diff --git a/DIRECTORY.md b/DIRECTORY.md
index 4ffd20da58de..a12ed78d64f2 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -16,6 +16,7 @@
   * [All Subsequences](https://github.com/TheAlgorithms/Python/blob/master/backtracking/all_subsequences.py)
   * [Coloring](https://github.com/TheAlgorithms/Python/blob/master/backtracking/coloring.py)
   * [Hamiltonian Cycle](https://github.com/TheAlgorithms/Python/blob/master/backtracking/hamiltonian_cycle.py)
+  * [Knight Tour](https://github.com/TheAlgorithms/Python/blob/master/backtracking/knight_tour.py)
   * [Minimax](https://github.com/TheAlgorithms/Python/blob/master/backtracking/minimax.py)
   * [N Queens](https://github.com/TheAlgorithms/Python/blob/master/backtracking/n_queens.py)
   * [Rat In Maze](https://github.com/TheAlgorithms/Python/blob/master/backtracking/rat_in_maze.py)
@@ -71,6 +72,8 @@
 ## Compression
   * [Burrows Wheeler](https://github.com/TheAlgorithms/Python/blob/master/compression/burrows_wheeler.py)
   * [Huffman](https://github.com/TheAlgorithms/Python/blob/master/compression/huffman.py)
+  * [Lempel Ziv](https://github.com/TheAlgorithms/Python/blob/master/compression/lempel_ziv.py)
+  * [Lempel Ziv Decompress](https://github.com/TheAlgorithms/Python/blob/master/compression/lempel_ziv_decompress.py)
   * [Peak Signal To Noise Ratio](https://github.com/TheAlgorithms/Python/blob/master/compression/peak_signal_to_noise_ratio.py)
 
 ## Computer Vision
@@ -199,6 +202,7 @@
   * [Longest Increasing Subsequence O(Nlogn)](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/longest_increasing_subsequence_o(nlogn).py)
   * [Longest Sub Array](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/longest_sub_array.py)
   * [Matrix Chain Order](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/matrix_chain_order.py)
+  * [Max Non Adjacent Sum](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/max_non_adjacent_sum.py)
   * [Max Sub Array](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/max_sub_array.py)
   * [Max Sum Contiguous Subsequence](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/max_sum_contiguous_subsequence.py)
   * [Minimum Partition](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/minimum_partition.py)
diff --git a/dynamic_programming/factorial.py b/dynamic_programming/factorial.py
index 546478441f31..1c9c927f5af3 100644
--- a/dynamic_programming/factorial.py
+++ b/dynamic_programming/factorial.py
@@ -1,36 +1,25 @@
 # Factorial of a number using memoization
-result = [-1] * 10
-result[0] = result[1] = 1
 
+from functools import lru_cache
 
-def factorial(num):
+
+@lru_cache
+def factorial(num: int) -> int:
     """
     >>> factorial(7)
     5040
     >>> factorial(-1)
-    'Number should not be negative.'
-    >>> [factorial(i) for i in range(5)]
-    [1, 1, 2, 6, 24]
+    Traceback (most recent call last):
+      ...
+    ValueError: Number should not be negative.
+    >>> [factorial(i) for i in range(10)]
+    [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
     """
-
     if num < 0:
-        return "Number should not be negative."
-    if result[num] != -1:
-        return result[num]
-    else:
-        result[num] = num * factorial(num - 1)
-        # uncomment the following to see how recalculations are avoided
-        # print(result)
-        return result[num]
+        raise ValueError("Number should not be negative.")
 
+    return 1 if num in (0, 1) else num * factorial(num - 1)
 
-# factorial of num
-# uncomment the following to see how recalculations are avoided
-# result=[-1]*10
-# result[0]=result[1]=1
-# print(factorial(5))
-# print(factorial(3))
-# print(factorial(7))
 
 if __name__ == "__main__":
     import doctest