answered 2 python exercises

Author: Luke-Manyamazi

Sprint-1/Python/has_pair_with_sum/has_pair_with_sum.py

@@ -42,4 +42,6 @@ def has_pair_with_sum(numbers: List[Number], target_sum: Number) -> bool:
 O(N)(Linear Space). We introduce the seen_numbers set, which, in the worst case, 
 will store up to N elements from the input list.
 
+Resources: https://www.w3schools.com/python/ref_set_intersection.asp
+
 '''

Sprint-1/Python/remove_duplicates/remove_duplicates.py

@@ -1,25 +1,35 @@
-from typing import List, Sequence, TypeVar
+from typing import List, Sequence, TypeVar, Set
 
 ItemType = TypeVar("ItemType")
 
 
 def remove_duplicates(values: Sequence[ItemType]) -> List[ItemType]:
     """
     Remove duplicate values from a sequence, preserving the order of the first occurrence of each value.
+    Refactored to use a set for O(1) average time lookups, achieving O(N) overall time complexity.
 
-    Time complexity:
-    Space complexity:
-    Optimal time complexity:
+    Time complexity: O(N)
+    Space complexity: O(N)
+    Optimal time complexity: O(N)
     """
-    unique_items = []
+    seen: Set[ItemType] = set()
+    unique_items: List[ItemType] = []
 
     for value in values:
-        is_duplicate = False
-        for existing in unique_items:
-            if value == existing:
-                is_duplicate = True
-                break
-        if not is_duplicate:
+        if value not in seen:
+            seen.add(value)
             unique_items.append(value)
 
     return unique_items
+
+""" 
+Explanation:
+The inner loop performs a linear scan through the unique_items list to check for duplicates, which is the source of the high time complexity.
+
+The only effective way to reduce O(N^2) complexity for this problem is to replace the 
+linear search (for existing in unique_items) with an O(1) average time lookup, 
+which requires a hash set (set in Python).The optimal approach is to use a set to track seen items, achieving O(N)$ time complexity.
+
+Resource: https://www.w3schools.com/python/ref_set_intersection.asp
+
+"""