#2363

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Merge Similar Items

Merge Similar Items combines values and weights from two lists, returning the result sorted by value.

Problem Statement

You are given two 2D integer arrays, items1 and items2, representing two sets of items. Each item consists of a value and a weight. Your task is to return a 2D array where each entry represents the value and the sum of all weights of items with that value across both input arrays.

Note that the resulting array must be sorted by the item values in ascending order. Each value is unique within its respective array, and the arrays' lengths range from 1 to 1000.

Examples

Example 1

Input: items1 = [[1,1],[4,5],[3,8]], items2 = [[3,1],[1,5]]

Output: [[1,6],[3,9],[4,5]]

The item with value = 1 occurs in items1 with weight = 1 and in items2 with weight = 5, total weight = 1 + 5 = 6. The item with value = 3 occurs in items1 with weight = 8 and in items2 with weight = 1, total weight = 8 + 1 = 9. The item with value = 4 occurs in items1 with weight = 5, total weight = 5. Therefore, we return [[1,6],[3,9],[4,5]].

Example 2

Input: items1 = [[1,1],[3,2],[2,3]], items2 = [[2,1],[3,2],[1,3]]

Output: [[1,4],[2,4],[3,4]]

The item with value = 1 occurs in items1 with weight = 1 and in items2 with weight = 3, total weight = 1 + 3 = 4. The item with value = 2 occurs in items1 with weight = 3 and in items2 with weight = 1, total weight = 3 + 1 = 4. The item with value = 3 occurs in items1 with weight = 2 and in items2 with weight = 2, total weight = 2 + 2 = 4. Therefore, we return [[1,4],[2,4],[3,4]].

Example 3

Input: items1 = [[1,3],[2,2]], items2 = [[7,1],[2,2],[1,4]]

Output: [[1,7],[2,4],[7,1]]

The item with value = 1 occurs in items1 with weight = 3 and in items2 with weight = 4, total weight = 3 + 4 = 7. The item with value = 2 occurs in items1 with weight = 2 and in items2 with weight = 2, total weight = 2 + 2 = 4. The item with value = 7 occurs in items2 with weight = 1, total weight = 1. Therefore, we return [[1,7],[2,4],[7,1]].

Constraints

1 <= items1.length, items2.length <= 1000
items1[i].length == items2[i].length == 2
1 <= valuei, weighti <= 1000
Each valuei in items1 is unique.
Each valuei in items2 is unique.

Solution Approach

Hash Map for Weight Sum

We use a hash map to store the cumulative weights of each value. Iterate through the first array and add each value's weight to the corresponding key. Then, iterate through the second array and update the weights by adding the corresponding values to the same keys in the hash map.

Sorting the Result

After combining the weights, extract the keys (unique values) and sort them in ascending order. The result will be a sorted 2D array, where each element contains the value and the total weight.

Time and Space Complexity Consideration

This approach has a time complexity of O(n log n) due to the sorting step. The space complexity is O(n) as we need a hash map to store the values and their weights.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The overall time complexity is O(n log n) due to sorting the final result. The space complexity is O(n) because of the hash map storing the merged values and their total weights.

What Interviewers Usually Probe

The candidate should demonstrate understanding of hash maps and their use for combining weighted values.
An optimal solution should focus on the use of array scanning and hash lookups for merging data efficiently.
Sorting the results after merging the values and their weights should be handled efficiently, using a fast sorting algorithm.

Common Pitfalls or Variants

Common pitfalls

Not sorting the final result by value.
Failing to handle edge cases, such as when one of the arrays is empty.
Overcomplicating the solution by using inefficient data structures for merging.

Follow-up variants

What if the values in both arrays are guaranteed to be distinct?
What if the items are instead represented as objects with multiple attributes, including a value and weight?
What if the two arrays contain the same values but their weights are not guaranteed to be unique?

FAQ

How do I solve the Merge Similar Items problem?

You can solve it using hash maps to merge the weights by their values and then sort the result by value.

What is the time complexity of solving Merge Similar Items?

The time complexity is O(n log n) due to the sorting step after merging the weights.

Can Merge Similar Items be solved without using sorting?

No, sorting is necessary to return the result in ascending order by value.

What happens if one of the arrays is empty in Merge Similar Items?

If one array is empty, the result will just be the non-empty array's items, with weights unchanged.

What data structure should I use to solve Merge Similar Items?

You should use a hash map to store the sums of weights, mapping values to their cumulative weights.

terminal

Solution

Solution 1: Hash Table or Array

We can use a hash table or array `cnt` to count the total weight of each item in `items1` and `items2`. Then, we traverse the values in ascending order, adding each value and its corresponding total weight to the result array.

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class Solution:
    def mergeSimilarItems(
        self, items1: List[List[int]], items2: List[List[int]]
    ) -> List[List[int]]:
        cnt = Counter()
        for v, w in chain(items1, items2):
            cnt[v] += w
        return sorted(cnt.items())

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