diff --git a/DIRECTORY.md b/DIRECTORY.md
index 23cd7f799..54de20c0e 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -228,6 +228,7 @@
   * [Bfs](https://github.com/TheAlgorithms/Python/blob/master/graphs/bfs.py)
   * [Bfs Shortest Path](https://github.com/TheAlgorithms/Python/blob/master/graphs/bfs_shortest_path.py)
   * [Bidirectional A Star](https://github.com/TheAlgorithms/Python/blob/master/graphs/bidirectional_a_star.py)
+  * [Bidirectional Breadth First Search](https://github.com/TheAlgorithms/Python/blob/master/graphs/bidirectional_breadth_first_search.py)
   * [Breadth First Search](https://github.com/TheAlgorithms/Python/blob/master/graphs/breadth_first_search.py)
   * [Breadth First Search Shortest Path](https://github.com/TheAlgorithms/Python/blob/master/graphs/breadth_first_search_shortest_path.py)
   * [Check Bipartite Graph Bfs](https://github.com/TheAlgorithms/Python/blob/master/graphs/check_bipartite_graph_bfs.py)
@@ -325,6 +326,7 @@
   * [Chudnovsky Algorithm](https://github.com/TheAlgorithms/Python/blob/master/maths/chudnovsky_algorithm.py)
   * [Collatz Sequence](https://github.com/TheAlgorithms/Python/blob/master/maths/collatz_sequence.py)
   * [Combinations](https://github.com/TheAlgorithms/Python/blob/master/maths/combinations.py)
+  * [Entropy](https://github.com/TheAlgorithms/Python/blob/master/maths/entropy.py)
   * [Eulers Totient](https://github.com/TheAlgorithms/Python/blob/master/maths/eulers_totient.py)
   * [Explicit Euler](https://github.com/TheAlgorithms/Python/blob/master/maths/explicit_euler.py)
   * [Extended Euclidean Algorithm](https://github.com/TheAlgorithms/Python/blob/master/maths/extended_euclidean_algorithm.py)
diff --git a/graphs/bidirectional_breadth_first_search.py b/graphs/bidirectional_breadth_first_search.py
index d6e3ebd64..d941c0db5 100644
--- a/graphs/bidirectional_breadth_first_search.py
+++ b/graphs/bidirectional_breadth_first_search.py
@@ -43,6 +43,7 @@ class BreadthFirstSearch:
     [(0, 0), (1, 0), (2, 0), (3, 0), (3, 1), (4, 1),
      (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (6, 5), (6, 6)]
     """
+
     def __init__(self, start, goal):
         self.start = Node(start[1], start[0], goal[1], goal[0], None)
         self.target = Node(goal[1], goal[0], goal[1], goal[0], None)
@@ -111,6 +112,7 @@ class BidirectionalBreadthFirstSearch:
     [(0, 0), (0, 1), (0, 2), (1, 2), (2, 2), (2, 3),
      (2, 4), (3, 4), (3, 5), (3, 6), (4, 6), (5, 6), (6, 6)]
     """
+
     def __init__(self, start, goal):
         self.fwd_bfs = BreadthFirstSearch(start, goal)
         self.bwd_bfs = BreadthFirstSearch(goal, start)
diff --git a/maths/entropy.py b/maths/entropy.py
index eb6bf1a5a..c380afd3b 100644
--- a/maths/entropy.py
+++ b/maths/entropy.py
@@ -54,7 +54,7 @@ def calculate_prob(text: str) -> None:
     3.0
     """
     single_char_strings, two_char_strings = analyze_text(text)
-    my_alphas = list(' ' + ascii_lowercase)
+    my_alphas = list(" " + ascii_lowercase)
     # what is our total sum of probabilities.
     all_sum = sum(single_char_strings.values())