#!/usr/bin/env python
# coding: utf-8

# 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).

# # Solution Notebook

# ## Problem: Find the shortest path between two nodes in a graph.
# 
# * [Constraints](#Constraints)
# * [Test Cases](#Test-Cases)
# * [Algorithm](#Algorithm)
# * [Code](#Code)
# * [Unit Test](#Unit-Test)

# ## Constraints
# 
# * Is the graph directed?
#     * Yes
# * Is the graph weighted?
#     * No
# * Can we assume we already have Graph and Node classes?
#     * Yes
# * Are the inputs two Nodes?
#     * Yes
# * Is the output a list of Node keys that make up the shortest path?
#     * Yes
# * If there is no path, should we return None?
#     * Yes
# * Can we assume this is a connected graph?
#     * Yes
# * Can we assume the inputs are valid?
#     * Yes
# * Can we assume this fits memory?
#     * Yes

# ## Test Cases
# 
# Input:
# * `add_edge(source, destination, weight)`
# 
# ```
# graph.add_edge(0, 1)
# graph.add_edge(0, 4)
# graph.add_edge(0, 5)
# graph.add_edge(1, 3)
# graph.add_edge(1, 4)
# graph.add_edge(2, 1)
# graph.add_edge(3, 2)
# graph.add_edge(3, 4)
# ```
# 
# Result:
# * search_path(start=0, end=2) -> [0, 1, 3, 2]
# * search_path(start=0, end=0) -> [0]
# * search_path(start=4, end=5) -> None

# ## Algorithm
# 
# To determine the shorted path in an unweighted graph, we can use breadth-first search keeping track of the previous nodes ids for each node.  Previous nodes ids can be a dictionary of key: current node id and value: previous node id.
# 
# * If the start node is the end node, return True
# * Add the start node to the queue and mark it as visited
#     * Update the previous node ids, the previous node id of the start node is None
# * While the queue is not empty
#     * Dequeue a node and visit it
#     * If the node is the end node, return the previous nodes
#     * Set the previous node to the current node
#     * Iterate through each adjacent node
#         * If the node has not been visited, add it to the queue and mark it as visited
#             * Update the previous node ids
# * Return None
# 
# Walk the previous node ids backwards to get the path.
# 
# Complexity:
# * Time: O(V + E), where V = number of vertices and E = number of edges
# * Space: O(V + E)

# ## Code

# In[1]:


get_ipython().run_line_magic('run', '../graph/graph.py')


# In[2]:


from collections import deque


class GraphShortestPath(Graph):

    def shortest_path(self, source_key, dest_key):
        if source_key is None or dest_key is None:
            return None
        if source_key is dest_key:
            return [source_key]
        prev_node_keys = self._shortest_path(source_key, dest_key)
        if prev_node_keys is None:
            return None
        else:
            path_ids = [dest_key]
            prev_node_key = prev_node_keys[dest_key]
            while prev_node_key is not None:
                path_ids.append(prev_node_key)
                prev_node_key = prev_node_keys[prev_node_key]
            return path_ids[::-1]

    def _shortest_path(self, source_key, dest_key):
        queue = deque()
        queue.append(self.nodes[source_key])
        prev_node_keys = {source_key: None}
        self.nodes[source_key].visit_state = State.visited
        while queue:
            node = queue.popleft()
            if node.key is dest_key:
                return prev_node_keys
            prev_node = node
            for adj_node in node.adj_nodes.values():
                if adj_node.visit_state == State.unvisited:
                    queue.append(adj_node)
                    prev_node_keys[adj_node.key] = prev_node.key
                    adj_node.visit_state = State.visited
        return None


# ## Unit Test

# In[3]:


get_ipython().run_cell_magic('writefile', 'test_shortest_path.py', "import unittest\n\n\nclass TestShortestPath(unittest.TestCase):\n\n    def test_shortest_path(self):\n        nodes = []\n        graph = GraphShortestPath()\n        for id in range(0, 6):\n            nodes.append(graph.add_node(id))\n        graph.add_edge(0, 1)\n        graph.add_edge(0, 4)\n        graph.add_edge(0, 5)\n        graph.add_edge(1, 3)\n        graph.add_edge(1, 4)\n        graph.add_edge(2, 1)\n        graph.add_edge(3, 2)\n        graph.add_edge(3, 4)\n\n        self.assertEqual(graph.shortest_path(nodes[0].key, nodes[2].key), [0, 1, 3, 2])\n        self.assertEqual(graph.shortest_path(nodes[0].key, nodes[0].key), [0])\n        self.assertEqual(graph.shortest_path(nodes[4].key, nodes[5].key), None)\n\n        print('Success: test_shortest_path')\n\n\ndef main():\n    test = TestShortestPath()\n    test.test_shortest_path()\n\n\nif __name__ == '__main__':\n    main()\n")


# In[4]:


get_ipython().run_line_magic('run', '-i test_shortest_path.py')