Exercise 4 20= 10+4+6 The rod-cutting problem consists of a rod of n units long that can be cut into integer-length pieces. The sale price of a piece i units long is Pi for i = 1,...,n. We want to apply dynamic programming to find the maximum total sale price of the rod. Let F(k) be the maximum price for a given rod of length k. 1. Give the recurrence on F(k) and its initial condition(s). 2. What are the time and space efficiencies of your algorithm? Now, consider the following instance of the rod-cutting problem: a rod of length n=5, and the following sale prices P1=2, P2=3, P3=7, P4=2 and P5=5.

Exercise 4 20= 10+4+6 The rod-cutting problem consists of a rod of n units long that can be cut into integer-length pieces. The sale price of a piece i units long is Pi for i = 1,...,n. We want to apply dynamic programming to find the maximum total sale price of the rod. Let F(k) be the maximum price for a given rod of length k. 1. Give the recurrence on F(k) and its initial condition(s). 2. What are the time and space efficiencies of your algorithm? Now, consider the following instance of the rod-cutting problem: a rod of length n=5, and the following sale prices P1=2, P2=3, P3=7, P4=2 and P5=5.

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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A given Knapsack with maximal Weight capacity is 8Kg. There are some items can be chosen and taken into Knapsack. Each item has own weight and profit shown as follows. Please find the maximal profit of Knapsack after some items are selected and put into this Knapsack and its maximal Weight capacity isn't exceeded. item ID Weight 4Kg 5Kg 2Kg 1kg 6Kg A B с D E Profit 4500 5700 2250 1100 8700 The maximal profit of this Knapsack to taken some items and total weight is no exceeded the weight capacity : The last item is taken and put into this Knapsack is: The second item is taken and put into this Knapsack is : The first item is taken and put into this Knapsack is:
I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(n log n) as stated in the question.
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A robot can move horizontally or vertically to any square in the same row or in the same column of a board. Find the number of the shortest paths by which a robot can move from one corner of a board to the diagonally opposite corner. The length of a path is measured by the number of squares it passes through, including the ﬁrst and the least squares. Write the recurrence relation if you solve the problem by a dynamic programming algorithm.
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