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- Do( ii )question Correctly else downvotedRequired: Amitabh had a magical cat. That cat once fell down an empty well. As the walls of the well were not completely vertical, the cat could climb up the well. In one day, the cat can climb 1 unit height and the height of the well is h units. The cat starts at the bottom. Every day, a cat would divide into 2 cats. One of them would climb up 1 unit. The other would wait for help. But while waiting it would fall asleep and roll down 1 unit, unless it is already at the bottom, in which case it just remains there. When a cat would reach the top, it would run home toAmitabh. (Schrodinger doesn't know that some of the cats are in a well and so he can't rescue them). It has been d days since the cat fell into the well. How many cats would come out of the well today? You would notice that the number of cats grows very large with each passing day, so output the answer modulo 10^9+7. d = 0 means that the cat has fallen just now and so there's just one cat at the bottom of the well. So you…2, Towers of Hanoi Problem. (10 points) The Towers of Hanoi is a famous problem for studying recursion in computer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. Answer the following questions. (1) Determine a state representation for this problem. (4points) (2) What is the size of the state space? (3 points) (3) Supposing K=3, N=4, what is the start state by using your proposed state representation method and what is the goal state? (3 points)
- Transcribed Image Text Alex is playing Poker card game. He starts with a deck of N cards, where for each valid (i), the ith card has an integer A¡ written on it. Now the dealer starts dealing the cards one by one in the order from card 1 to card N. Alex wins if at some moment in time, the sum of all the cards dealt so far is between X and Y inclusive; if this never happens, Alex loses. You are now helping Alex to win the game, so without him noticing, you will swap some pairs of cards before the game starts. Develop a python script to find the smallest number of swaps we need so that Alex would win the game, or find that it is impossible to make Alex win. Display a single line containing one integer i.e., the smallest required number of swaps or -1 if Alex cannot win.Let L₁ = {aa, bb}, L₂ = {A, a, aa}, L3 = {x | x = {a,b}* ^ |x| ≤ 3} = {A, a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, bab, bba, bbb}. Evaluate: (L₁n L3) · L2 = •Q4: Getting the GradeMichael is taking n courses this semester, numbered from 1 to n.Each of these courses has a final exam. Unfortunately, these examsare all held on the same day.Michael has d days left to study for the exams. In each of these days,he has exactly h hours of free time he can use to study (note thath might be greater than 24 as Michael lives in a different universe witha different time system).Moreover, for the i-th course Michael is taking,he has a learning rate l[i] indicating the number of marks he getson the exam per hour of studying for that course.Michael studies for his exams in 1 hour blocks; for example,he can't study for an exam for 40 minutes then switch to another one.Note that in Michael's universe, final exam grades aren'tcapped at 100. In fact, there's no upper limit on how high they can go.If Michael takes an exam without studying for it, he'll get a 0 on that exam.In order to qualify for a nice scholarship, Michael needsto get at least m marks on each…