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..9313743 100644
--- a/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
+++ b/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
@@ -1,18 +1,22 @@
 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.
     """
+    if len(strings) < 2:
+        return ""
+    
+    strings.sort()
+
     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 +26,8 @@ def find_common_prefix(left: str, right: str) -> str:
         if left[i] != right[i]:
             return left[:i]
     return left[:min_length]
+
+# Complexity for old version code where we hade a nested loop and slicer, and compared every string with other string is
+# leading to O(n^2*m+n^2), while on the new script we have complexity sorting O(n log n *m) and comparison O(n*m). Even after using sorting
+# which is consuming and costly, the overall complexity is lower because we compare fewer pairs.
+# O(n^2*m) and 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..9d1b46d 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 +1,26 @@
-def count_letters(s: str) -> int:
+def count_letters(string: str) -> int:
     """
     count_letters returns the number of letters which only occur in upper case in the passed string.
     """
-    only_upper = set()
-    for letter in s:
-        if is_upper_case(letter):
-            if letter.lower() not in s:
-                only_upper.add(letter)
-    return len(only_upper)
 
+    lower_case_set = set()
+    upper_case_set = set()
+    
+    for letter in string:
+        if letter.islower():
+            lower_case_set.add(letter)
+        elif letter.isupper():
+            upper_case_set.add(letter)
 
-def is_upper_case(letter: str) -> bool:
+    count = 0
+    for letter in upper_case_set:
+       if letter.lower() not in lower_case_set:
+        count += 1
+    return count
+
+# The Space complexity for new and old script is O(n), but Time complexity the old one is O(n)^2 which is insufficient compare
+# to new code Time complexity O(n).
+
+
+def is_upper_case(letter: str) -> bool:    
     return letter == letter.upper()