Python Coding Test Course, Representing Sets

Hello! In this session, we will solve an algorithm problem using sets. A set is an important fundamental concept in mathematics and is also a commonly used data structure in programming. In Python, sets are provided as a built-in data structure that is very easy to use.

Problem Description

Problem: Given two integer arrays, find the intersection of the two arrays. The result should be returned as a set, excluding duplicate elements.

Input Format

arr1: List[int]  # The first integer array
arr2: List[int]  # The second integer array

Output Format

Set[int]  # The intersection of the two arrays

Example

Input: arr1 = [1, 2, 2, 3], arr2 = [2, 3, 4]
Output: {2, 3}

Problem Solving Strategy

There are several ways to solve this problem, but utilizing the properties of sets is the most efficient. Since sets do not allow duplicate elements, converting the given arrays to sets automatically removes duplicates. Then, we can compute the intersection of the two sets and return the result.

Step-by-Step Approach

  1. Convert the given arrays to sets.
  2. Find the intersection between the two sets.
  3. Return the result of the intersection.

Code Implementation

Now, let’s implement the Python code based on the above steps.

def intersection(arr1, arr2):
    set1 = set(arr1)
    set2 = set(arr2)
    return set1 & set2  # & operator denotes intersection.

Code Explanation

The code is quite simple. First, we convert the two given arrays to sets and then use the & operator to find the intersection. This operator returns only the common elements from both sets.

Test Cases

Now, let’s create some test cases to check if the code works correctly.

# Test cases
print(intersection([1, 2, 2, 3], [2, 3, 4]))  # Output: {2, 3}
print(intersection([5, 6, 7], [6, 8, 9]))     # Output: {6}
print(intersection([1, 1, 1], [2, 2, 2]))     # Output: set()
print(intersection([], [1, 2, 3]))              # Output: set()

Test Results Explanation

Looking at the results of each test case:

  • The first case contains both 2 and 3 in both arrays, returning {2, 3}.
  • The second case returns the set {6}.
  • The third case returns an empty set since there are no common elements between the two arrays.
  • The fourth case returns an empty set because the first array is empty.

Complexity Analysis

Now, let’s analyze the time complexity. Let n be the size of one array and m of the other:

  • It takes O(n) and O(m) time to convert each array to a set.
  • Finding the intersection between the two sets consumes O(min(n, m)) time.

In summary, the total time complexity is O(n + m). The space complexity is also O(n + m) as space is required to store the sets.

Conclusion

In this lecture, we learned about the utility of sets through the problem of finding the intersection of arrays. Sets are a very useful data structure and can be used in a variety of algorithmic problems, not just this one. We look forward to covering more valuable algorithmic techniques in the next lecture!