
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Transcribed Image Text:2. Solve the following instance of the 0/1 knapsack problem using dynamic programming
approach. Assume that the knapsack capacity is 9.
Benefit
$8
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- Recall the rod cutting problem we discussed in class and in the book. While it might be possible for a theoretical person to cut the rod of length n, up to n times to achieve the maximum possible sale value, enterprising children do not possess the stamina to cut the rod so many times. They instead get tired or bored after only k cuts. Design a dynamic programming algorithm to maximize the value of selling cut rods if at most we can cut the rod k times. Please use elements in the table P to calculate the value of a continuous rod, e.g. an uncut rod of length i has value pi. Further you should analyze: 1. The time complexity of a baseline solution that does not use dynamic programming or memoization that exhaustively explores all potential solutions 2. The time complexity of your dynamic programming solution 3. Describe how you could change your algorithm to so to reconstruct the actual cuts in order achieve the highest value for the rod pieces.arrow_forward1. Let S = {1,2...n} be a set activities, where activity i € S has a start time si, a finish time f; and a profit p, asSociated with it. Design an dynamic programming algorithm for computing a set of compatible activities of maximum profit. Argue that the time complexity of you algorithm is O(n log(n)). (You must start with the correct definitions, and then write a recurrence relation.)arrow_forwardQ1 Dan has a list of problems suitable for the assignment. The difficulties of these problems are stored in a list of integers a. The i-th problem’s difficulty is represented by a[i] (the higher the integer, the more difficult the problem). Dan is too busy eating saltines to worry about assignment decisions, so he asks Michael to select at least two problems from the list for the assignment. Since there are many possible subsets of the problems to consider and Michael has a life, he decides to consider only sublists (definition follows) of the list of problems. To make grading the assignment easier, Michael wants to pick problems that don’t vary too much in difficulty. What is the smallest difference between the difficulties of the most difficult selected problem and the least difficult selected problem he can achieve by selecting a sublist of length at least 2 of the original list of problems? Definition: A sublist of a list a is any list you can obtain by removing some (possibly 0)…arrow_forward
- Rod cutting problem: A cutting factory buys long steel rods and then and cuts them into shorter rods, which it then sells. Each cut is free. The selling price is based on the length of the cut. The factory want to determine the best cuts in order to maximize its revenue. Below, the price that the factory can make for each length of rod is given. Determine the maximum revenue, rn, obtainable by cutting up the rod and selling the pieces using bottom-up dynamic-programming approach. Length, I 1 2 3 4 5 6 7 Price, pi 2 4 5 6 9 10 12 r5 = ?arrow_forwardPROBLEM IN IN PYTHON 3. THIS IS A CODING PROBLEM. NOT A MULTIPLE CHOICE PROBLEM. ANSWER SHOULD BE IN PYTHON. IF YOU DO NOT KNOW HOW TO SOLVE AND THINK IT IS A MULTIPLE CHOICE PROBLEM, DO NOT ANSWER. class Solution: """ RAW_TRADE_HEADER = ["trade_id", "trade_date", "time_of_trade", "portfolio", "exchange", "product", "product_type", "expiry_dt", "qty", "strike_price", "side"] """ def process_raw_trade(self, raw_trade: List): def run(self) -> List[Tuple[str, str]]:arrow_forward
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