Algorithm Analysis Start with 102 coins on a table, 98 showing heads and 4 showing tails. There are two ways to change the coins: • flip over any ten coins, or • place n+ 1 additional coins, all showing tails, on the table where n is the number of heads currently showing on the table. For example, you might begin by flipping nine heads and one tail, yielding 90 heads and 12 tails, then add 91 tails, yielding 90 heads and 103 tails. (a) Model this situation as a state machine, carefully defining the set of states, the start state, and the possible state transitions. (b) Optionally, explain how to reach a state with exactly one tail showing. (c) Consider the following derived variables:
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- with T=4, n=12 and A=(3,5,8,8,9,16,29,41,50,63,64,67). Draw the corresponding walkthrough as shownTiling: 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?This challenge is based on the classic videogame "Snake". Assume the game screen is an n * n square, and the snake starts the game with length 1 (i.e. just the head) positioned on the top left corner. For example, if n = 7 the game looks something like this: BEGINNING In this version of the game, the length of the snake doubles each time it eats food (e.g. if the length is 4, after eating it becomes 8). Create a function that takes the siden of the game screen and returns the number of times the snake can eat before it runs out of space in the game screen. Examples FIRST MOVE snakefill (3) snakefill (6) - 5 snakefill (24) → 9 3
- A number maze is an n × n grid of positive integers. A token starts in the upper left corner; your goal is to move the token to the lower-right corner. On each turn, you are allowed to move the token up, down, left, or right; the distance you may move the token is determined by the number on its current square. For example, if the token is on a square labeled 3, then you may move the token three steps up, three steps down, three steps left, or three steps right. However, you are never allowed to move the token off the edge of the board. 6 3574 5 315 3 283 35 74 6 53 15 1 4 2 8 3 1 4 4 5 7 2 3 4 5 7 2 3 3 1 3 2★ 3 KT3 A 5 × 5 maze that can be solved in eight moves In this problem, you will design and analyze an efficient algorithm that either returns the minimum number of moves required to solve a given number maze, or correctly reports that the maze has no solution. Describe the solution to this problem at a high level, justify why it works, write down the pseudocode for your algorithm…3. 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 languageStart with any positive number n. If n is even divide it by 2, if n is odd multiply by 3 and add 1. Repeat until n becomes 1. The sequence that is generated is called a bumpy sequence. For example, the bumpy sequence that starts at n = 10 is: 10, 5, 16, 8, 4, 2, 1and the one that starts at 11 is11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 Write a function named lengthBumpy that returns the length of the bumpy sequence generated by its integer argument. The signature of the function is int lengthBumpy(int n) Examples:lengthBumpy(10) returns 7, and lengthBumpy(11) returns 15. You may assume that the argument n is positive and that the sequence converges to 1 without arithmetic overflow.
- A number maze is a k ×k grid of positive integers. A token starts in the upper left corner and your goal is to move the token to the lower-right corner. On each turn, you are allowed to move the token up, down, left, or right; the distance you may move the token is determined by the number on its current square. For example, if the token is on a square labeled 3, then you may move the token exactly three steps up, three steps down, three steps left, or three steps right. However, you are never allowed to move the token off the edge of the board. Design and analyze an algorithm that in O(k2) time determines if there is a way to move the token in the given number maze or not.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. DA robot is initially located at position (0, 0) in a grid [−5, 5] × [−5, 5]. The robot can move randomly in any of the directions: up, down, left, right. The robot can only move one step at a time. For each move, print the direction of the move and the current position of the robot. If the robot makes a circle, which means it moves back to the original place, print “Back to the origin!” to the console and stop the program. If it reaches the boundary of the grid, print “Hit the boundary!” to the console and stop the program. A successful run of your code may look like: Down (0,-1) Down (0,-2) Up (0,-1) Left (-1,-1) Left (-2,-1) Up (-2,0) Left (-3,0) Left (-4,0) Left (-5,0) Hit the boundary! or Left (-1,0) Down (-1,-1) Right (0,-1) Up (0,0) Back to the origin! Instructions: This program is to give you practice using the control flow, the random number generator, and output formatting. You may not use stdafx.h. Include header comments. Include <iomanip> to format your output. Name…
- The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid's algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner: 1. Compute the remainder of dividing the larger number by the smaller number. 2. Replace the larger number with the smaller number and the smaller number with the remainder. 3. Repeat this process until the smaller number is zero. The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their GCD. An example of the program input and output is shown below: Enter the smaller number: 5 Enter the larger number: 15 The greatest common divisor is 5please 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 16 11 12 13 8 9 points = [10, 7, 4, 1] scores=0 15 16 17 18 19 20 21 22 23 29 38 31 32 33 34 35 36 37 38 39 40 41 This project is a fun game that generates a random number in a certain specified range and the user must guess the number after receiving hints. Every time a user's guess is wrong they are prompted with more hints to make it easier at the cost of reducing the score. from random import randint 44 45 24 25 26 27 def guessNumber(): 28 def generateNumber(): 51 52 53 54 55 56 57 return randint (10, 20) def generateHint (secretNumber, userGuess, rounds): if rounds == 0: hint = "The number is between 10 and 20" elif rounds == 1: hint= "The number is a even number" if secretNumber % 2 == 0 else "The number is an odd number" else: hint = "The number is lesser" if userGuess > secretNumber else "The number is greater" return hint secretNumber = generateNumber() for eachRound in range(0, 4): user Input = int(input("Enter your guess: ")) if userInput == secretNumber: print("Hurray! You…