From 25951c03bd680f1a68115dcaa723d6ce9593a491 Mon Sep 17 00:00:00 2001
From: Fithi Teklom <fthiteklom@gmail.com>
Date: Tue, 20 Oct 2026 22:08:21 +0100
Subject: [PATCH 1/3] Optimize longest common prefix search by sorting strings

---
 .../common_prefix/common_prefix.py                 | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

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 f4839e70..48a26536 100644
--- a/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
+++ b/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
@@ -7,12 +7,16 @@ def find_longest_common_prefix(strings: List[str]):
 
     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 ""
+    
+    sorted_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(sorted_strings) - 1):
+        common = find_common_prefix(sorted_strings[i], sorted_strings[i + 1])
+        if len(common) > len(longest):
+            longest = common
     return longest
 
 

From f040003dfe6bcddb58ee4603e3f617e162f72eed Mon Sep 17 00:00:00 2001
From: Fithi Teklom <fthiteklom@gmail.com>
Date: Tue, 20 Oct 2026 22:31:07 +0100
Subject: [PATCH 2/3] Improve count_letters.py with precomputing

---
 .../improve_with_precomputing/count_letters/count_letters.py   | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

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 62c3ec07..d564419c 100644
--- a/Sprint-2/improve_with_precomputing/count_letters/count_letters.py
+++ b/Sprint-2/improve_with_precomputing/count_letters/count_letters.py
@@ -2,10 +2,11 @@ def count_letters(s: str) -> int:
     """
     count_letters returns the number of letters which only occur in upper case in the passed string.
     """
+    lowercase_letters = {letter for letter in s if letter.islower()}
     only_upper = set()
     for letter in s:
         if is_upper_case(letter):
-            if letter.lower() not in s:
+            if letter.lower() not in lowercase_letters:
                 only_upper.add(letter)
     return len(only_upper)
 

From 506c094423cec7aa130fde8dbe1e46cf0d73a98a Mon Sep 17 00:00:00 2001
From: Fithi Teklom <fthiteklom@gmail.com>
Date: Wed, 21 Oct 2026 15:58:06 +0100
Subject: [PATCH 3/3] Explain the complexity for the new improvement with
 precomputing.

---
 .../improve_with_precomputing/common_prefix/common_prefix.py | 4 ++++
 .../improve_with_precomputing/count_letters/count_letters.py | 5 +++++
 2 files changed, 9 insertions(+)

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 48a26536..82a5b76b 100644
--- a/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
+++ b/Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py
@@ -26,3 +26,7 @@ def find_common_prefix(left: str, right: str) -> str:
         if left[i] != right[i]:
             return left[:i]
     return left[:min_length]
+
+# The original code compares every pair of strings, giving it (O(m^2)) pair comparisons. 
+# The new version sorts the strings and compares only neighbouring pairs, reducing the number of comparisons.
+# Its approximate time complexity improves from (O(m^2L)) to (O(mL\log 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 d564419c..60d18b9d 100644
--- a/Sprint-2/improve_with_precomputing/count_letters/count_letters.py
+++ b/Sprint-2/improve_with_precomputing/count_letters/count_letters.py
@@ -13,3 +13,8 @@ def count_letters(s: str) -> int:
 
 def is_upper_case(letter: str) -> bool:
     return letter == letter.upper()
+
+# 
+# The original code searches the string repeatedly, giving it (O(n^2)) time complexity.
+# The new version stores lowercase letters in a set first, so it can check them faster.
+# This reduces the expected time complexity to (O(n)), but uses extra memory.