mirror of
https://github.com/donnemartin/interactive-coding-challenges
synced 2026-01-08 10:28:03 +00:00
Tweaked ordering of graph and bst challenges.
This commit is contained in:
Donne Martin
240
graphs_trees/graph_path_exists/path_exists_solution.ipynb
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240
graphs_trees/graph_path_exists/path_exists_solution.ipynb
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{
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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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"<small><i>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).</i></small>"
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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: Determine whether there is a path between two nodes in a graph.\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 the graph directed?\n",
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" * Yes\n",
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"* Can we assume we already have Graph and Node classes?\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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"Input:\n",
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"* `add_edge(source, destination, weight)`\n",
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"\n",
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"```\n",
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"graph.add_edge(0, 1, 5)\n",
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"graph.add_edge(0, 4, 3)\n",
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"graph.add_edge(0, 5, 2)\n",
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"graph.add_edge(1, 3, 5)\n",
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"graph.add_edge(1, 4, 4)\n",
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"graph.add_edge(2, 1, 6)\n",
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"graph.add_edge(3, 2, 7)\n",
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"graph.add_edge(3, 4, 8)\n",
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"```\n",
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"\n",
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"Result:\n",
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"* search_path(start=0, end=2) -> True\n",
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"* search_path(start=0, end=0) -> True\n",
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"* search_path(start=4, end=5) -> 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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"## Algorithm\n",
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"\n",
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"We use breadth-first search to determine the shortest path. Depth-first search is easier to implement with just straight recursion, but often results in a longer path.\n",
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"\n",
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"* Add the start node to the queue and mark it as visited\n",
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"* If the start node is the end node, return True\n",
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"* While the queue is not empty\n",
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" * Dequeue a node and visit it\n",
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" * If the node is the end node, return True\n",
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" * Iterate through each adjacent node\n",
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" * If the node has not been visited, add it to the queue and mark it as visited\n",
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"* Return False\n",
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"\n",
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"Complexity:\n",
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"* Time: O(V + E), where V = number of vertices and E = number of edges\n",
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"* Space: O(V + E)"
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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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"collapsed": true
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},
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"outputs": [],
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"source": [
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"%run ../graph/graph.py"
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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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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from collections import deque\n",
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"\n",
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"\n",
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"def path_exists(start, end):\n",
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" if start is None or end is None:\n",
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" return False\n",
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" if start is end:\n",
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" return True\n",
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" queue = deque()\n",
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" queue.append(start)\n",
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" start.visited = True\n",
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" while queue:\n",
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" node = queue.popleft()\n",
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" if node is None:\n",
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" continue\n",
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" if node is end:\n",
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" return True\n",
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" for adj_node in node.adjacent:\n",
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" if not adj_node.visited:\n",
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" queue.append(adj_node)\n",
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" adj_node.visited = True\n",
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" return 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": 3,
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"metadata": {
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"collapsed": false
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},
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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_path_exists.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_path_exists.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestPathExists(object):\n",
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"\n",
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" def test_path_exists(self):\n",
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" nodes = []\n",
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" graph = Graph()\n",
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" for id in range(0, 6):\n",
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" nodes.append(graph.add_node(id))\n",
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" graph.add_edge(0, 1, 5)\n",
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" graph.add_edge(0, 4, 3)\n",
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" graph.add_edge(0, 5, 2)\n",
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" graph.add_edge(1, 3, 5)\n",
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" graph.add_edge(1, 4, 4)\n",
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" graph.add_edge(2, 1, 6)\n",
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" graph.add_edge(3, 2, 7)\n",
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" graph.add_edge(3, 4, 8)\n",
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"\n",
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" assert_equal(path_exists(nodes[0], nodes[2]), True)\n",
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" assert_equal(path_exists(nodes[0], nodes[0]), True)\n",
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" assert_equal(path_exists(nodes[4], nodes[5]), False)\n",
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"\n",
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" print('Success: test_path_exists')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestPathExists()\n",
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" test.test_path_exists()\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": 4,
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"metadata": {
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"collapsed": false
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},
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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_path_exists\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_path_exists.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 2",
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"language": "python",
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"name": "python2"
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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": 2
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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": "ipython2",
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"version": "2.7.10"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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