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interactive-coding-challenges/graphs_trees/tree_lca/tree_lca_solution.ipynb
Donne Martin 98b7887245 Add tree lca challenge
2017-03-30 05:38:53 -04:00

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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
},
"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"
]
}
],
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