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- The puzzle called the Towers of Hanoi consists of three pegs, one of which contains several rings stacked in order of descending diameter from bottom to top. The problem is to move the stack of rings to another peg. You are allowed to move only one ring at a time, and at no time is a ring to be placed on top of a smaller one. Observe that if the puzzle involved only one ring, it would be extremely easy. Moreover, when faced with the problem of moving several rings, if you could move all but the largest ring to another peg, the largest ring could then be placed on the third peg, and then the problem would be to move the remaining rings on top of it. Using this observation, develop a recursive algorithm for solving the Towers of Hanoi puzzle for an arbitrary number of rings.Computer science. Correct answer will be upvoted else downvoted. Think about a n by n chessboard. Its columns are numbered from 1 to n from the top to the base. Its sections are numbered from 1 to n from the passed on to one side. A cell on a convergence of x-th line and y-th section is indicated (x,y). The fundamental corner to corner of the chessboard is cells (x,x) for all 1≤x≤n. A stage of {1,2,3,… ,n} is composed on the fundamental slanting of the chessboard. There is actually one number composed on every one of the cells. The issue is to segment the cells under and on the principle askew (there are by and large 1+2+… +n such cells) into n associated areas fulfilling the accompanying imperatives: Each district ought to be associated. That implies that we can move from any cell of a locale to some other cell of a similar area visiting just cells of a similar district and moving from a cell to a neighboring cell. The x-th area ought to contain cell on the fundamental…8. Convert the automaton of question 6 to DFA by showing all the steps. 6. Compute ϵ-closure for each state for the following transition table: Solve Question 8 Only
- A tile of a monkey puzzle has four monkey halves that can be labelled as north(N), east (E), south (S), and west (W) half. In addition to the shape of the borderrectangle, these halves determine which edges can be placed next one other. There isalso another way to define how the tiles can be placed: Each tile corner (i.e. compassdirections NE, SE, SW, and NW) has a monkey quarter. If we abstract this quarter, forexample, with a letter, only the tiles with the same letter in their touching corners canbe adjacent. illustrates one valid solution for this quarter monkey puzzle.Are the two monkey puzzle representations equivalent in the sense that if we have apile of ‘half monkey’ tiles H, it is possible to define a pile of ‘quarter monkey’ tilesQ that gives exactly the same set of solutions for the puzzle (and vice versa)?a. Correctness of dynamic programming algorithm: Usually, a dynamic programming algorithm can be seen as a recursion and proof by induction is one of the easiest way to show its correctness. The structure of a proof by strong induction for one variable, say n, contains three parts. First, we define the Proposition P(n) that we want to prove for the variable n. Next, we show that the proposition holds for Base case(s), such as n = 0, 1, . . . etc. Finally, in the Inductive step, we assume that P(n) holds for any value of n strictly smaller than n' , then we prove that P(n') also holds. Use the proof by strong induction properly to show that the algorithm of the Knapsack problem above is correct. b. Bounded Knapsack Problem: Let us consider a similar problem, in which each item i has ci > 0 copies (ci is an integer). Thus, xi is no longer a binary value, but a non-negative integer at most equal to ci , 0 ≤ xi ≤ ci . Modify the dynamic programming algorithm seen at class for this…1. A certain computer algorithm executes four times as many operations when it is run with an input of size n as when it is run with an input of size n – 1. Here, n > 1 is an integer. When the algorithm is run with an input of size 1, it executes 12 operations. How many operations does the algorithm execute when it is run with an input of size 5? How many operations does the algorithm execute when it is run with an input of size n?
- Graph Neural Network: Consider the un-directed graph shown in the Fig. The values inside the node refer to the feature value of the node. The order of the nodes is A,B,C,D when following the matrix form in below questions.(You can use python or other languages to find the eigen values and other operation for this question): 1.Consider the values in the circle to be the values of the input feature of the data point. Find the spectral representation of the data point.2.Let W = 2, B = 1 and a ReLU activation function f(x) = max(0,x) as explained in question 1. Find one step updated features h(1)v for all nodes using the Graph Convolution Network (GCN) algorithmThe following questions are related to regular expression and regular language: (i) Let r,, r2, r be regular expressions. Find all the regular ones from the following expressions: a·p, r³, r* · 0, (r*)), r + r2 – r, (4) +r + 12, n+r, ÷ r,, r*), (r, r2), {rn + r2}, a+¢ (ii) Let E= {a, b}. Given regular expressions r = a*b", r' = ba* ab* + (ab)* (ba)* and Ir" = (a* + b)bb(a + b)*,- nd L(r), Lr), and L(r"), the languages defined by r, r', r", respectively. (iii) Let Z = {a, b}. Given the language L = {aa" b"b, (ba)*, bb: n, m 2 0 and h 2 1}, find the regular expression r such that L(r) = L.2. [15 points] Draw a state diagram of a Turing machine accepting the language L = {x#ry | x € {0,1}* and y E {0,1,#}*}, i.e., L consists of all strings which have a prefix of the form x#x with x E {0, 1}*. Assume the tape alphabet is I = {0, 1, #, &, -}.
- Plot the orbit in 3D using a suitably dimensioned sphere for the Earth. [6]: # YOUR CODE HERE raise NotImplementedError() Not Implemented Error Cell In [6], line 2 1 # YOUR CODE HERE ----> 2 raise NotImplementedError() Not ImplementedError: Problem 1.6 Plot the Specific Energies (i.e., all three Kinetic, Potential and Total Energy) in the same plot as a function of time. The x-axis must show time (in hours) and y axis must show the Energy (in km² /s²). [7] # YOUR CODE HERE Traceback (most recent call last) raise NotImplementedError()PLEASE HELP!!!! Write these rules in Python #name – a simple name for the rule (e.g., up, left, down, right) #• precondition function – a Boolean function that accepts a state and returns true if the rule is applicable to state #• action function – a function that accepts a state and returns the successor state obtained by applying the ruleCorrect answer will be upvoted else Multiple Downvoted. Computer science. Berland local ICPC challenge has quite recently finished. There were m members numbered from 1 to m, who contended on a problemset of n issues numbered from 1 to n. Presently the article is going to happen. There are two issue creators, every one of them will tell the instructional exercise to precisely k back to back errands of the problemset. The creators pick the section of k continuous errands for themselves autonomously of one another. The sections can correspond, meet or not cross by any means. The I-th member is keen on paying attention to the instructional exercise of all continuous errands from li to ri. Every member consistently decides to pay attention to just the issue creator that tells the instructional exercises to the most extreme number of assignments he is keen on. Leave this greatest number alone artificial intelligence. No member can pay attention to both of the creators, regardless of…