algoadvance

Problem Statement

2363. Merge Similar Items

You are given two 2D lists items1 and items2, where each list contains items represented as pairs [value, weight]. Merge the two lists into a single list of unique items, summed by their weights. Output the merged list sorted by the value of the items.

Clarifying Questions

1. Input Format: Can items1 or items2 be empty?
   • Yes, they can be empty.
2. Element Uniqueness: Are the values in each of the input lists unique?
   • Values may repeat within the lists, but the goal is to merge them by summing their weights.
3. Output Requirements: Should the result be sorted by the value of the items?
   • Yes, the result should be sorted by the item values in ascending order.

Strategy

1. Data Structure Choice: Use a dictionary to facilitate the merging process. The dictionary’s keys will be the item values, and the values will be the cumulative weights.

2. Processing:
   • Iterate through items1 and items2, and for each item, update the dictionary with the item value as the key and sum the weights.
   • Convert the dictionary back to a list of [value, weight] pairs.
   • Sort the merged list by the item values.
3. Sorting: Python’s in-built sorted() function efficiently sorts the list.

Code

def mergeSimilarItems(items1, items2):
    # Initialize a dictionary to store the merged items
    merged_items = {}

    # Function to add items to the dictionary
    def add_items_to_dict(items):
        for value, weight in items:
            if value in merged_items:
                merged_items[value] += weight
            else:
                merged_items[value] = weight

    # Add items from both lists to the dictionary
    add_items_to_dict(items1)
    add_items_to_dict(items2)

    # Convert the dictionary to a sorted list of pairs
    merged_list = [[value, weight] for value, weight in merged_items.items()]
    merged_list.sort()

    return merged_list

# Test the function with an example
items1 = [[1, 1], [4, 5], [3, 8]]
items2 = [[3, 1], [1, 5]]
print(mergeSimilarItems(items1, items2))
# Output: [[1, 6], [3, 9], [4, 5]]

Time Complexity

• Inserting into dictionary: O(n + m), where n and m are the lengths of items1 and items2, respectively. This is because we iterate through both lists once.
• Sorting the dict items: O(k log k), where k is the number of unique item values.

Thus, the overall time complexity is O((n + m) + k log k), which should be efficient for most reasonable input sizes.

This solution ensures that the items are merged appropriately and sorted by their values as required.

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