Question

Question 3 - Find the Most Valuable Object [30%] You have a group of $m$ objects where each object has a distinct price $p_i$ and value $v_i$ ($1 \le i \le m$, $p_i$, $v_i$ are positive integers). Design a data structure that takes $O(m)$ space to store the objects, such that it supports the following operation: Given two prices $x$ and $y$ ($x < y$), return the most valuable object (i.e., the one with the highest value) whose price is between $x$ and $y$ ($x < p_i < y$). You may assume that there is at least one object with the price $x < p_i < y$. The operation should take $O(\log m)$ time. In your answer, please write clearly on: \begin{itemize} \item The construction method, details (e.g., type of data structure, attributes, etc.) and space complexity of the data structure. \item The pseudo-code of the algorithm to find the most valuable object. You should also give brief verbal explanations on it and prove it's time complexity. \end{itemize} Note that you can directly use conclusions from lecture notes without proof, e.g., from lecture note xxx, we know...

          Question 3 - Find the Most Valuable Object [30%]
You have a group of $m$ objects where each object has a distinct price $p_i$ and value $v_i$ ($1 \le i \le m$, $p_i$, $v_i$ are positive integers). Design a data structure that takes $O(m)$ space to store the objects, such that it supports the following operation:
Given two prices $x$ and $y$ ($x < y$), return the most valuable object (i.e., the one with the highest value) whose price is between $x$ and $y$ ($x < p_i < y$). You may assume that there is at least one object with the price $x < p_i < y$. The operation should take $O(\log m)$ time.
In your answer, please write clearly on:
\begin{itemize}
    \item The construction method, details (e.g., type of data structure, attributes, etc.) and space complexity of the data structure.
    \item The pseudo-code of the algorithm to find the most valuable object. You should also give brief verbal explanations on it and prove it's time complexity.
\end{itemize}
Note that you can directly use conclusions from lecture notes without proof, e.g., from lecture note xxx, we know...

Show more…

Question 3 - Find the Most Valuable Object [30%]
You have a group of m objects where each object has a distinct price pi and value vi (1 ≤ i ≤ m, pi, vi are positive integers). Design a data structure that takes O(m) space to store the objects, such that it supports the following operation:
Given two prices x and y (x < y), return the most valuable object (i.e., the one with the highest value) whose price is between x and y (x < pi < y). You may assume that there is at least one object with the price x < pi < y. The operation should take O(log m) time.
In your answer, please write clearly on:

* The construction method, details (e.g., type of data structure, attributes, etc.) and space complexity of the data structure.

* The pseudo-code of the algorithm to find the most valuable object. You should also give brief verbal explanations on it and prove it's time complexity.

Note that you can directly use conclusions from lecture notes without proof, e.g., from lecture note xxx, we know...

Added by Tina U.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Supreeta N

06/07/2023

Step 1

Step 2: The pseudo-code for the algorithm to find the most valuable object is as follows: Show more…

Show all steps

lock

Thanks for your feedback!

Answer: The construction method for the data structure is a balanced binary search tree, which has a space complexity of O(m). The pseudo-code for the algorithm to find the most valuable object is as follows: 1. Create a balanced binary search tree and insert all the objects with their prices and values. 2. Define a function findMostValuableObject(x, y) that takes in two prices x and y. 3. Traverse the binary search tree to find the object with the highest value whose price is between x and y. 4. Return the most valuable object found. The time complexity of the findMostValuableObject algorithm is O(log m) because the binary search tree allows for efficient searching and retrieval of objects based on their prices.

Play audio

Feedback

Powered by NumerAI

Supreeta N and 69 other subject AP CS educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:02 Hello students, to minimize the time to search for a given record we need to find the value of m.

00:12 So to find that is the minimizing the total search time considering both the disk access time and the main memory processing time.

00:22 So let's break down the total search time into its components.

00:26 So first component we can take it as a disk access time.

00:31 So first we need as a disk access time.

00:36 So for this access time we have as 90 plus 0 .07 into m that has been calculated in milliseconds in milliseconds fine.

01:02 So the second thing we need is the main memory processing.

01:06 So the main memory processing time the main memory processing processing time be as a plus b log 2 m that is also been calculated in a milliseconds fine.

01:38 So the third thing we need is total search of time that is a total search of time search of time.

01:51 So we can give it as a disk access time plus the main processing time.

02:00 It is nothing but which is this access time as well as the main processing time.

02:06 So since we want to minimize the total search time we can ignore the constant a.

02:13 So we can here ignore the constant a and focus on the dominant term which is the excess.

02:20 So which is so our dominant term here is the disk access time.

02:26 So let us set up an equation to find the optimization value of m.

02:30 So to find the total optimization value of m we will substitute all this into this total search of time...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later