#2215

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Find the Difference of Two Arrays

Find the Difference of Two Arrays helps you identify unique elements between two integer arrays using array scanning and hash lookups.

array hash table

Problem Statement

Given two 0-indexed integer arrays, nums1 and nums2, your task is to return a list, answer, of size 2. The first list in answer should contain elements that are in nums1 but not in nums2, and the second list should contain elements that are in nums2 but not in nums1.

Note that the integers in both lists can be in any order. Your solution should be efficient and run within O(N + M) time complexity, where N is the length of nums1 and M is the length of nums2.

Examples

Example 1

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

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

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],[]]

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

Solution Approach

Array Scanning with Hash Set

To solve this problem, iterate through both arrays, using hash sets to track the presence of each element. For each element in nums1, check if it exists in nums2 using the hash set, and do the reverse for nums2. This approach ensures an efficient solution with a time complexity of O(N + M).

Efficient Lookup with Hashing

Leverage a hash table to store elements from nums2. Then, iterate over nums1 and check for each element’s presence in the hash table. This approach allows for quick lookup times, making the solution scalable even with large input sizes, ensuring time complexity stays at O(N + M).

Dealing with Duplicates

Handle duplicates by ensuring that each number is only included once in the final result. If an element appears more than once in one array and not in the other, only include it once in the result list corresponding to its array.

Complexity Analysis

Metric	Value
Time	O(N + M)
Space	O(N + M)

The time complexity of the solution is O(N + M), where N and M are the lengths of nums1 and nums2, respectively. We scan both arrays once and use a hash table for efficient lookup, making this solution both time and space efficient.

What Interviewers Usually Probe

Look for a candidate who can efficiently use hash tables to optimize lookup times.
Ensure the candidate handles duplicate values properly and avoids unnecessary extra work.
Check if the candidate can explain how they minimize time complexity with this approach.

Common Pitfalls or Variants

Common pitfalls

Forgetting to handle duplicates correctly can result in incorrect output.
Not using a hash table or performing inefficient lookups can lead to slower solutions.
Overcomplicating the solution by trying to sort or use nested loops unnecessarily.

Follow-up variants

Consider variations where arrays may contain negative numbers or zeros.
Challenge the candidate with larger arrays to test the performance of the solution.
Test the solution on edge cases, such as when both arrays are empty or have only one element.

FAQ

How do I efficiently solve the Find the Difference of Two Arrays problem?

Use array scanning combined with hash lookup to check the presence of elements between nums1 and nums2 in O(N + M) time.

What is the time complexity of solving the Find the Difference of Two Arrays problem?

The time complexity is O(N + M), where N and M are the lengths of nums1 and nums2, respectively.

What are common mistakes when solving Find the Difference of Two Arrays?

Common mistakes include failing to handle duplicates correctly and not using hash sets or hash tables for efficient lookups.

What is the primary pattern for solving Find the Difference of Two Arrays?

The primary pattern is array scanning plus hash lookup to efficiently check element presence between the two arrays.

How can GhostInterview assist with the Find the Difference of Two Arrays problem?

GhostInterview provides instant feedback on your solution, helps optimize performance, and warns against common mistakes.

terminal

Solution

Solution 1: Hash Table

We define two hash tables $s1$ and $s2$ to store the elements in arrays $nums1$ and $nums2$ respectively. Then we traverse each element in $s1$. If this element is not in $s2$, we add it to the first list in the answer. Similarly, we traverse each element in $s2$. If this element is not in $s1$, we add it to the second list in the answer.

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class Solution:
    def findDifference(self, nums1: List[int], nums2: List[int]) -> List[List[int]]:
        s1, s2 = set(nums1), set(nums2)
        return [list(s1 - s2), list(s2 - s1)]

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