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.<\/p>\n
Problem: Given two integer arrays, find the intersection of the two arrays. The result should be returned as a set, excluding duplicate elements.<\/p>\n
arr1: List[int] # The first integer array\narr2: List[int] # The second integer array<\/code><\/pre>\nOutput Format<\/h3>\nSet[int] # The intersection of the two arrays<\/code><\/pre>\n\nExample<\/h4>\nInput: arr1 = [1, 2, 2, 3], arr2 = [2, 3, 4]\nOutput: {2, 3}<\/code><\/pre>\n<\/div>\nProblem Solving Strategy<\/h2>\n
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.<\/p>\n
Step-by-Step Approach<\/h3>\n\n- Convert the given arrays to sets.<\/li>\n
- Find the intersection between the two sets.<\/li>\n
- Return the result of the intersection.<\/li>\n<\/ol>\n
Code Implementation<\/h2>\n
Now, let’s implement the Python code based on the above steps.<\/p>\n
def intersection(arr1, arr2):\n set1 = set(arr1)\n set2 = set(arr2)\n return set1 & set2 # & operator denotes intersection.<\/code><\/pre>\nCode Explanation<\/h3>\n
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.<\/p>\n
Test Cases<\/h2>\n
Now, let’s create some test cases to check if the code works correctly.<\/p>\n
# Test cases\nprint(intersection([1, 2, 2, 3], [2, 3, 4])) # Output: {2, 3}\nprint(intersection([5, 6, 7], [6, 8, 9])) # Output: {6}\nprint(intersection([1, 1, 1], [2, 2, 2])) # Output: set()\nprint(intersection([], [1, 2, 3])) # Output: set()<\/code><\/pre>\nTest Results Explanation<\/h3>\n
Looking at the results of each test case:<\/p>\n
\n- The first case contains both 2 and 3 in both arrays, returning {2, 3}.<\/li>\n
- The second case returns the set {6}.<\/li>\n
- The third case returns an empty set since there are no common elements between the two arrays.<\/li>\n
- The fourth case returns an empty set because the first array is empty.<\/li>\n<\/ul>\n
Complexity Analysis<\/h2>\n
Now, let\u2019s analyze the time complexity. Let n be the size of one array and m of the other:<\/p>\n