From 98b788724576ec01a3a6392b6b503ad337c2393a Mon Sep 17 00:00:00 2001
From: Donne Martin <donne.martin@gmail.com>
Date: Thu, 30 Mar 2017 05:38:53 -0400
Subject: [PATCH] Add tree lca challenge

---
 graphs_trees/tree_lca/__init__.py             |   0
 graphs_trees/tree_lca/test_lca.py             |  45 +++
 .../tree_lca/tree_lca_challenge.ipynb         | 221 ++++++++++++
 graphs_trees/tree_lca/tree_lca_solution.ipynb | 314 ++++++++++++++++++
 4 files changed, 580 insertions(+)
 create mode 100644 graphs_trees/tree_lca/__init__.py
 create mode 100644 graphs_trees/tree_lca/test_lca.py
 create mode 100644 graphs_trees/tree_lca/tree_lca_challenge.ipynb
 create mode 100644 graphs_trees/tree_lca/tree_lca_solution.ipynb

diff --git a/graphs_trees/tree_lca/__init__.py b/graphs_trees/tree_lca/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/graphs_trees/tree_lca/test_lca.py b/graphs_trees/tree_lca/test_lca.py
new file mode 100644
index 0000000..1a25af3
--- /dev/null
+++ b/graphs_trees/tree_lca/test_lca.py
@@ -0,0 +1,45 @@
+from nose.tools import assert_equal
+
+
+class TestLowestCommonAncestor(object):
+
+    def test_lca(self):
+        node10 = Node(10)
+        node5 = Node(5)
+        node12 = Node(12)
+        node3 = Node(3)
+        node1 = Node(1)
+        node8 = Node(8)
+        node9 = Node(9)
+        node18 = Node(18)
+        node20 = Node(20)
+        node40 = Node(40)
+        node3.left = node1
+        node3.right = node8
+        node5.left = node12
+        node5.right = node3
+        node20.left = node40
+        node9.left = node18
+        node9.right = node20
+        node10.left = node5
+        node10.right = node9
+        root = node10
+        node0 = Node(0)
+        binary_tree = BinaryTree()
+        assert_equal(binary_tree.lca(root, node0, node5), None)
+        assert_equal(binary_tree.lca(root, node5, node0), None)
+        assert_equal(binary_tree.lca(root, node1, node8), node3)
+        assert_equal(binary_tree.lca(root, node12, node8), node5)
+        assert_equal(binary_tree.lca(root, node12, node40), node10)
+        assert_equal(binary_tree.lca(root, node9, node20), node9)
+        assert_equal(binary_tree.lca(root, node3, node5), node5)
+        print('Success: test_lca')
+
+
+def main():
+    test = TestLowestCommonAncestor()
+    test.test_lca()
+
+
+if __name__ == '__main__':
+    main()
\ No newline at end of file
diff --git a/graphs_trees/tree_lca/tree_lca_challenge.ipynb b/graphs_trees/tree_lca/tree_lca_challenge.ipynb
new file mode 100644
index 0000000..a1443da
--- /dev/null
+++ b/graphs_trees/tree_lca/tree_lca_challenge.ipynb
@@ -0,0 +1,221 @@
+{
+ "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": [
+    "# Challenge Notebook"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem: Find the lowest common ancestor in a binary tree.\n",
+    "\n",
+    "* [Constraints](#Constraints)\n",
+    "* [Test Cases](#Test-Cases)\n",
+    "* [Algorithm](#Algorithm)\n",
+    "* [Code](#Code)\n",
+    "* [Unit Test](#Unit-Test)\n",
+    "* [Solution Notebook](#Solution-Notebook)"
+   ]
+  },
+  {
+   "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",
+    "Refer to the [Solution Notebook]().  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "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": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "class BinaryTree(object):\n",
+    "\n",
+    "    def lca(self, root, node1, node2):\n",
+    "        # TODO: Implement me\n",
+    "        pass"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Unit Test"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**The following unit test is expected to fail until you solve the challenge.**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# %load 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": "markdown",
+   "metadata": {},
+   "source": [
+    "## Solution Notebook\n",
+    "\n",
+    "Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/graphs_trees/tree_lca/tree_lca_solution.ipynb b/graphs_trees/tree_lca/tree_lca_solution.ipynb
new file mode 100644
index 0000000..4fc621f
--- /dev/null
+++ b/graphs_trees/tree_lca/tree_lca_solution.ipynb
@@ -0,0 +1,314 @@
+{
+ "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
+   },
+   "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"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "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
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success: test_lca\n"
+     ]
+    }
+   ],
+   "source": [
+    "%run -i test_lca.py"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}