Manchester | 25-SDC-Nov | Rahwa Haile | Sprint 2 | improve_with_precomputing

Sprint-2/improve_with_precomputing/README.md

@@ -3,3 +3,23 @@ Each directory contains implementations that can be made faster by using pre-com
 The problem they solve is described in docstrings and tests.
 
 Speed up the solutions by introducing precomputing. You may rewrite as much of the solution as you want, and may add any tests, but must not modify existing tests.
+
+## Improvements Made
+
+### common_prefix
+
+**Original Approach (Nested Loops):**
+- Time Complexity: **O(n² × m)** - Compares every string with every other string (n²) pairs, each taking O(m) comparisons
+
+**Optimized Approach (Sort + Adjacent Pairs):**
+- Time Complexity: **O(n log n + n × m)** - Sort once (n log n), then compare only adjacent pairs (n comparisons)
+- **Why better:** The longest common prefix will be found in the first and last strings after sorting, eliminating unnecessary comparisons. Reduces from O(n²) to O(n) pair comparisons.
+
+### count_letters
+
+**Original Approach (Repeated String Checks):**
+- Time Complexity: **O(n²)** - For each letter, checking if lowercase version exists in string is O(n), done n times
+
+**Optimized Approach (Precomputed Set):**
+- Time Complexity: **O(n)** - Precompute lowercase letters into a set (O(n)), then check membership is O(1) each time
+- **Why better:** Replaces repeated O(n) string searches with single O(n) precomputation and O(1) set lookups, reducing overall from O(n²) to O(n).

Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py

@@ -2,17 +2,16 @@
 
 
 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.
+
+    if len(strings) < 2:
+        return ""
 
-    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.
-    """
+    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 index in range(len(sorted_strings) - 1):
+        common = find_common_prefix(sorted_strings[index], sorted_strings[index + 1])
+        if len(common) > len(longest):
+            longest = common
     return longest
 
 

Sprint-2/improve_with_precomputing/count_letters/count_letters.py

@@ -1,11 +1,10 @@
 def count_letters(s: str) -> int:
-    """
-    count_letters returns the number of letters which only occur in upper case in the passed string.
-    """
+
+    lower_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 lower_letters:
                 only_upper.add(letter)
     return len(only_upper)