Find the Difference of Two Arrays

Problem Statement

The task involves two integer arrays, nums1 and nums2, which are indexed starting from 0. We need to determine the elements from each of these arrays that are not present in the other array. The final output should be a list called answer containing two sub-lists:

1. The first sub-list should include all unique integers from nums1 that are absent in nums2.
2. The second sub-list should feature all distinct integers from nums2 that do not appear in nums1.

It's important to note that the order in which integers appear in the sub-lists is irrelevant, and only distinct integers from each list should be considered, ensuring no repetitions within the sub-lists.

Examples

Example 1

Input:

nums1 = [1,2,3], nums2 = [2,4,6]

Output:

[[1,3],[4,6]]

Explanation:

For nums1, nums1[1] = 2 is present at index 0 of nums2, whereas nums1[0] = 1 and nums1[2] = 3 are not present in nums2. Therefore, answer[0] = [1,3].
For nums2, nums2[0] = 2 is present at index 1 of nums1, whereas nums2[1] = 4 and nums2[2] = 6 are not present in nums1. Therefore, answer[1] = [4,6].

Example 2

Input:

nums1 = [1,2,3,3], nums2 = [1,1,2,2]

Output:

[[3],[]]

Explanation:

For nums1, nums1[2] and nums1[3] are not present in nums2. Since nums1[2] == nums1[3], their value is only included once and answer[0] = [3].
Every integer in nums2 is present in nums1. Therefore, answer[1] = [].

Constraints

• 1 <= nums1.length, nums2.length <= 1000
• -1000 <= nums1[i], nums2[i] <= 1000

Approach and Intuition

The primary goal is to compare two lists and efficiently find unique elements in each that are absent in the other. Let's break down the approach using the given examples, incorporating practical constraints:

1. Convert each list (nums1 and nums2) into a set to eliminate any duplicate items, ensuring all elements we handle are distinct.
2. To find elements in nums1 not present in nums2, subtract the set derived from nums2 from the set of nums1.
3. Similarly, derive elements exclusive to nums2 by subtracting the set of nums1 from the set of nums2.
4. Compile these resulting sets into two sublist components of the final answer list.

Steps to Implement:

1. Initialize two sets, set1 and set2, from nums1 and nums2 respectively.
2. Calculate the difference between set1 and set2 to create the first sublist in the answer.
3. Compute the difference between set2 and set1 for the second sublist in the answer.
4. Construct the final output list using these two differences.

This approach is efficient given the constraints, as set operations such as difference are typically fast, and converting the arrays to sets also removes any duplicate items, simplifying our process. Moreover, handling up to 1000 elements in each list is computationally feasible with this method.

Solutions

class Solution {
public:
    vector<int> uniqueElements(vector<int>& list1, vector<int>& list2) {
        unordered_set<int> distinctElements;
        unordered_set<int> setList2(list2.begin(), list2.end());
    
        for (int item : list1) {
            if (setList2.find(item) == setList2.end()) {
                distinctElements.insert(item);
            }
        }
    
        return vector<int>(distinctElements.begin(), distinctElements.end());
    }
    
    vector<vector<int>> findDifference(vector<int>& nums1, vector<int>& nums2) {
        return {uniqueElements(nums1, nums2), uniqueElements(nums2, nums1)};
    }
};