Fix #27: Add Breadth-First Search [Python] (#539)

* add python breadth first search

* update README with python bfs

* Implement breadth first **search** instead of just traversal

Author: SteadBytes

README.md

@@ -20,7 +20,7 @@ Community (college) maintained list of Algorithms and Data Structures implementa
 |:--------------|:----------------:|:----------------:|:----------------:|:-----------------:|:-----------------:|:-----------------:| :-----------------:|
 | [Bin Sort](http://www.cdn.geeksforgeeks.org/bucket-sort-2/)| [:white_check_mark:](bin_sort/bin_sort.c) | |[:white_check_mark:](bin_sort/BinSort.java) | [:white_check_mark:](bin_sort/bin_sort.py) | [:white_check_mark:](bin_sort/bin_sort.go) | | |
 | [Binary Search](https://en.wikipedia.org/wiki/Binary_search_algorithm) | [:white_check_mark:](binary_search/binary_search.c) | | [:white_check_mark:](binary_search/BinarySearch.java) | [:white_check_mark:](binary_search/binary_search.py) | [:white_check_mark:](binary_search/binary_search.go) | [:white_check_mark:](binary_search/binarySearch.js) | [:white_check_mark:](binary_search/BinarySearch.cs) |
-| [Breadth First Search](https://en.wikipedia.org/wiki/Breadth-first_search) | | | [:white_check_mark:](breadth_first_search/BreadthFirstSearch.java) | | | | |
+| [Breadth First Search](https://en.wikipedia.org/wiki/Breadth-first_search) | | | [:white_check_mark:](breadth_first_search/BreadthFirstSearch.java) | [:white_check_mark:](breadth_first_search/breadth_first_search.py) | | | |
 | [Coin Change Problem](http://www.algorithmist.com/index.php/Coin_Change) | [:white_check_mark:](coin_change_problem/coin_change_problem.c) | | [:white_check_mark:](coin_change_problem/CoinChangeProblem.java) | [:white_check_mark:](coin_change_problem/coin_change_problem.py) | [:white_check_mark:](coin_change_problem/coin_change_problem.go) | [:white_check_mark:](coin_change_problem/coinChangeProblem.js) | |
 | [Counting Sort](http://www.geeksforgeeks.org/counting-sort/)| [:white_check_mark:](counting_sort/counting_sort.c) | | [:white_check_mark:](counting_sort/CountingSort.java) | [:white_check_mark:](counting_sort/counting_sort.py) | [:white_check_mark:](counting_sort/counting_sort.go) | [:white_check_mark:](counting_sort/countingSort.js) | [:white_check_mark:](counting_sort/CountingSort.cs) |
 | [Depth First Traversal](http://www.geeksforgeeks.org/depth-first-traversal-for-a-graph/) | | | [:white_check_mark:](depth_first_traversal/DepthFirstTraversal.java) | [:white_check_mark:](depth_first_traversal/DepthFirstTraversal.py) | | | |

breadth_first_search/breadth_first_search.py

@@ -0,0 +1,78 @@
+"""
+Breadth-first search (BFS) is an algorithm for searching tree or
+graph data structures. It produces a set of actions to be follwed to reach a
+target state from the start state. Starting at the initial state (often the
+root node for a tree) it explores all neighbor nodes at each level
+before moving to the next level.
+"""
+
+from collections import deque, namedtuple
+
+
+def breadth_first_search(graph, start, target):
+    """ Performs a breadth-first search on a graph
+
+    Args:
+        graph (list of list of int): Adjacency matrix representation of graph
+        source (int): Index of source vertex to begin search from
+
+    Returns:
+        tuple (path, distance): path traversed from start to target, total
+            distance of path
+        None,None if target not found
+    """
+    vertex_info = {}
+    VistitedVertex = namedtuple("VisitedVertex", "parent distance")
+    vertex_info[start] = VistitedVertex(None, 0)
+
+    search_queue = deque()
+    visited = set()
+    search_queue.append(start)
+
+    while search_queue:
+        u = search_queue.popleft()
+        if u == target:
+            return construct_path(u, vertex_info)
+        for v in graph[u]:
+            if v not in visited:
+                if v not in search_queue:
+                    vertex_info[v] = VistitedVertex(
+                        u, vertex_info[u].distance + 1)
+                    search_queue.append(v)
+        visited.add(u)
+    return None, None
+
+
+def construct_path(vertex, vertex_info):
+    path = []
+    distance = vertex_info[vertex].distance
+    while True:
+        path.append(vertex)
+        if vertex_info[vertex].parent is not None:
+            vertex = vertex_info[vertex].parent
+        else:
+            break
+    return path[::-1], distance
+
+
+def main():
+    graph_adj_list = [
+        [1],
+        [0, 4, 5],
+        [3, 4, 5],
+        [2, 6],
+        [1, 2],
+        [1, 2, 6],
+        [3, 5],
+        []
+    ]
+
+    start = 0
+    target = 10
+    path, distance = breadth_first_search(graph_adj_list, start, target)
+    print('Path from vertex {} to vertex {}: {}'.format(start, target, path))
+    print('Path distance: {}'.format(distance))
+
+
+if __name__ == '__main__':
+    main()