diff --git a/README.md b/README.md
index 3061cbe..8edc4cf 100644
--- a/README.md
+++ b/README.md
@@ -203,13 +203,13 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup
| Challenge | Static Notebooks |
|--------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------|
-| Implement a binary search tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst/bst_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst/bst_solution.ipynb) |
| Implement depth-first search (pre-, in-, post-order) on a tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_dfs/dfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_dfs/dfs_solution.ipynb) |
| Implement breadth-first search on a tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_bfs/bfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_bfs/bfs_solution.ipynb) |
| Determine the height of a tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb) |
-| Implement a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph/graph_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph/graph_solution.ipynb) |
+| Implement a binary search tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst/bst_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst/bst_solution.ipynb) |
| Implement depth-first search on a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_solution.ipynb) |
| Implement breadth-first search on a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_bfs/bfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_bfs/bfs_solution.ipynb) |
+| Implement a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph/graph_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph/graph_solution.ipynb) |
| Print a tree using pre-order traversal without recursion | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
| Determine the lowest common ancestor of two nodes | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
| Transform a binary tree into a heap | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
diff --git a/graphs_trees/graph_path_exists/__init__.py b/graphs_trees/graph_path_exists/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/graphs_trees/graph_path_exists/path_exists_challenge.ipynb b/graphs_trees/graph_path_exists/path_exists_challenge.ipynb
new file mode 100644
index 0000000..ab5626d
--- /dev/null
+++ b/graphs_trees/graph_path_exists/path_exists_challenge.ipynb
@@ -0,0 +1,199 @@
+{
+ "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: Determine whether there is a path between two nodes in a graph.\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 the graph directed?\n",
+ " * Yes\n",
+ "* Can we assume we already have Graph and Node classes?\n",
+ " * Yes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Test Cases\n",
+ "\n",
+ "Input:\n",
+ "* `add_edge(source, destination, weight)`\n",
+ "\n",
+ "```\n",
+ "graph.add_edge(0, 1, 5)\n",
+ "graph.add_edge(0, 4, 3)\n",
+ "graph.add_edge(0, 5, 2)\n",
+ "graph.add_edge(1, 3, 5)\n",
+ "graph.add_edge(1, 4, 4)\n",
+ "graph.add_edge(2, 1, 6)\n",
+ "graph.add_edge(3, 2, 7)\n",
+ "graph.add_edge(3, 4, 8)\n",
+ "```\n",
+ "\n",
+ "Result:\n",
+ "* search_path(start=0, end=2) -> True\n",
+ "* search_path(start=0, end=0) -> True\n",
+ "* search_path(start=4, end=5) -> False"
+ ]
+ },
+ {
+ "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": [
+ "%run ../graph/graph.py\n",
+ "%load ../graph/graph.py"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "def path_exists(start, end):\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_path_exists.py\n",
+ "from nose.tools import assert_equal\n",
+ "\n",
+ "\n",
+ "class TestPathExists(object):\n",
+ "\n",
+ " def test_path_exists(self):\n",
+ " nodes = []\n",
+ " graph = Graph()\n",
+ " for id in range(0, 6):\n",
+ " nodes.append(graph.add_node(id))\n",
+ " graph.add_edge(0, 1, 5)\n",
+ " graph.add_edge(0, 4, 3)\n",
+ " graph.add_edge(0, 5, 2)\n",
+ " graph.add_edge(1, 3, 5)\n",
+ " graph.add_edge(1, 4, 4)\n",
+ " graph.add_edge(2, 1, 6)\n",
+ " graph.add_edge(3, 2, 7)\n",
+ " graph.add_edge(3, 4, 8)\n",
+ "\n",
+ " assert_equal(path_exists(nodes[0], nodes[2]), True)\n",
+ " assert_equal(path_exists(nodes[0], nodes[0]), True)\n",
+ " assert_equal(path_exists(nodes[4], nodes[5]), False)\n",
+ "\n",
+ " print('Success: test_path_exists')\n",
+ "\n",
+ "\n",
+ "def main():\n",
+ " test = TestPathExists()\n",
+ " test.test_path_exists()\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 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/graphs_trees/graph_path_exists/path_exists_solution.ipynb b/graphs_trees/graph_path_exists/path_exists_solution.ipynb
new file mode 100644
index 0000000..c6ac3ed
--- /dev/null
+++ b/graphs_trees/graph_path_exists/path_exists_solution.ipynb
@@ -0,0 +1,240 @@
+{
+ "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: Determine whether there is a path between two nodes in a graph.\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 the graph directed?\n",
+ " * Yes\n",
+ "* Can we assume we already have Graph and Node classes?\n",
+ " * Yes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Test Cases\n",
+ "\n",
+ "Input:\n",
+ "* `add_edge(source, destination, weight)`\n",
+ "\n",
+ "```\n",
+ "graph.add_edge(0, 1, 5)\n",
+ "graph.add_edge(0, 4, 3)\n",
+ "graph.add_edge(0, 5, 2)\n",
+ "graph.add_edge(1, 3, 5)\n",
+ "graph.add_edge(1, 4, 4)\n",
+ "graph.add_edge(2, 1, 6)\n",
+ "graph.add_edge(3, 2, 7)\n",
+ "graph.add_edge(3, 4, 8)\n",
+ "```\n",
+ "\n",
+ "Result:\n",
+ "* search_path(start=0, end=2) -> True\n",
+ "* search_path(start=0, end=0) -> True\n",
+ "* search_path(start=4, end=5) -> False"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Algorithm\n",
+ "\n",
+ "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",
+ "\n",
+ "* Add the start node to the queue and mark it as visited\n",
+ "* If the start node is the end node, return True\n",
+ "* While the queue is not empty\n",
+ " * Dequeue a node and visit it\n",
+ " * If the node is the end node, return True\n",
+ " * Iterate through each adjacent node\n",
+ " * If the node has not been visited, add it to the queue and mark it as visited\n",
+ "* Return False\n",
+ "\n",
+ "Complexity:\n",
+ "* Time: O(V + E), where V = number of vertices and E = number of edges\n",
+ "* Space: O(V + E)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Code"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "%run ../graph/graph.py"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "from collections import deque\n",
+ "\n",
+ "\n",
+ "def path_exists(start, end):\n",
+ " if start is None or end is None:\n",
+ " return False\n",
+ " if start is end:\n",
+ " return True\n",
+ " queue = deque()\n",
+ " queue.append(start)\n",
+ " start.visited = True\n",
+ " while queue:\n",
+ " node = queue.popleft()\n",
+ " if node is None:\n",
+ " continue\n",
+ " if node is end:\n",
+ " return True\n",
+ " for adj_node in node.adjacent:\n",
+ " if not adj_node.visited:\n",
+ " queue.append(adj_node)\n",
+ " adj_node.visited = True\n",
+ " return False"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Unit Test"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Overwriting test_path_exists.py\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%writefile test_path_exists.py\n",
+ "from nose.tools import assert_equal\n",
+ "\n",
+ "\n",
+ "class TestPathExists(object):\n",
+ "\n",
+ " def test_path_exists(self):\n",
+ " nodes = []\n",
+ " graph = Graph()\n",
+ " for id in range(0, 6):\n",
+ " nodes.append(graph.add_node(id))\n",
+ " graph.add_edge(0, 1, 5)\n",
+ " graph.add_edge(0, 4, 3)\n",
+ " graph.add_edge(0, 5, 2)\n",
+ " graph.add_edge(1, 3, 5)\n",
+ " graph.add_edge(1, 4, 4)\n",
+ " graph.add_edge(2, 1, 6)\n",
+ " graph.add_edge(3, 2, 7)\n",
+ " graph.add_edge(3, 4, 8)\n",
+ "\n",
+ " assert_equal(path_exists(nodes[0], nodes[2]), True)\n",
+ " assert_equal(path_exists(nodes[0], nodes[0]), True)\n",
+ " assert_equal(path_exists(nodes[4], nodes[5]), False)\n",
+ "\n",
+ " print('Success: test_path_exists')\n",
+ "\n",
+ "\n",
+ "def main():\n",
+ " test = TestPathExists()\n",
+ " test.test_path_exists()\n",
+ "\n",
+ "\n",
+ "if __name__ == '__main__':\n",
+ " main()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Success: test_path_exists\n"
+ ]
+ }
+ ],
+ "source": [
+ "%run -i test_path_exists.py"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/graphs_trees/graph_path_exists/test_path_exists.py b/graphs_trees/graph_path_exists/test_path_exists.py
new file mode 100644
index 0000000..a99bca0
--- /dev/null
+++ b/graphs_trees/graph_path_exists/test_path_exists.py
@@ -0,0 +1,33 @@
+from nose.tools import assert_equal
+
+
+class TestPathExists(object):
+
+ def test_path_exists(self):
+ nodes = []
+ graph = Graph()
+ for id in range(0, 6):
+ nodes.append(graph.add_node(id))
+ graph.add_edge(0, 1, 5)
+ graph.add_edge(0, 4, 3)
+ graph.add_edge(0, 5, 2)
+ graph.add_edge(1, 3, 5)
+ graph.add_edge(1, 4, 4)
+ graph.add_edge(2, 1, 6)
+ graph.add_edge(3, 2, 7)
+ graph.add_edge(3, 4, 8)
+
+ assert_equal(path_exists(nodes[0], nodes[2]), True)
+ assert_equal(path_exists(nodes[0], nodes[0]), True)
+ assert_equal(path_exists(nodes[4], nodes[5]), False)
+
+ print('Success: test_path_exists')
+
+
+def main():
+ test = TestPathExists()
+ test.test_path_exists()
+
+
+if __name__ == '__main__':
+ main()
\ No newline at end of file