What is the optimal time complexity of solving Activity Selection?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Activity Selection?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Activity Selection?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Activity Selection?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Activity Selection

Learn how to solve the 'Activity Selection' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function activity_selection(start, end) that takes two lists start and end representing the start and end times of activities. Find the maximum number of activities that can be performed by a single person, assuming that a person can only work on a single activity at a time. Two activities are non-overlapping if the start time of the second is greater than or equal to the end time of the first.

Constraints

•1 <= len(start) == len(end) <= 10^5
•0 <= start[i] < end[i] <= 10^9

Examples

Example 1

Input

activity_selection([1, 3, 0, 5, 8, 5], [2, 4, 6, 7, 9, 9])

Output

Explanation

A person can perform at most 4 activities: [1,2], [3,4], [5,7], and [8,9].

Example 2

Input

activity_selection([10, 12, 20], [20, 25, 30])

Output

Explanation

Two activities can be performed: [10,20] and [20,30].

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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