Employee Free Time

To find the common free time intervals for all employees, we need to flatten the intervals, sort them, and then check the gaps between consecutive intervals. The gaps will represent the common free time for all employees.

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class Solution:
    def employeeFreeTime(self, schedule: '[[Interval]]') -> '[Interval]':
        # Flatten the intervals
        intervals = [interval for employee in schedule for interval in employee]

        # Sort the intervals by start time
        intervals.sort(key=lambda x: x.start)

        # Initialize the end time of the previous interval and the result list
        prev_end = intervals[0].end
        result = []

        # Iterate through the sorted intervals
        for interval in intervals[1:]:
            # If there is a gap between the end time of the previous interval and the start time of the current interval
            if interval.start > prev_end:
                # Add the gap to the result
                result.append(Interval(prev_end, interval.start))

            # Update the end time of the previous interval
            prev_end = max(prev_end, interval.end)

        return result

This code will efficiently calculate the common free time intervals by sorting the flattened intervals and then checking for gaps. The result will be a list of Interval objects representing the common free time for all employees.

Identifying Problem Isomorphism

“Employee Free Time” can be mapped to “Merge Intervals”.

Both problems deal with intervals and require sorting and merging of these intervals. In “Employee Free Time”, you need to find gaps in the merged schedules of employees, i.e., free time. In “Merge Intervals”, you’re given a collection of intervals, and you need to merge all overlapping intervals. The difference lies in the final step: “Employee Free Time” requires you to find the gaps in the merged intervals, whereas “Merge Intervals” just requires you to return the merged intervals.

“Merge Intervals” is simpler because it doesn’t involve finding the gaps in the merged intervals, which is an additional step in the “Employee Free Time” problem.

10 Prerequisite LeetCode Problems

“Employee Free Time” involves intervals and how to manipulate and compare them. First tackle simpler problems related to intervals and sorting. Here are 10 problems as good preparation:

“Merge Intervals” (LeetCode Problem #56): This problem provides a good introduction to dealing with intervals and overlapping time periods.
“Insert Interval” (LeetCode Problem #57): This problem further builds on the concepts learned in the “Merge Intervals” problem.
“Non-overlapping Intervals” (LeetCode Problem #435): This problem introduces the idea of choosing intervals in a way to avoid overlap, a concept that could be useful in the “Employee Free Time” problem.
“Interval List Intersections” (LeetCode Problem #986): This problem deals with finding intersections of intervals, which requires careful handling of interval boundaries.
“Meeting Rooms II” (LeetCode Problem #253): This problem involves figuring out a schedule, given intervals of time, which can be helpful practice for “Employee Free Time”.
“Find Right Interval” (LeetCode Problem #436): This problem involves searching for specific intervals, which can help you get better at dealing with interval data.
“Range Module” (LeetCode Problem #715): This problem involves adding and deleting ranges, as well as querying about them.
“Data Stream as Disjoint Intervals” (LeetCode Problem #352): This problem is similar to “Range Module”, but the ranges come in a data stream.
“My Calendar I” (LeetCode Problem #729): In this problem, you have to determine if you can book appointments without overlap, which is similar to scheduling employee free time.
“Partition Labels” (LeetCode Problem #763): This problem requires breaking a sequence into chunks such that no value is in two different chunks. It involves sorting and dealing with interval-like structures.

Problem Classification

Problem Statement: Analyze the provided problem statement. Categorize it based on its domain, ignoring ‘How’ it might be solved. Identify and list out the ‘What’ components. Based on these, further classify the problem. Explain your categorizations.

Visual Model of the Problem

How to visualize the problem statement for this problem?

Problem Restatement

Could you start by paraphrasing the problem statement in your own words? Try to distill the problem into its essential elements and make sure to clarify the requirements and constraints. This exercise should aid in understanding the problem better and aligning our thought process before jumping into solving it.

Abstract Representation of the Problem

Could you help me formulate an abstract representation of this problem?

Given this problem, how can we describe it in an abstract way that emphasizes the structure and key elements, without the specific real-world details?

Terminology

Are there any specialized terms, jargon, or technical concepts that are crucial to understanding this problem or solution? Could you define them and explain their role within the context of this problem?

Problem Simplification and Explanation

Could you please break down this problem into simpler terms? What are the key concepts involved and how do they interact? Can you also provide a metaphor or analogy to help me understand the problem better?

Constraints

Given the problem statement and the constraints provided, identify specific characteristics or conditions that can be exploited to our advantage in finding an efficient solution. Look for patterns or specific numerical ranges that could be useful in manipulating or interpreting the data.

What are the key insights from analyzing the constraints?

Case Analysis

Could you please provide additional examples or test cases that cover a wider range of the input space, including edge and boundary conditions? In doing so, could you also analyze each example to highlight different aspects of the problem, key constraints and potential pitfalls, as well as the reasoning behind the expected output for each case? This should help in generating key insights about the problem and ensuring the solution is robust and handles all possible scenarios.

Identification of Applicable Theoretical Concepts

Can you identify any mathematical or algorithmic concepts or properties that can be applied to simplify the problem or make it more manageable? Think about the nature of the operations or manipulations required by the problem statement. Are there existing theories, metrics, or methodologies in mathematics, computer science, or related fields that can be applied to calculate, measure, or perform these operations more effectively or efficiently?

Problem Breakdown and Solution Methodology

Given the problem statement, can you explain in detail how you would approach solving it? Please break down the process into smaller steps, illustrating how each step contributes to the overall solution. If applicable, consider using metaphors, analogies, or visual representations to make your explanation more intuitive. After explaining the process, can you also discuss how specific operations or changes in the problem’s parameters would affect the solution? Lastly, demonstrate the workings of your approach using one or more example cases.

Inference of Problem-Solving Approach from the Problem Statement

How did you infer from the problem statement that this problem can be solved using ?

Could you please provide a stepwise refinement of our approach to solving this problem?
How can we take the high-level solution approach and distill it into more granular, actionable steps?
Could you identify any parts of the problem that can be solved independently?
Are there any repeatable patterns within our solution?

Solution Approach and Analysis

Thought Process

Explain the thought process by thinking step by step to solve this problem from the problem statement and code the final solution. Write code in Python3. What are the cues in the problem statement? What direction does it suggest in the approach to the problem? Generate insights about the problem statement.

From Brute Force to Optimal Solution

Could you please begin by illustrating a brute force solution for this problem? After detailing and discussing the inefficiencies of the brute force approach, could you then guide us through the process of optimizing this solution? Please explain each step towards optimization, discussing the reasoning behind each decision made, and how it improves upon the previous solution. Also, could you show how these optimizations impact the time and space complexity of our solution?

Coding Constructs

Consider the following piece of complex software code.

What are the high-level problem-solving strategies or techniques being used by this code?
If you had to explain the purpose of this code to a non-programmer, what would you say?
Can you identify the logical elements or constructs used in this code, independent of any programming language?
Could you describe the algorithmic approach used by this code in plain English?
What are the key steps or operations this code is performing on the input data, and why?
Can you identify the algorithmic patterns or strategies used by this code, irrespective of the specific programming language syntax?

Language Agnostic Coding Drills

Your mission is to deconstruct this code into the smallest possible learning units, each corresponding to a separate coding concept. Consider these concepts as unique coding drills that can be individually implemented and later assembled into the final solution.

Dissect the code and identify each distinct concept it contains. Remember, this process should be language-agnostic and generally applicable to most modern programming languages.
Once you’ve identified these coding concepts or drills, list them out in order of increasing difficulty. Provide a brief description of each concept and why it is classified at its particular difficulty level.
Next, describe the problem-solving approach that would lead from the problem statement to the final solution. Think about how each of these coding drills contributes to the overall solution. Elucidate the step-by-step process involved in using these drills to solve the problem. Please refrain from writing any actual code; we’re focusing on understanding the process and strategy.

Targeted Drills in Python

Now that you’ve identified and ordered the coding concepts from a complex software code in the previous exercise, let’s focus on creating Python-based coding drills for each of those concepts.

Begin by writing a separate piece of Python code that encapsulates each identified concept. These individual drills should illustrate how to implement each concept in Python. Please ensure that these are suitable even for those with a basic understanding of Python.
In addition to the general concepts, identify and write coding drills for any problem-specific concepts that might be needed to create a solution. Describe why these drills are essential for our problem.
Once all drills have been coded, describe how these pieces can be integrated together in the right order to solve the initial problem. Each drill should contribute to building up to the final solution.

Remember, the goal is to not only to write these drills but also to ensure that they can be cohesively assembled into one comprehensive solution.