A and B stand in a line at random with 10 other people. What is the probability that there are exactly 3 people between A and B?
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- You are given a N*N maze with a rat placed at maze[0][0]. Find whether any path exist that rat can follow to reach its destination i.e. maze[N-1][N-1]. Rat can move in any direction ( left, right, up and down).Value of every cell in the maze can either be 0 or 1. Cells with value 0 are blocked means rat cannot enter into those cells and those with value 1 are open.Input FormatLine 1: Integer NNext N Lines: Each line will contain ith row elements (separated by space)Output Format :The output line contains true if any path exists for the rat to reach its destination otherwise print false.Sample Input 1 :31 0 11 0 11 1 1Sample Output 1 :trueSample Input 2 :31 0 11 0 10 1 1Sample Output 2 : false Solution: //// public class Solution { public static boolean ratInAMaze(int maze[][]){ int n = maze.length; int path[][] = new int[n][n]; return solveMaze(maze, 0, 0, path); } public static boolean solveMaze(int[][] maze, int i, int j, int[][] path) {//…A group of people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After x number of passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. For example: number of passes = 1 and number of players = 5, the order of elimination is 2, 4, 1, 5. Write a program for general values of X and N. Ask a user for the number of people and number of passes To speed up the input and debugging, you may wish to store the names of the people in a file. Make sure no two names start the same letter ( Alex and Ana are not OK). Alternatively, you can number the players. Output number and/or the name of a person being eliminated Output number and the name of the winner Do not expect a user to do the right thing, error check the user input; among other things, what do you think a reasonable…A group of people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After x number of passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. For example: number of passes = 1 and number of players = 5, the order of elimination is 2, 4, 1, 5. Write a program for general values of X and N. Ask a user for the number of people and number of passes To speed up the input and debugging, you may wish to store the names of the people in a file. Make sure no two names start the same letter ( Alex and Ana are not OK). Alternatively, you can number the players. Output number and/or the name of a person being eliminated Output number and the name of the winner Do not expect a user to do the right thing, error check the user input; among other things, what do you think a reasonable…
- In a school, students of 5th Grade are going for a picnic. For a particular game between 10 players, they needs to be organized in the ascending order of their height. Teacher selects a one random student out of 10. That student acts as a mediator, all students having height less than mediator goes on left and rest on his right. The same process repeats again between the left and right group. The process continues and will stop when all the players are in ascending order of their height. Signify which sorting algorithm can be helpful to design this model and how. What additional functionality can you add to this. Implement the given model using C language.In a school, students of 5th Grade are going for a picnic. For a particular game between 10 players, they needs to be organized in the ascending order of their height. Teacher selects a one random student out of 10. That student acts as a mediator, all students having height less than mediator goes on left and rest on his right. The same process repeats again between the left and right group. The process continues and will stop when all the players are in ascending order of their height. Signify which sorting algorithm can be helpful to design this model and how. What additional functionality can you add to this. Implement the given model. Write a C program for that and this program take user input like his/her name, height etc.There is an upcoming football tournament, and the n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English.Please give time complexity. list of results mean Any combination of wins, losses and draws. You may wish to view this as a mapping from the set of…
- In a tournament, there are n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all [n(n-1)/2] matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain EnglishIn a tournament, there are n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all [n(n-1)/2] matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English. PLease give the total time complexity.A certain cat shelter has devised a novel way of making prospective adopters choose their new pet. To remove pet owners’ biases regarding breed, age, or looks, they are led blindfolded into a room containing all the cats up for adoption and must bring home whichever they pick up. Suppose you are trying to adopt two cats, and the shelter contains a total of N cats in one of only two colors: black or orange. is it still possible to pick up two black cats with probability ½, given that there is an even number of orange cats in the room? If so, how many cats should be in the room? How many black, how many orange?
- Dingyu is playing a game defined on an n X n board. Each cell (i, j) of the board (1 2, he may only go to (2, n).) The reward he earns for a move from cell C to cell D is |value of cell C – value of cell D|. The game ends when he reaches (n, n). The total reward - is the sum of the rewards for each move he makes. For example, if n = 1 2 and A = 3 the answer is 4 since he can visit (1, 1) → (1, 2) → (2, 2), and no other solution will get a higher reward. A. Write a recurrence relation to express the maximum possible reward Dingyu can achieve in traveling from cell (1, 1) to cell (n, n). Be sure to include any necessary base cases. B. State the asymptotic (big-O) running time, as a function of n, of a bottom-up dynamic programming algorithm based on your answer from the previous part. Briefly justify your answer. (You do not need to write down the algorithm itself.)There are 2016 passengers about to board a plane, numbered 1 through 2016 in that order. Each passenger is assigned to a seat equal to his or her own number. However, the first passenger disregards instructions and instead of sitting in seat number 1, chooses and sits down in a randomly chosen seat. Each subsequent passenger acts according to the following scheme: if their assigned seat is available, they will sit there; otherwise, they will pick at random from the remaining available seats and sit there. What is the probability that the 1512th passenger ends up sitting in their assigned seat? A. 1/2016 B. 1/2 C. 5/8 D. 3/4 E. None of the aboveImagine 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.