2. Alternating glasses a. There are 2n glasses standing next to each other in a row, the first n of them filled with a soda drink and the remaining n glasses empty. Make the glasses alternate in a filled-empty-filled-empty pattern in the minimum number of glass moves. [Gar78] b. Solve the same problem if 2n glasses–n with a drink and n empty-are initially in a random order.
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- This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".There are n students who studied at a late-night study for final exam. The time has come to order pizzas. Each student has his own list of required toppings (e.g. mushroom, pepperoni, onions, garlic, sausage, etc). Everyone wants to eat at least half a pizza, and the topping of that pizza must be in his reqired list. A pizza may have only one topping. How to compute the minimum number of pizzas to order to make everyone happy?Correct answer will upvoted else downvoted. playing a game on a round board with n (2≤n≤106) cells. The cells are numbered from 1 to n so that for every I (1≤i≤n−1) cell I is contiguous cell i+1 and cell 1 is nearby cell n. At first, every cell is unfilled. Omkar and Akmar alternate setting either An or a B on the board, with Akmar going first. The letter should be set on a vacant cell. What's more, the letter can't be put nearby a cell containing a similar letter. A player loses when it is their move and there are not any more substantial moves. Output the number of conceivable particular games where the two players play ideally modulo 109+7. Note that we just consider games where some player has lost and there are not any more substantial moves. Two games are considered unmistakable if the number of turns is unique or for some turn, the letter or cell number that the letter is put on were unique. A move is considered ideal if the move amplifies the player's shot at…
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Artem is building another robot. He has a network a comprising of n lines and m sections. The cell situated on the I-th line from the top and the j-th segment from the left has a worth ai,j written in it. In the event that two nearby cells contain a similar worth, the robot will break. A lattice is called acceptable if no two adjoining cells contain a similar worth, where two cells are called nearby on the off chance that they share a side. Artem needs to increase the qualities in certain cells by one to make a decent. All the more officially, find a decent network b that fulfills the accompanying condition — For all substantial (i,j), either bi,j=ai,j or bi,j=ai,j+1. For the imperatives of this issue, it tends to be shown that such a framework b consistently exists. In case there are a few such tables, you can output any of them. Kindly note that you don't need to limit…Correct answer will be upvoted else Multiple Downvoted. Computer science. Gildong has a square board comprising of n lines and n sections of square cells, each comprising of a solitary digit (from 0 to 9). The cell at the j-th section of the I-th line can be addressed as (i,j), and the length of the side of every cell is 1. Gildong prefers enormous things, so for every digit d, he needs to find a triangle with the end goal that: Every vertex of the triangle is in the focal point of a cell. The digit of each vertex of the triangle is d. Somewhere around one side of the triangle is corresponding to one of the sides of the board. You might expect that a side of length 0 is corresponding to the two sides of the board. The space of the triangle is boosted. Obviously, he can't simply be content with tracking down these triangles with no guarantees. Along these lines, for every digit d, he will change the digit of precisely one cell of the board to d, then, at that point, track…Given a deck of 52 playing cards, we place all cards in random order face up next to each other. Then we put a chip on each card that has at least one neighbour with the same face value (e.g., on that has another queen next to it), we put a chip. Finally, we collect all chips that were each queen placed on the cards. For example, for the sequence of cards A♡, 54, A4, 10O, 10♡, 104, 94, 30, 3♡, Q4, 34 we receive 5 chips: One chip gets placed on each of the cards 100, 10♡, 104, 30, 3♡. (a) Let p5 be the probability that we receive a chip for the 5th card (i.e., the face value of the 5th card matches the face value of one of its two neighbours). Determine p5 (rounded to 2 decimal places). (b) Determine the expected number of chips we receive in total (rounded to 2 decimal places). (c) For the purpose of this question, you can assume that the expectation of part (b) is 6 or smaller. Assume that each chip is worth v dollars. Further, assume that as a result of this game we receive at least…
- The rook is a chess piece that may move any number of spaces either horizontally or vertically. Consider the “rooks problem” where we try to place 8 rooks on an 8x8 chess board in such a way that no pair attacks each other. a. How many different solutions are there to this?b. Suppose we place the rooks on the board one by one, and we care about the order in which we put them on the board. We still cannot place them in ways that attack each other. How many different full sequences of placing the rooks (ending in one of the solutions from a) are there?An agent is trying to eat all the food in a maze that contains obstacles, but he now has the help of his friends! An agent cannot occupy a squarethat has an obstacle. There are initially k pieces of food (represented by dots), at positions (f1,...,fk). Thereare also n agents at positions (p1,...,pn). Initially, all agents start at random locations in the maze. Consider a search problem in which all agents move simultaneously;that is, in each step each agent moves into some adjacent position (N, S, E, or W, or STOP). Note that any number of agents may occupy the same position. Figure 1: A maze with 3 agents Give a search formulation to the problem of looking for both gold and diamondin a maze (wirte step with detail)? Knowing that you have M squares in the maze that do not have an What is the maximum size of the state space.Josefine and her friends has invented a new game called Pillar Jumpers. In this game, a sequence of N pillars of non decreasing heights are placed next to each other. The player starts on the first pillar, and the target is to reach the la pillar in at most J jumps. The player has a certain jump strength S that determines how far he can jump. Let h; be t height of the i'th pillar for i e [1...N). The player can jump from pillar i to j iff. iThere are 22 gloves in a drawer: 5 pairs of red gloves, 4pairs of yellow, and 2 pairs of green. You select the gloves in the dark andcan check them only after a selection has been made. What is the smallestnumber of gloves you need to select to have at least one matching pair inthe best case? In the worst case?ProblemGiven a value `value`, if we want to make change for `value` cents, and we have infinitesupply of each of coins = {S1, S2, .. , Sm} valued `coins`, how many ways can we make the change?The order of `coins` doesn't matter.For example, for `value` = 4 and `coins` = [1, 2, 3], there are four solutions:[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3].So output should be 4. For `value` = 10 and `coins` = [2, 5, 3, 6], there are five solutions: [2, 2, 2, 2, 2], [2, 2, 3, 3], [2, 2, 6], [2, 3, 5] and [5, 5].So the output should be 5. Time complexity: O(n * m) where n is the `value` and m is the number of `coins`Space complexity: O(n)""" def count(coins, value): """ Find number of combination of `coins` that adds upp to `value` Keyword arguments: coins -- int[] value -- int """ # initialize dp array and set base case as 1 dp_array = [1] + [0] * value) ++.Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.SEE MORE QUESTIONS