Please help me solve this and write the answer as the handwritten note 2. Say you have a problem. You know of an algorithm which can solve it in e(2") time, andyou know a method that takes O(n) time to check and see if a proposed answer is validfor any given problem instance. Is this enough to know whether or not the problem is ineach of the three complexity classes below? Explain each answer.2a) P2b) NP2c) NP-complete

Detailed explanation: Solution:Given:Algorithm to solve the problem takes O(2^n) time.Verifying a…

Answered: 2. Say you have a problem. You know of…

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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Question: What does it mean for a problem to be NP-complete?
Suppose Professor Weine described a deterministic algorithm that runs in polynomial time for a known NP-Complete problem such as the Satisfiability problem How would this impact the class NP (the class of problems that can be solved nondeterministically in polynomial time)? 0. The class P would be strictly larger than the class NP 0. The class NP would be equal to the class P O.It would only impact P but not NP O.It would have no impact on the class NP
In computational complexity theory, we study mostly decision problems (e.g., determine if aBoolean formula has a satisfying assignment), instead of the search problems that are typicallywhat practicing computer scientists really want to solve (e.g., determine if a Boolean formula hasa satisfying assignment, and then output the assignment). It is natural to wonder whether we arestudying the wrong thing. In this exercise, you will show that the difficulty of decision problems isin fact linked closely to that of search problems.Show that if P = NP, then every NP search problem can be solved in polynomial time. In otherwords, for each language A ∈ NP, with a polynomial-time verifier algorithm VA taking inputs x, w,where x ∈ A ⇐⇒ (∃w) VA(x, w) accepts, then there is a polynomial-time algorithm S that, oninput x, does the following. If x ̸∈ A, then S(x) outputs “no”. If x ∈ A, then S(x) outputs w suchthat VA(x, w) accepts.Hint: Build up the witness w bit by bit, by asking NP questions about…
Suppose Professor Weise described a deterministic algorithm that runs in polynomial time for a known NP-Complete problem such as the Satisfiability problem. How would this impact the class NP (the class of problems that can be solved nondeterministically in polynomial time)? OL The class P would be strictly larger than the class NP Ⓒ. The class NP would be equal to the class P O.It would only impact P but not NP IV. It would have no impact on the class NP
A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) ... Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select ] If we know that an algorithm cannot exist for solving Problem S, what does that tell us about Problem T? [Select ] [ Select ] An algorithm cannot exist for solving Problem TT. what does that tell us about Problem S? If we know An algorithm exists for solving Problem T Nothing [ Select] If we know that an algorithm cannot exist for solving Problem T, what does that tell us about Problem S? [ Select ]
A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) ... Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm cannot exist for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm exists for solving Problem T, what does that tell us about Problem S? [ Select ] [ Select ] An algorithm cannot exist for solving Problem S,r solving Problem T, what does that tell us about Nothing An algorithm exists for solving Problem S
I just need the proof for the puzzle problem being NP-Complete.
An NP-complete problem is a fascinating kind of problem because till now no one has discovered the polynomial-time algorithm to solve it and also no one has proved that no polynomial-time algorithm can exist for any NP-complete problem. It is an open research problem since it was first posed in 1971 to prove P#NP. The NxN Queens problem can be summarized as follows: putting N chess queens on an N×N chessboard such that none of them is able to attack any other queen using the standard chess queen's moves (row-column- diagonal). Thus, a solution requires that no two queens share the same row, column, or diagonal. Solutions exist only for N = 1 or N 2 4. Use the given function below to test whether a queen is attacked by another or not. You are not allowed to use any other code to check if a queen is safe. Implement a backtracking solution for the algorithm in Java that finds all possible solutions for N queens and measure the execution time it takes for N=4 to 12 and compare them…
Pseudo-random numbers Randomly generating numbers is a crucial subroutine of many algorithms in computer sci- ence. Because computers execute deterministic code, it is not possible (without external influence) to generate truly random numbers. Hence, computers actually generate psuedo- random numbers. The linear congruential method is a simple method for generating pseudo-random numbers. Let m be a positive integer and a be an integer 2 < a <m, and c be an integer 0 ≤ c<m. A linear congruential method uses the following recurrence relation to define a sequence of pseudo-random numbers: In+1=a+c mod m (a) Use the linear congruence method with a = 8, c=5, and m = 14, to compute the first 15 pseudo-random numbers when co= 1. That is, compute zo,X1, X 14- (b) From part (a) we should notice that, with m = 14, the sequence does not contain all 14 numbers in the set Z14. In particular because the sequence is periodic. Using m = 8, determine the value of a which does give all 8…
Provide short answers to the following questions: (a) Suppose we know that a problem X is NP-complete. Suppose we discover a polynomialtime algorithm for X. Would that imply that the SATISFIABILITY problem can besolved in polynomial time? Explain your answer. (b) Suppose we know that a problem X belongs to the class NP. Suppose we discover thatthere is a polynomial time algorithm for X. Would that imply that the SATISFIABIL-ITY problem can be solved in polynomial time? Explain your answer. (c) Suppose we discover an O(n3) algorithm for SATISFIABILITY. Would that imply thatevery problem in NP can be solved in O(n3) time? Why or why not?
Now suppose that n is not 2i for any integer i. How would we change the algorithmso that it handles the case when n is odd? I have two solutions: one that modifiesthe recursive algorithm directly, and one that combines the iterative algorithm andthe recursive algorithm. You only need to do one of the two (as long as it works anddoes not increase the BigOh of the running time.)
The Knapsack Problem is a famous computer science problem that is defined as follows: imagine you are carrying a knapsack with capacity to hold a total of weight C. You are selecting among n items with values A={a_1, a_2, ... , a_n} and associated weights W={w_1, w_2, ... , w_n}. Here the weights and values are all positive (but not necessarily unique). You wish to maximize the total value of the items you select not exceeding the given weight capacity, i.e. maximize sum_{a in A} such that sum_{w in W} <= C. Please note that you can only select your items once. a) We can reformulate this as a 2D bottom-up dynamic programming problem as follows. Define T_{i,j} as the highest possible value sum considering items 1 through i and total weight capacity j (j <= C). What is the base case i.e. T_{0,j} for all j and T_{i,0} for all i?, and What is the loop statement?

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