diff --git a/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py b/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
index f4839e7..90f3c52 100644
--- a/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
+++ b/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
@@ -2,17 +2,17 @@
 
 
 def find_longest_common_prefix(strings: List[str]):
-    """
-    find_longest_common_prefix returns the longest string common at the start of any two strings in the passed list.
 
-    In the event that an empty list, a list containing one string, or a list of strings with no common prefixes is passed, the empty string will be returned.
-    """
+    if len(strings) < 2:
+        return ""
+    
+    strings = sorted(strings)
+    
     longest = ""
-    for string_index, string in enumerate(strings):
-        for other_string in strings[string_index+1:]:
-            common = find_common_prefix(string, other_string)
-            if len(common) > len(longest):
-                longest = common
+    for i in range(len(strings) - 1):
+        common = find_common_prefix(strings[i], strings[i + 1])
+        if len(common) > len(longest):
+            longest = common
     return longest
 
 
@@ -22,3 +22,14 @@ def find_common_prefix(left: str, right: str) -> str:
         if left[i] != right[i]:
             return left[:i]
     return left[:min_length]
+
+
+"""
+The new implementation sorts a string first, then compares each string
+with the one that comes after it. On the other hand, the original imple-
+mentation compares each string with every single while looping through
+nested for loop. 
+As a result, the compelxity time drops from the original O(n^2 * m) to
+around O(n log n * m).
+
+"""
\ No newline at end of file
diff --git a/Sprint-2/improve_with_precomputing/count_letters/count_letters.py b/Sprint-2/improve_with_precomputing/count_letters/count_letters.py
index 62c3ec0..1c69df2 100644
--- a/Sprint-2/improve_with_precomputing/count_letters/count_letters.py
+++ b/Sprint-2/improve_with_precomputing/count_letters/count_letters.py
@@ -1,14 +1,27 @@
 def count_letters(s: str) -> int:
-    """
-    count_letters returns the number of letters which only occur in upper case in the passed string.
-    """
+    only_lower = set()
+    for letter in s:
+        if letter.islower():
+            only_lower.add(letter)
+
     only_upper = set()
     for letter in s:
         if is_upper_case(letter):
-            if letter.lower() not in s:
+            if letter.lower() not in only_lower:
                 only_upper.add(letter)
     return len(only_upper)
 
 
 def is_upper_case(letter: str) -> bool:
     return letter == letter.upper()
+
+
+
+"""
+The old implementation scans through the entire string for every uppercase letter
+we check against, therefore complexity in the worst case is O(n^2). However, in the
+new implementation the lowercase letters a store beforehand in a set. This allows
+checking against every uppercase letter without scanning through the entire string.
+As a result, the complexixty time goes down to O(n) with the new implementation.
+
+"""