mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
305 lines
8.5 KiB
Python
305 lines
8.5 KiB
Python
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solution Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Find the lowest common ancestor of two nodes in a binary tree.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Is this a binary search tree?\n",
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" * No\n",
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"* Can we assume the two nodes are in the tree?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"<pre>\n",
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" _10_\n",
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" / \\\n",
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" 5 9\n",
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" / \\ / \\\n",
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" 12 3 18 20\n",
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" / \\ /\n",
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" 1 8 40\n",
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"</pre>\n",
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"\n",
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"* 0, 5 -> None\n",
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"* 5, 0 -> None\n",
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"* 1, 8 -> 3\n",
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"* 12, 8 -> 5\n",
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"* 12, 40 -> 10\n",
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"* 9, 20 -> 9\n",
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"* 3, 5 -> 5"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"* Verify both nodes are in the tree\n",
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"* Base cases\n",
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" * If the root is None, return None\n",
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" * If the root is either node, return the root\n",
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"* Recursively search left and right\n",
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"* If the left and right are both nodes\n",
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" * The return the root\n",
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"* Else, left or right, whichever is valid\n",
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"\n",
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"Complexity:\n",
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"* Time: O(h), where h is the height of the tree\n",
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"* Space: O(h), where h is the recursion depth"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"class Node(object):\n",
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"\n",
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" def __init__(self, key, left=None, right=None):\n",
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" self.key = key\n",
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" self.left = left\n",
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" self.right = right\n",
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"\n",
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" def __repr__(self):\n",
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" return str(self.key)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"class BinaryTree(object):\n",
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"\n",
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" def lca(self, root, node1, node2):\n",
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" if None in (root, node1, node2):\n",
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" return None\n",
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" if (not self._node_in_tree(root, node1) or\n",
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" not self._node_in_tree(root, node2)):\n",
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" return None\n",
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" return self._lca(root, node1, node2)\n",
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"\n",
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" def _node_in_tree(self, root, node):\n",
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" if root is None:\n",
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" return False\n",
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" if root is node:\n",
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" return True\n",
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" left = self._node_in_tree(root.left, node)\n",
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" right = self._node_in_tree(root.right, node)\n",
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" return left or right\n",
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"\n",
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" def _lca(self, root, node1, node2):\n",
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" if root is None:\n",
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" return None\n",
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" if root is node1 or root is node2:\n",
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" return root\n",
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" left_node = self._lca(root.left, node1, node2)\n",
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" right_node = self._lca(root.right, node1, node2)\n",
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" if left_node is not None and right_node is not None:\n",
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" return root\n",
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" else:\n",
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" return left_node if left_node is not None else right_node"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"class LcaResult(object):\n",
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"\n",
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" def __init__(self, node, is_ancestor):\n",
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" self.node = node\n",
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" self.is_ancestor = is_ancestor\n",
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"\n",
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"\n",
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"class BinaryTreeOptimized(object):\n",
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"\n",
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" def lca(self, root, node1, node2):\n",
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" if root is None:\n",
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" raise TypeError('root cannot be None')\n",
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" result = self._lca(root, node1, node2)\n",
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" if result.is_ancestor:\n",
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" return result.node\n",
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" return None\n",
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"\n",
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" def _lca(self, curr_node, node1, node2):\n",
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" if curr_node is None:\n",
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" return LcaResult(None, is_ancestor=False)\n",
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" if curr_node is node1 and curr_node is node2:\n",
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" return LcaResult(curr_node, is_ancestor=True)\n",
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" left_result = self._lca(curr_node.left, node1, node2)\n",
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" if left_result.is_ancestor:\n",
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" return left_result\n",
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" right_result = self._lca(curr_node.right, node1, node2)\n",
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" if right_result.is_ancestor:\n",
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" return right_result\n",
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" if left_result.node is not None and right_result.node is not None:\n",
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" return LcaResult(curr_node, is_ancestor=True)\n",
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" elif curr_node is node1 or curr_node is node2:\n",
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" is_ancestor = left_result.node is not None or \\\n",
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" right_result.node is not None\n",
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" return LcaResult(curr_node, is_ancestor)\n",
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" else:\n",
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" return LcaResult(left_result.node if left_result.node is not None \\\n",
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" else right_result.node, is_ancestor=False)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_lca.py\n"
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]
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}
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],
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"source": [
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"%%writefile test_lca.py\n",
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"import unittest\n",
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"\n",
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"\n",
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"class TestLowestCommonAncestor(unittest.TestCase):\n",
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"\n",
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" def test_lca(self):\n",
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" node10 = Node(10)\n",
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" node5 = Node(5)\n",
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" node12 = Node(12)\n",
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" node3 = Node(3)\n",
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" node1 = Node(1)\n",
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" node8 = Node(8)\n",
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" node9 = Node(9)\n",
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" node18 = Node(18)\n",
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" node20 = Node(20)\n",
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" node40 = Node(40)\n",
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" node3.left = node1\n",
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" node3.right = node8\n",
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" node5.left = node12\n",
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" node5.right = node3\n",
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" node20.left = node40\n",
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" node9.left = node18\n",
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" node9.right = node20\n",
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" node10.left = node5\n",
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" node10.right = node9\n",
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" root = node10\n",
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" node0 = Node(0)\n",
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" binary_tree = BinaryTree()\n",
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" self.assertEqual(binary_tree.lca(root, node0, node5), None)\n",
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" self.assertEqual(binary_tree.lca(root, node5, node0), None)\n",
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" self.assertEqual(binary_tree.lca(root, node1, node8), node3)\n",
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" self.assertEqual(binary_tree.lca(root, node12, node8), node5)\n",
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" self.assertEqual(binary_tree.lca(root, node12, node40), node10)\n",
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" self.assertEqual(binary_tree.lca(root, node9, node20), node9)\n",
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" self.assertEqual(binary_tree.lca(root, node3, node5), node5)\n",
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" print('Success: test_lca')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestLowestCommonAncestor()\n",
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" test.test_lca()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Success: test_lca\n"
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]
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}
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],
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"source": [
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"%run -i test_lca.py"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 1
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}
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