(Simulation: coupon collector’s problem) Coupon collector is a classic statistics problem with many practical applications. The problem is to repeatedly pick objects from a set of objects and find out how many picks are needed for all the objects to be picked at least once. A variation of the problem is to pick cards from a shuffled deck of 52 cards repeatedly, and find out how many picks are needed before you see one of each suit. Assume a picked card is placed back in the deck before picking another. Write a
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- Union-Find: Maze Write a program that generates mazes of arbitrary size using the union-find algorithm. A simple algorithm to generate the maze is to start by creating an N x M grid of cells separated by walls on all sides, except for entrance and exit. Then continually choose a wall randomly, and knock it down if the cells are not already connected to each other. If we repeat the process until the starting and ending cells are connected, we have a maze. It is better to continue knocking down the walls until every cell is reachable from every cell as this would generate more false leads in the maze. Test you algorithm by creating a 15 x 15 grid, and print all the walls that have been knocked down. Darrow_forwardplease code in python You place a pawn at the top left corner of an n-by-n chess board, labeled (0,0). For each move, you have a choice: move the pawn down a single space, or move the pawn down one space and right one space. That is, if the pawn is at position (i,j), you can move the pawn to (i+1,j) or (i+1, j+1). Ask the user for the size of a chessboard, n (integer). Find the number of different paths starting from (0,0) that the pawn could take to reach each position on the chess board. For example, there are two different paths the pawn can take to reach (2,1). Look at the diagrams below to convince yourself of this. You can see the four paths that you can take by move 2. Start -> Move 1 -> Move 2 (0,0) -> (1,0) -> (2,1) (0,0) -> (1,0) -> (2,0) (0,0) -> (1,1) -> (2,1) (0,0) -> (1,1) -> (2,2) Print the board with the number of ways to reach each square labeled as shown below. For example: Enter a board size: 4 1 0 0 0 1 1 0 0 1 2 1 0 1 3 3 1arrow_forwardNationality. Prove the function works by testing it 2. BLACKJACK: Sample two cards from a "deck of cards" (ace, 2-10, jack, queen, king). Find the total of the two cards (ace counts as 11 and facecards count as 10). If the total is 21 print "BLACKJACK!" otherwise print "Try again". Keep drawing pairs of two cards until you get blackjack. Set your seed to 30 at the start of this problem ? Write 2 that ohe to frame for NAe If NA is found it should replace NA with thearrow_forward
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. anglers have recently gotten back from a fishing excursion. The I-th angler has gotten a fish of weight man-made intelligence. Anglers will flaunt the fish they got to one another. To do as such, they initially pick a request where they show their fish (every angler shows his fish precisely once, in this way, officially, the request for showing fish is a stage of integers from 1 to n). Then, at that point, they show the fish they discovered by the picked request. At the point when an angler shows his fish, he may either become glad, become dismal, or stay content. Assume an angler shows a fish of weight x, and the most extreme load of a formerly shown fish is y (y=0 if that angler is quick to show his fish). Then, at that point: in the event that x≥2y, the angler becomes cheerful; in the event that 2x≤y, the angler becomes miserable; in the event that none of these two…arrow_forwardTiling: The precondition to the problem is that you are given threeintegers n, i, j, where i and j are in the range 1 to 2n. You have a 2n by 2n squareboard of squares. You have a sufficient number of tiles each with the shape . Your goalis to place nonoverlapping tiles on the board to cover each of the 2n × 2n tiles except forthe single square at location i, j. Give a recursive algorithm for this problem in whichyou place one tile yourself and then have four friends help you. What is your base case?arrow_forwardOne variation on the game of nim is described in Luger. The game begins with a single pile of stones. The move by a player consists of dividing a pile into two piles that contain an unequal number of stones. For example, if one pile contains six stones, it could be subdivided into piles of five and one, or four and two, but not three and three. The first player who cannot make a move loses the game. (5.1) Draw the complete game tree for this version of Nim if the start state consists of six stones. (5.2) Perform a minimax evaluation for this game. Let 1 denote a win and 0 a loss.arrow_forward
- Knight's Tour: The Knight's Tour is a mathematical problem involving a knight on a chessboard. The knight is placed on the empty board and, moving according to the rules of chess, must visit each square exactly once. There are several billion solutions to the problem, of which about 122,000,000 have the knight finishing on the same square on which it begins. When this occurs the tour is said to be closed. Your assignment is to write a program that gives a solution to the Knight's Tour problem recursively. You must hand in a solution in C++ AND Java. The name of the C++ file should be "main.cc" and the name of the Java file should be "Main.java". Write C++ only with a file name of main.cc Please run in IDE and check to ensure that there are no errors occuring Output should look similar to: 1 34 3 18 49 32 13 16 4 19 56 33 14 17 50 31 57 2 35 48 55 52 15 12 20 5 60 53 36 47 30 51 41 58 37 46 61 54 11 26 6 21 42 59 38 27 64 29 43 40 23 8 45 62 25 10 22 7 44 39 24 9 28 63arrow_forwardUsing a Java program solve the following problem using arrays: Past A: Coupon collector is a classic statistic problem with many practical applications. The problem is to pick objects from a set of objects repeatedly and determine how many picks are needed for all the objects to be picked at least once. A variation of the problem is to pick cards from a shuffled deck of 52 cards repeatedly and find out how many picks are needed before you see one of each suit. Assume a picked card is placed back in the deck before picking another. Write a program to simulate the number of picks needed to get total of four cards from each different suit and display the four cards picked (it is possible that a card may be picked twice). Here is a sample run of the program: Queen of Spades 5 of Clubs Queen of Hearts 4 of Diamonds Number of picks: 12 Sample run explanation: As you see in the above run, 12 picks are made to get the four cards from different suits. The other 8 picks (12-4-8) were from the…arrow_forward3. Suppose you have been hired to develop a musical chair game. In this game there will be 7 participants and all of them will be moving clockwise around a set of 7 chairs organized in a circular manner while music will be played in the background. You will control the music using random numbers between 0-3.lf the generated random number is 1, you will stop the music and if the number of participants who are still in the game is n, the participants at position (n/2) will be eliminated. Each time a participant is eliminated, a chair will be removed and you have to print the player names who are still in the game. The game will end when there will be only one participant left. At the end of the game, display the name of the winner. [Hint: You will need to invoke a built-in method to generate a random number between 0 (inclusive) to 3 (inclusive)] Use Python languagearrow_forward
- C++ Programming, Arrays Lights The park is illuminated by n (1 < n < 100) lights. Each of them shines all night or not. Of course, which lights were on the first night and which were not. Every other night the condition of the lamps shall be determined by the following rules: the lamp will not illuminate if both of its neighbors were lit last night; the lamp shall illuminate if one of its neighbors was illuminated last night and the other was not; if neither of the first two rules applies to the lamp, it will illuminate when the night is even and will not illuminate when the night is odd. Create a program to determine which lights are on and which will not be lit when k (1 < k < 100) nights have elapsed, and to find which night the most lights were lit and which the least. If there are several identical nights with the most or least lights lit, the night with the lower number must be indicated. The first line of the original data file contains two integers: the number of…arrow_forwardLet A = {a, b, c} and B = {u, v}. Write a. A × B b. B × Aarrow_forwardObjectives Java refresher (including file I/O) Use recursion Description For this project, you get to write a maze solver. A maze is a two dimensional array of chars. Walls are represented as '#'s and ' ' are empty squares. The maze entrance is always in the first row, second column (and will always be an empty square). There will be zero or more exits along the outside perimeter. To be considered an exit, it must be reachable from the entrance. The entrance is not an exit.Here are some example mazes:mazeA 7 9 # # ##### # # # # # # # ### # # # # ##### # # # ######### mazeB 7 12 # ########## # # # # # # # #### # # # # # # ##### ## # # # # ############ mazeC 3 5 # # # ## ## Requirements Write a MazeSolver class in Java. This program needs to prompt the user for a maze filename and then explore the maze. Display how many exits were found and the positions (not indices) of the valid exits. Your program can display the…arrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr