[Unbalanced Rod]Given a set of n weights {w₁,..., wn} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown in the figurebelow.-1"./10231224We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights to hooks, wecan compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks).where 0 ≤ Pi≤n-1 is the position of weight along the rod.For example, in the figure shown above, the center of mass is computed asC=C =i Wi PiΣi Wi10 0+2 1+3·2+4·3+12.4 +2.510+2+3+4+12+27833The problem is to find an assignment of weights to hooks that makes the center of mass as far as possible to the left, i.e., minimize the value of c.Answer the following questions.1. Describe a greedy algorithm that finds the assignments that minimizes the value of c.2. Prove the optimality of your algorithm.3. Establish the running time of your algorithm.= 2.36

Greedy Algorithm A greedy algorithm is an algorithmic approach that follows the heuristic of making…

[Unbalanced kod] Given a set of n weights {w₁,..., w} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown i below. -1" /10 2 3 4 12 2 We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks). Σi Wi-Pi C= Σ; wi where 0 ≤p; ≤ n - 1 is the position of weight i along the rod. pole in the fourro shoum abou

[Unbalanced kod] Given a set of n weights {w₁,..., w} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown i below. -1" /10 2 3 4 12 2 We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks). Σi Wi-Pi C= Σ; wi where 0 ≤p; ≤ n - 1 is the position of weight i along the rod. pole in the fourro shoum abou

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.

Question

[Unbalanced Rod]
Given a set of n weights {w₁,..., wn} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown in the figure
below.
-1".
/10
2
3
12
2
4
We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights to hooks, we
can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks).
where 0 ≤ Pi≤n-1 is the position of weight along the rod.
For example, in the figure shown above, the center of mass is computed as
C=
C =
i Wi Pi
Σi Wi
10 0+2 1+3·2+4·3+12.4 +2.5
10+2+3+4+12+2
78
33
The problem is to find an assignment of weights to hooks that makes the center of mass as far as possible to the left, i.e., minimize the value of c.
Answer the following questions.
1. Describe a greedy algorithm that finds the assignments that minimizes the value of c.
2. Prove the optimality of your algorithm.
3. Establish the running time of your algorithm.
= 2.36

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