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..61bc8fa 100644
--- a/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
+++ b/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
@@ -1,24 +1,20 @@
 from typing import List
 
-
-def find_longest_common_prefix(strings: List[str]):
+def find_longest_common_prefix(strings: List[str]) -> 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.
+    find_longest_common_prefix returns the longest string common at the start 
+    of any two strings in the passed list.
     """
-    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
-    return longest
-
+    if len(strings) < 2:
+        return ""
+    
+    sorted_strings = sorted(strings)
+    
+    return find_common_prefix(sorted_strings[0], sorted_strings[-1])
 
 def find_common_prefix(left: str, right: str) -> str:
     min_length = min(len(left), len(right))
     for i in range(min_length):
         if left[i] != right[i]:
             return left[:i]
-    return left[:min_length]
+    return left[:min_length]
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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..ba27292 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 +1,17 @@
 def count_letters(s: str) -> int:
     """
-    count_letters returns the number of letters which only occur in upper case in the passed string.
+    count_letters returns the number of letters which only occur in upper case 
+    in the passed string.
     """
+    
+    lowercase_set = set(letter for letter in s if letter == letter.lower())
+    
     only_upper = set()
     for letter in s:
         if is_upper_case(letter):
-            if letter.lower() not in s:
+            if letter.lower() not in lowercase_set:  # O(1) lookup instead of O(n)
                 only_upper.add(letter)
     return len(only_upper)
 
-
 def is_upper_case(letter: str) -> bool:
-    return letter == letter.upper()
+    return letter == letter.upper()
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