An international round table conference will be held in india. Presidents from all over the world representing their respective countries will be attending the conference. The task is to find the possible number of ways (P) to make the N members sit around the circular table such that. The president and prime minister of India will always sit next to each other. Example 1: Input : 4 Value of N(No. of members) Output: 12 -> Possible ways of seating the members
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- Sudoku is a popular logic puzzle that uses a 9 by 9 array of squares that are organized into 3 by 3 subarrays. The puzzle solver must fill in the squares with the digits 1 to 9 such that no digit is repeated in any row, any column, or any of the nine 3 by 3 subgroups of squares. Initially, some squares are filled in already and cannot be changed. For example, the following might be a starting configuration for a Sudoku puzzle: Create a class SudokuPuzzle.java Download SudokuPuzzle.java that has the attributes • board—a 9 by 9 array of integers that represents the current state of the puzzle, where 0 indicates a blank square • start—a 9 by 9 array of boolean values that indicates which squares in board are given values that cannot be changed and the following methods: • SudokuPuzzle—a constructor that creates an empty puzzle • toString—returns a string representation of the puzzle that can be printed • addInitial(row, col, value)—sets the given square to the given value as an…You are the chief commander of US Army; you have been deployed in an ongoing war training of defusing the mine. Mines are placed on the ground which can be considered as a gird of size N*M. Each block (i, j) has a mine in it if and only if the summation of the block coordinates is divisible by 2. Your task is to move from the first row to the last row. The mines will not blow if the given rules are followed: • If you are on even row you can move to any cell that is in the neighborhood • If you are on odd row, you can only go the odd row that has mine on that and same with the unmined row. You have to develop a python program to calculate the number of ways to reach row number N starting from row number 1. Test Cases: 4 8 Output: 10Admission to college is just beginning and Chef has also just finished his high school. There are N colleges, listed from 11 to N, and listed from 11 to N. Each college has only one seat left. To apply for a college, each student must submit the same examination, the result of which determines their future, that is, the best student (the highest scorer) gets the first choice of college. Each student has a list of favourite colleges. They will want to get to the top ranked college on their list. If they can't get into it, they'll want to get into a second-ranked college in the middle of their list, and so on. If one vacant college seat is filled, that year's admission closes at that college. Then, people who have applied for that college should look for a lower college in their preferred list as long as it still has vacancies. Looking at the information about MM students, about their exam scores (given as standards) and the college IDs they apply for, find out which college the Chef…
- 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 aboveA town wishes to build a trail between city A, city B, city C, city D, and city E. The distances, in miles, between any two of the destinations are given in the table. Use the table to answer parts (a) and (b) below. A B C D E A * 154 134 216 129 B 154 * 195 51 243 C 134 195 * 225 220 D 216 51 225 * 308 E 129 243 220 308 * a) Use Kruskal's algorithm to determine the minimum-cost spanning tree that would link each location to create the least expensive trail. Choose the correct graph below. A. ABCD154216225E129 B. ABCD15419551E129 C. ABCD15413451E129 D. ABCD154134216E129 b) If the cost of building such a trail is $3700 per mile, what is the cost of building the trail determined in part (a)? The cost is: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.)
- A group of m people is considering sharing the cost of buying some items for their summer camp. There are a total of n possible items to purchase. Each person writes a list of the items they are interested in purchasing on a paper. For example, person one may write “boat, trampoline, hot tub,” whereas person two may write “ hot tub, kayak, paddleboard”. There is no limit to how many items a person registers on their sheet. The goal is to determine if at least k items can be purchased. The following rules apply 1. The cost of any purchased item must be split equally among all those who listed that item on their sheet. No person can refuse to contribute to an item chosen for purchase, which is listed on their sheet. 2. Since each person has a limited budget, they may only contribute to at most one item on their list. The problem of determining if at least k items can be purchased is called SummerCamp. Show that this problem is NP-complete.Question-2: A pyramids are discovered, each has a triangular base with equal sides. An n meters high pyramid is constructed by forming n layers of triangles using Im cubical stones. Then layers are stacked on top of each other. The first layer is the triangle with n meters base, on top, n-1 meters base, until the top level which has only 1 stone. You are asked to calculate the number of stones needed to build a pyramid with the height n. WAIT! We just discovered that some pyramids have a secret room inside. This room is also of the same shape and structure as the pyramid with m layers of stones removed. In order for the room to be secret, mIn 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.Assignment Write a program that calculates the revenue of a trip of a train composed of several train-cars. For the train, the user will give the total allowed train- car count (int), total allowed weight (double), and base speed (double). Then, the user will give train-car information for ALL train-cars that will TRY TO BE ADDED to the train. First, the number of train-cars will be given (int). For each train-car, three information will be given: type of the cargo (std:string), weight of the train-car (double), and how full the train-car is (int). After getting all this information, the program will TRY TO ADD each train-car to the train according to the train-car count and total allowed weight values. You CANNOT ADD a train-car to a train if it exceeds its train-car count. You CANNOT ADD a train-car to a train if by adding this train-car, the total weight of the train exceeds the train's total allowed weight. Each added train-car reduces the speed of the train by half its weight.…During Eid, it is a tradition for every father to give his children money to spend on entertainment. Chef has N coins; denote the value of the coin i by vi. Since today is Eid, Chef gives one coin to each of his two children. He wants the absolute value of the difference between the values of the coins given to the two children to be as small as possible to be as fair as possible. Help the chef by telling him the minimum possible difference between the values of the coins given to the two children. Of course, the chef cannot give the same coin to both children. Note: Please answer in python only Possible input 1 3 142 Required Output 1SEE MORE QUESTIONS