Refactor Python array utilities to improve time complexity

Author: PratiAmalden

Sprint-1/Python/calculate_sum_and_product/calculate_sum_and_product.py

@@ -12,20 +12,22 @@ def calculate_sum_and_product(input_numbers: List[int]) -> Dict[str, int]:
         "sum": 10, // 2 + 3 + 5
         "product": 30 // 2 * 3 * 5
     }
-    Time Complexity:
-    Space Complexity:
+    Areas of inefficiency in original version:
+    - Two separate loops over the same list
+
+    Time Complexity: O(n)
+    Space Complexity: O(1)
     Optimal time complexity:
     """
     # Edge case: empty list
     if not input_numbers:
         return {"sum": 0, "product": 1}
 
-    sum = 0
-    for current_number in input_numbers:
-        sum += current_number
+    total_sum = 0
+    total_product = 1
 
-    product = 1
     for current_number in input_numbers:
-        product *= current_number
+        total_sum += current_number
+        total_product *= current_number
 
-    return {"sum": sum, "product": product}
+    return {"sum": total_sum, "product": total_product}

Sprint-1/Python/find_common_items/find_common_items.py

@@ -9,13 +9,21 @@ def find_common_items(
     """
     Find common items between two arrays.
 
-    Time Complexity:
-    Space Complexity:
-    Optimal time complexity:
+    Areas of inefficiency in original version:
+    - Nested loops compare every element in first_sequence to every element
+    in second_sequence (O(n * m)).
+
+    Time Complexity: O(n + m) avrage
+    Space Complexity: O(m + k)
+    Optimal time complexity: O(n + m)
     """
+    second_set = set(second_sequence)
     common_items: List[ItemType] = []
-    for i in first_sequence:
-        for j in second_sequence:
-            if i == j and i not in common_items:
-                common_items.append(i)
+    seen = set()
+
+    for item in first_sequence:
+        if item in second_set and item not in seen:
+            seen.add(item)
+            common_items.append(item)
+
     return common_items

Sprint-1/Python/has_pair_with_sum/has_pair_with_sum.py

@@ -7,12 +7,21 @@ def has_pair_with_sum(numbers: List[Number], target_sum: Number) -> bool:
     """
     Find if there is a pair of numbers that sum to a target value.
 
-    Time Complexity:
-    Space Complexity:
-    Optimal time complexity:
+    Areas of inefficiency in original version:
+    - Nested loops check all possible pairs, leading to quadratic time
+
+    Time Complexity: O(n) average
+    Space Complexity: O(n)
+    Optimal time complexity: O(n)
+
+    - set to track previously seen values.
     """
-    for i in range(len(numbers)):
-        for j in range(i + 1, len(numbers)):
-            if numbers[i] + numbers[j] == target_sum:
-                return True
+    seen = set()
+
+    for number in numbers:
+        complement = target_sum - number
+        if complement in seen:
+            return True
+        seen.add(number)
+
     return False

Sprint-1/Python/remove_duplicates/remove_duplicates.py

@@ -6,20 +6,20 @@
 def remove_duplicates(values: Sequence[ItemType]) -> List[ItemType]:
     """
     Remove duplicate values from a sequence, preserving the order of the first occurrence of each value.
-
-    Time complexity:
-    Space complexity:
-    Optimal time complexity:
+    
+    Areas of inefficiency in original version:
+    - For each value scans the growing list of unique items.
+    
+    Time complexity: O(n) average
+    Space complexity: O(n)
+    Optimal time complexity: O(n)
     """
-    unique_items = []
+    seen = 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