perf(py): optimize calculate_sum_and_product (2n → n)

Author: AliQassab

Sprint-1/Python/calculate_sum_and_product/calculate_sum_and_product.py

@@ -12,20 +12,50 @@ 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:
-    Optimal time complexity:
+    
+    Time Complexity: O(n) - Single pass through the list
+    Space Complexity: O(1) - Only using constant extra space
+    Optimal Time Complexity: O(n) - Cannot do better than linear time
     """
+    # OPTIMIZED IMPLEMENTATION: O(n) time complexity
+    # Previous implementation: O(2n) due to two separate loops
+    
+    sum_total = 0      # O(1) space
+    product = 1   # O(1) space 
+
+    #  O(n) time complexity
+    for current_number in input_numbers:
+        sum_total += current_number      # O(1) 
+        product *= current_number  # O(1) 
+
+    return {"sum": sum_total, "product": product}
+
+
+# ORIGINAL IMPLEMENTATION (for comparison):
+"""
+def calculate_sum_and_product(input_numbers: List[int]) -> Dict[str, int]:
     # Edge case: empty list
     if not input_numbers:
         return {"sum": 0, "product": 1}
 
     sum = 0
-    for current_number in input_numbers:
+    for current_number in input_numbers:    # First pass: O(n)
         sum += current_number
 
     product = 1
-    for current_number in input_numbers:
+    for current_number in input_numbers:     # Second pass: O(n)
         product *= current_number
 
-    return {"sum": sum, "product": product}
+    return {"sum": sum, "product": product}  # Total: O(2n) = O(n) time
+
+COMPLEXITY ANALYSIS OF ORIGINAL:
+- First loop: O(n) iterations to calculate sum
+- Second loop: O(n) iterations to calculate product
+- Total: O(2n) = O(n) time complexity
+- Space: O(1) - only using loop variables
+
+IMPROVEMENTS MADE:
+1. Reduced from 2n to n operations (50% fewer iterations)
+2. Single pass through list instead of two separate loops
+3. Same O(n) time complexity but with better constant factors
+"""