A store owner needs to keep track of their inventory (the number of each item they have). When items are purchased, the inventory needs to decrease. When items are restocked, the inventory needs to increase. Outline an algorithm that can be used by this owner, describing necessary data structures and computational thinking concepts. Explain the concept of Big-O notation and describe the efficiency of the algorithms you just designed when the inventory needs to be updated or printed.

Answer 1

To keep track of inventory efficiently, we can design an algorithm that utilizes appropriate data structures and considers computational complexity. Below is an outline of the algorithm along with the necessary data structures and an explanation of Big-O notation.

Algorithm Outline

1. Data Structure Selection:

   • Dictionary (Hash Map): Use a dictionary (hash map) to store the inventory items. Each item will have a unique identifier (e.g., SKU or item name) as the key, and the value will be an integer representing the quantity in stock.
   • Optionally, a list or array can be used to track items that are low in stock.

2. Initialization:

   • Create an empty dictionary called inventory.

3. Function Definitions:

   • Add Item:

     def add_item(item_name, quantity):
         if item_name in inventory:
             inventory[item_name] += quantity  # Increase quantity
         else:
             inventory[item_name] = quantity  # Add new item
     

   • Remove Item (for sales):

     def remove_item(item_name, quantity):
         if item_name in inventory and inventory[item_name] >= quantity:
             inventory[item_name] -= quantity  # Decrease quantity
             if inventory[item_name] == 0:
                 del inventory[item_name]  # Optional: remove item if quantity is zero
         else:
             print("Insufficient quantity or item not found.")
     

   • Display Inventory:

     def display_inventory():
         for item, quantity in inventory.items():
             print(f"{item}: {quantity}")
     

4. Operations:

   • To restock, call add_item(item_name, quantity).
   • To sell, call remove_item(item_name, quantity).
   • To print the inventory, call display_inventory().

Efficiency Analysis with Big-O Notation

Big-O notation is a way to describe the performance or complexity of an algorithm in terms of time as the input size grows. It helps in understanding how the runtime or space requirements grow as the inputs enlarge.

1. Update Operations:

   • Add Item:
     • Average Case: O(1)
     • Worst Case: O(n) (if rehashing occurs in the hash table, but this is infrequent)
   • Remove Item:
     • Average Case: O(1)
     • Worst Case: O(n) (as hash collisions might require searching through a chain, but this is generally rare)

   So, both add_item() and remove_item() have an average time complexity of O(1), making them quite efficient for keeping the inventory updated.

2. Display Inventory:

   • Display Inventory: O(n), where n is the number of unique items in the inventory. This is because we iterate through each item in the dictionary to print the inventory.

Summary

• The algorithm utilizes a dictionary to maintain the inventory efficiently. Additions and removals of items are generally O(1), while displaying the inventory is O(n).
• Big-O notation helps communicate the efficiency of the algorithm, and it indicates that the inventory management can handle a significant number of items without substantial performance degradation in update operations.