
(a)
To show that there will always be a point where maximum overlap is an endpoint of one of the segments.
(a)

Explanation of Solution
Given Information: A point of maximum overlap in a set of intervals is a point with the largest number of intervals in the set that overlap it.
Explanation:
Consider that there is no point of maximum overlap in an endpoint of a segment. The maximum overlap occurs in the interior of m segments. Here, the point P is the intersection of those m points.
There must be another point
Hence, it is proved that the there is always a point where maximum overlap has an endpoint of the segment.
(b)
To show that there will always be a point where maximum overlap is an endpoint of one of the segments.
(b)

Explanation of Solution
Explanation:
Consider a balanced binary tree of endpoints. For inserting the interval, it is necessary to insert the endpoints separately. Consider the endpoints as e . For left endpoint e , increase the value of e by 1 and for right endpoint e , decrease the overlap by 1.
For multiple endpoints with same value, insert the left endpoints with the value before the right endpoints with the value.
Consider that
Where
Here, each node x store the new node that includes the endpoints
For bottom up approach to satisfy the conditions of red black tree following conditions must be hold:
Want to see more full solutions like this?
- module: java Question3: (30 MARKS) Passenger Rail Agency for South Africa Train Scheduling System Problem Statement Design and implement a train scheduling system for Prasa railway network. The system should handle the following functionalities: 1. Scheduling trains: Allow the addition of train schedules, ensuring that no two trains use the same platform at the same time at any station. 2. Dynamic updates: Enable adding new train schedules and canceling existing ones. 3. Real-time simulation: Use multithreading to simulate the operation of trains (e.g., arriving, departing). 4. Data management: Use ArrayList to manage train schedules and platform assignments. Requirements 1. Add Train Schedule, Cancel Scheduled Train, View Train Schedules and Platform Management 2. Concurrency Handling with Multithreading i.e Use threads to simulate train operations, Each…arrow_forwardjava: Question 1: (40 MARKS) E-Hailing Bicycle Management System Case Study:An e-hailing company that rents out bicycles needs a system to manage its bicycles, users, and borrowing process. Each user can borrow up to 2 bicycles at a time, specifically for families with children 18 years or below. The system must track the bicycles (name, make, type, and availability) and users (name, ID, and borrowed bicycles). The company also wants to ensure that the system uses a multidimensional array to store information about the bicycles. Requirements: Add and View Bicycles: Borrow Bicycles: Return Bicycles Display Borrowed Bicycles and Search for a bicycle Create a menu-driven program to implement the above. Sample Output: Add Bicycle View All Bicycles Borrow Bicycle Return Bicycle View Borrowed Bicycles Search Bicycle ExitEnter your choice: Question 2 (30 MARKS) Pentagonal Numbers Problem Statement Create a Java program that will display the first 40 pentagonal…arrow_forwardRequest for Java Programming Expert Assistance - Module: Java 731 Please assign this to a human expert for detailed Java programming solutions. The AI keeps attempting to answer it, but I need expert-level implementation. Question 1 (40 MARKS) - E-Hailing Bicycle Management System Case Study:An e-hailing company needs a Java system to manage bicycle rentals. Key requirements: Users (families with children ≤18) can borrow up to 2 bicycles. Track bicycles (name, make, type, availability) and users (name, ID, borrowed bikes). Use a multidimensional array for bicycle data. Functionalities: Add/view bicycles. Borrow/return bicycles. Display borrowed bikes and search functionality. Menu-driven program with the following options: Copy 1. Add Bicycle 2. View All Bicycles 3. Borrow Bicycle 4. Return Bicycle 5. View Borrowed Bicycles 6. Search Bicycle 7. Exit Question 2 (30 MARKS) - Pentagonal Numbers Problem Statement:Write a Java program to display the first 40…arrow_forward
- module , java 731 Question 1: (40 MARKS) E-Hailing Bicycle Management System Case Study:An e-hailing company that rents out bicycles needs a system to manage its bicycles, users, and borrowing process. Each user can borrow up to 2 bicycles at a time, specifically for families with children 18 years or below. The system must track the bicycles (name, make, type, and availability) and users (name, ID, and borrowed bicycles). The company also wants to ensure that the system uses a multidimensional array to store information about the bicycles. Requirements: Add and View Bicycles: Borrow Bicycles: Return Bicycles Display Borrowed Bicycles and Search for a bicycle Create a menu-driven program to implement the above. Sample Output: Add Bicycle View All Bicycles Borrow Bicycle Return Bicycle View Borrowed Bicycles Search Bicycle ExitEnter your choice:arrow_forwardthis module is java 371. please answer all questions correctly , include all comments etc and follow all requirements. Question 1: (40 MARKS) E-Hailing Bicycle Management System Case Study:An e-hailing company that rents out bicycles needs a system to manage its bicycles, users, and borrowing process. Each user can borrow up to 2 bicycles at a time, specifically for families with children 18 years or below. The system must track the bicycles (name, make, type, and availability) and users (name, ID, and borrowed bicycles). The company also wants to ensure that the system uses a multidimensional array to store information about the bicycles. Requirements: Add and View Bicycles: Borrow Bicycles: Return Bicycles Display Borrowed Bicycles and Search for a bicycle Create a menu-driven program to implement the above. Sample Output: Add Bicycle View All Bicycles Borrow Bicycle Return Bicycle View Borrowed Bicycles Search Bicycle ExitEnter your choice: Question 2…arrow_forwardthis module is java 371. please answer all questions correctly , include all comments etc and follow all requirements. Question 1: (40 MARKS) E-Hailing Bicycle Management System Case Study:An e-hailing company that rents out bicycles needs a system to manage its bicycles, users, and borrowing process. Each user can borrow up to 2 bicycles at a time, specifically for families with children 18 years or below. The system must track the bicycles (name, make, type, and availability) and users (name, ID, and borrowed bicycles). The company also wants to ensure that the system uses a multidimensional array to store information about the bicycles. Requirements: Add and View Bicycles: Borrow Bicycles: Return Bicycles Display Borrowed Bicycles and Search for a bicycle Create a menu-driven program to implement the above. Sample Output: Add Bicycle View All Bicycles Borrow Bicycle Return Bicycle View Borrowed Bicycles Search Bicycle ExitEnter your choice: Question 2…arrow_forward
- this module is java 371. please answer all questions correctly , include all comments etc and follow all requirements. Question 1: (40 MARKS) E-Hailing Bicycle Management System Case Study:An e-hailing company that rents out bicycles needs a system to manage its bicycles, users, and borrowing process. Each user can borrow up to 2 bicycles at a time, specifically for families with children 18 years or below. The system must track the bicycles (name, make, type, and availability) and users (name, ID, and borrowed bicycles). The company also wants to ensure that the system uses a multidimensional array to store information about the bicycles. Requirements: Add and View Bicycles: Borrow Bicycles: Return Bicycles Display Borrowed Bicycles and Search for a bicycle Create a menu-driven program to implement the above. Sample Output: Add Bicycle View All Bicycles Borrow Bicycle Return Bicycle View Borrowed Bicycles Search Bicycle ExitEnter your choice: Question 2…arrow_forwardthis module is human computer interaction 700. answer all correctly . QUESTION ONE 1.1 Define interaction design and explain its significance in modern technology. 1.2 Differentiate between good and poor design by providing two examples. 1.3 Explain how digital transformation has changed human interactions with technology. 1.4 What are the key considerations when designing an interactive product? (30 MARKS) (5 Marks) (5 Marks) (5 Marks) (5 Marks) 1.5 What are the essential characteristics of good designing. Identify and describe how these are important standards for designing (10 Marks) QUESTION TWO (30 MARKS) 2.1 What are conceptual models in interaction design?…arrow_forwardSubject: Computer databases please show all the work, draw the ER diagramarrow_forward
- COMPREHENSIVE MICROSOFT OFFICE 365 EXCEComputer ScienceISBN:9780357392676Author:FREUND, StevenPublisher:CENGAGE LC++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage LearningC++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
- Systems ArchitectureComputer ScienceISBN:9781305080195Author:Stephen D. BurdPublisher:Cengage LearningOperations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks ColeNp Ms Office 365/Excel 2016 I NtermedComputer ScienceISBN:9781337508841Author:CareyPublisher:Cengage



