0236 Lowest Common Ancestor of a Binary Tree

0236 Lowest Common Ancestor of a Binary Tree#

Problem#

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 p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Examples#

Example 1:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of nodes 5 and 1 is 3.

Example 2:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

Example 3:

Input: root = [1,2], p = 1, q = 2
Output: 1

Analysis#

Typical binary tree or binary search tree problem:

  • traversal or recursion as subproblem: for this problem, it seems we cannot get the results if we just traverse the tree once. Then we divide the problem into subproblems and do recursion.

  • subproblem:

    • for each node, what should know first??

      • if p or/and q are in the subtrees

    • for each node, what to do??

      • if p and q are in different subtrees (left and right), then root is an ancestor

      • if p and q are in the same subtree (left or right), then the node of the subtree is an ancestor

      • if root is p or q, and both nodes are in the subtree, then root is an ancestor

      • otherwise, p, q are not in subtree, no ancestor in current subtree

    • for each node, when to do it??

      • we need pass subtree information, it is easy to use post-order.

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