interactive-coding-challenges/graphs_trees/tree_lca/tree_lca_solution.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Find the lowest common ancestor of two nodes in a binary tree.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Is this a binary search tree?\n",
    "    * No\n",
    "* Can we assume the two nodes are in the tree?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "<pre>\n",
    "          _10_\n",
    "        /      \\\n",
    "       5        9\n",
    "      / \\      / \\\n",
    "     12  3    18  20\n",
    "        / \\       /\n",
    "       1   8     40\n",
    "</pre>\n",
    "\n",
    "* 0, 5 -> None\n",
    "* 5, 0 -> None\n",
    "* 1, 8 -> 3\n",
    "* 12, 8 -> 5\n",
    "* 12, 40 -> 10\n",
    "* 9, 20 -> 9\n",
    "* 3, 5 -> 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "* Verify both nodes are in the tree\n",
    "* Base cases\n",
    "    * If the root is None, return None\n",
    "    * If the root is either node, return the root\n",
    "* Recursively search left and right\n",
    "* If the left and right are both nodes\n",
    "    * The return the root\n",
    "* Else, left or right, whichever is valid\n",
    "\n",
    "Complexity:\n",
    "* Time: O(h), where h is the height of the tree\n",
    "* Space: O(h), where h is the recursion depth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "class Node(object):\n",
    "\n",
    "    def __init__(self, key, left=None, right=None):\n",
    "        self.key = key\n",
    "        self.left = left\n",
    "        self.right = right\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str(self.key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class BinaryTree(object):\n",
    "\n",
    "    def lca(self, root, node1, node2):\n",
    "        if None in (root, node1, node2):\n",
    "            return None\n",
    "        if (not self._node_in_tree(root, node1) or\n",
    "                not self._node_in_tree(root, node2)):\n",
    "            return None\n",
    "        return self._lca(root, node1, node2)\n",
    "\n",
    "    def _node_in_tree(self, root, node):\n",
    "        if root is None:\n",
    "            return False\n",
    "        if root is node:\n",
    "            return True\n",
    "        left = self._node_in_tree(root.left, node)\n",
    "        right = self._node_in_tree(root.right, node)\n",
    "        return left or right\n",
    "\n",
    "    def _lca(self, root, node1, node2):\n",
    "        if root is None:\n",
    "            return None\n",
    "        if root is node1 or root is node2:\n",
    "            return root\n",
    "        left_node = self._lca(root.left, node1, node2)\n",
    "        right_node = self._lca(root.right, node1, node2)\n",
    "        if left_node is not None and right_node is not None:\n",
    "            return root\n",
    "        else:\n",
    "            return left_node if left_node is not None else right_node"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "class LcaResult(object):\n",
    "\n",
    "    def __init__(self, node, is_ancestor):\n",
    "        self.node = node\n",
    "        self.is_ancestor = is_ancestor\n",
    "\n",
    "\n",
    "class BinaryTreeOptimized(object):\n",
    "\n",
    "    def lca(self, root, node1, node2):\n",
    "        if root is None:\n",
    "            raise TypeError('root cannot be None')\n",
    "        result = self._lca(root, node1, node2)\n",
    "        if result.is_ancestor:\n",
    "            return result.node\n",
    "        return None\n",
    "\n",
    "    def _lca(self, curr_node, node1, node2):\n",
    "        if curr_node is None:\n",
    "            return LcaResult(None, is_ancestor=False)\n",
    "        if curr_node is node1 and curr_node is node2:\n",
    "            return LcaResult(curr_node, is_ancestor=True)\n",
    "        left_result = self._lca(curr_node.left, node1, node2)\n",
    "        if left_result.is_ancestor:\n",
    "            return left_result\n",
    "        right_result = self._lca(curr_node.right, node1, node2)\n",
    "        if right_result.is_ancestor:\n",
    "            return right_result\n",
    "        if left_result.node is not None and right_result.node is not None:\n",
    "            return LcaResult(curr_node, is_ancestor=True)\n",
    "        elif curr_node is node1 or curr_node is node2:\n",
    "            is_ancestor = left_result.node is not None or \\\n",
    "                right_result.node is not None\n",
    "            return LcaResult(curr_node, is_ancestor)\n",
    "        else:\n",
    "            return LcaResult(left_result.node if left_result.node is not None \\\n",
    "                                 else right_result.node, is_ancestor=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_lca.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_lca.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestLowestCommonAncestor(object):\n",
    "\n",
    "    def test_lca(self):\n",
    "        node10 = Node(10)\n",
    "        node5 = Node(5)\n",
    "        node12 = Node(12)\n",
    "        node3 = Node(3)\n",
    "        node1 = Node(1)\n",
    "        node8 = Node(8)\n",
    "        node9 = Node(9)\n",
    "        node18 = Node(18)\n",
    "        node20 = Node(20)\n",
    "        node40 = Node(40)\n",
    "        node3.left = node1\n",
    "        node3.right = node8\n",
    "        node5.left = node12\n",
    "        node5.right = node3\n",
    "        node20.left = node40\n",
    "        node9.left = node18\n",
    "        node9.right = node20\n",
    "        node10.left = node5\n",
    "        node10.right = node9\n",
    "        root = node10\n",
    "        node0 = Node(0)\n",
    "        binary_tree = BinaryTree()\n",
    "        assert_equal(binary_tree.lca(root, node0, node5), None)\n",
    "        assert_equal(binary_tree.lca(root, node5, node0), None)\n",
    "        assert_equal(binary_tree.lca(root, node1, node8), node3)\n",
    "        assert_equal(binary_tree.lca(root, node12, node8), node5)\n",
    "        assert_equal(binary_tree.lca(root, node12, node40), node10)\n",
    "        assert_equal(binary_tree.lca(root, node9, node20), node9)\n",
    "        assert_equal(binary_tree.lca(root, node3, node5), node5)\n",
    "        print('Success: test_lca')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestLowestCommonAncestor()\n",
    "    test.test_lca()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_lca\n"
     ]
    }
   ],
   "source": [
    "%run -i test_lca.py"
   ]
  }
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