree as an example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. 
+ * But how about LCA of nodes 2 and 4? Should it be 6 or 2?
+ *
+ * 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).¡± Since a node can be a descendant of itself, the LCA of 2 and 
+ * 4 should be 2, according to this definition.
+ *
+ * Hint:
+ * A top-down walk from the root of the tree is enough.
+ */
+public class LowestCommonAncestorOfaBinarySearchTree {
+	public TreeNode LCA(TreeNode root, TreeNode p, TreeNode q) {
+		if (root == null || p == null || q == null)
+			return null;
+		if (Math.max(p.val, q.val) < root.val)
+			return LCA(root.left, p, q);
+		if (Math.min(p.val, q.val) > root.val)
+			return LCA(root.right, p, q);
+		return root;
+	}
+}