Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 18.1, Problem 1E
Program Plan Intro

To explain the reason of not allowing a minimum degree of t=1 .

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If A={8,12,16,20} and B={12,16,20,24,28}, what is the value of P (A and B)?
A hardware store is selling steel rods of various lengths. However, customers sometimes want to buy rods that the store doesn't carry. For example, if the store only carries 10cm and 30cm rods and a customer wants to buy a 25cm rod, then the order cannot be fulfilled. To boost sales, the store has come up with an idea to weld two rods together to make a longer rod. For example, if the store only carries 3cm and 5cm rods and a customer wants to buy a 8cm rod, then the order can be fulfilled by welding together 3-cm and 5-cm rods. Since rod welding can compromise the strength, the store will only weld up to TWO rods together. More precisely, this means, an order for x cm can be fulfilled if there is a single rod of length x or there are two rods (potentially of the same length) whose combined length is x. Your Task: Write a function process Orders (orders: List[int], sizes:List[int]) -> List[bool] to determine whether or not each of the given orders can be fulfilled. Here, orders is a…
TM M = (Q, E, I, 6, 90, 9a, qr), where Q = {90, 91, 92, 9a, 9r}, Σ = {0, 1}, r = {0, 1, L}, and 8 is: 8(qo, U) = (qr, U, R) 8(90, 0) = 8(go, 1) (91, 0, R) (qo, 1, R) = 8(g1, L) = (ga, U, R) 8(91,0) = (91, 0, R) 8(91, 1) = (92, 1, R) = (92, U, R) 8(92, U) 8(92, 0) = (90, 0, R) 8(92, 1) = (92, 1, R) i. Prove that M is NOT a decider. ii. Mathematically describe the language A that M recognises. Prove that A ≤ L(M). iii. Prove A = L(M). iv. Is A Turing-decidable? [Give clear reasons for your answer. No need for a formal proof.]
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