Add Breadth First Traversal [Python] (#617)

* add python breadth first search

* update README with python bfs

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

* add python breadth_first_traversal

* udpate README with python breadth first traversal

* add python breadth_first_search link

Author: SteadBytes

README.md

@@ -20,7 +20,8 @@ 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) | [:white_check_mark:](breadth_first_search/breadth_first_search.py) | | | |
+| [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) | | | |
+| [Breadth First Traversal](https://www.cs.bu.edu/teaching/c/tree/breadth-first/) | | |  |[:white_check_mark:](breadth_first_traversal/breadth_first_traversal.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_traversal/breadth_first_traversal.py

@@ -0,0 +1,92 @@
+"""
+Breadth-first-traversal is an algorithm for traversing a tree or
+graph data structure. Starting at the tree root (or some arbitrary node of a
+graph, sometimes referred to as a 'search key'[1]) and explores the neighbor
+nodes at that level first, before moving to the next level.
+"""
+
+from collections import deque
+
+
+def breadth_first_traversal(graph, source):
+    """ Performs a breadth-first traversal 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:
+        list of dicts describing each vertex in the searched graph
+            -> [{distance: _, predecessor: _ }]
+    """
+    vertex_info = []
+    for i in range(len(graph)):
+        vertex_info.append({"distance": None, "predecessor": None})
+    vertex_info[source]["distance"] = 0
+
+    search_queue = deque()
+    search_queue.append(source)
+
+    while search_queue:
+        u = search_queue.popleft()
+        for v in graph[u]:
+            if vertex_info[v]["distance"] is None:
+                vertex_info[v]["distance"] = vertex_info[u]["distance"] + 1
+                vertex_info[v]["predecessor"] = u
+                search_queue.append(v)
+    return vertex_info
+
+
+def main():
+    graph_adj_list = [
+        [1],
+        [0, 4, 5],
+        [3, 4, 5],
+        [2, 6],
+        [1, 2],
+        [1, 2, 6],
+        [3, 5],
+        []
+    ]
+    vertex_info = breadth_first_traversal(graph_adj_list, 3)
+
+    for i in range(len(graph_adj_list)):
+        print("vertex %s : distance = %s, predecessor = %s" %
+              (i, vertex_info[i]["distance"], vertex_info[i]["predecessor"]))
+
+    assert(vertex_info[0] == {
+        "distance": 4,
+        "predecessor": 1
+    })
+    assert(vertex_info[1] == {
+        "distance": 3,
+        "predecessor": 4
+    })
+    assert(vertex_info[2] == {
+        "distance": 1,
+        "predecessor": 3
+    })
+    assert(vertex_info[3] == {
+        "distance": 0,
+        "predecessor": None
+    })
+    assert(vertex_info[4] == {
+        "distance": 2,
+        "predecessor": 2
+    })
+    assert(vertex_info[5] == {
+        "distance": 2,
+        "predecessor": 2
+    })
+    assert(vertex_info[6] == {
+        "distance": 1,
+        "predecessor": 3
+    })
+    assert(vertex_info[7] == {
+        "distance": None,
+        "predecessor": None
+    })
+
+
+if __name__ == '__main__':
+    main()