Design and describe a general m-round winner tournament, Round-Winner-Tournament(P,m), for players P, where in each round 0, 1,...,m − 1 the players are paired randomly and the winners proceed to the next round. After round m − 1, the champion is selected randomly from the remaining players. Interestingly, this tournament structure has the following special cases: m = 0 is a random selection tournament, m = 1 is a random pairing tournament, and m = lg |P| is a single elimination seeding tournament

Design and describe a general m-round winner tournament, Round-Winner-Tournament(P,m), for players P, where in each round 0, 1,...,m − 1 the players are paired randomly and the winners proceed to the next round. After round m − 1, the champion is selected randomly from the remaining players. Interestingly, this tournament structure has the following special cases: m = 0 is a random selection tournament, m = 1 is a random pairing tournament, and m = lg |P| is a single elimination seeding tournament

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter13: Decision Making Under Uncertainty

Section13.4: Decision Trees

Problem 9P

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Create and describe a general m-round winner tournament for players P called Round-Winner-Tournament(P,m), where players are paired at random in rounds 0, 1,..., m 1 and the victors advance to the next round. The winner is chosen at random from the surviving players after round m 1. It's interesting to note that this tournament format has the following special cases: the random selection tournament (m = 0), the random pairing tournament (m = 1), and the single elimination seeding tournament (m = lg |P|).
Although the plot function is designed primarily for plotting standard xy graphs, it can be adapted for other kinds of plotting as well. b. Make a plot of the curve, which is defined parametrically by the equations x = 2cosθ + cos2θ, y = 2sinθ - sin2θ, where 0 < θ < 2π. Take a set of values of θ between zero and 2π and calculate x and y for each from the equations above, then plot y as a function of x. b. Taking this approach a step further, one can make a polar plot r = f(θ) for some function f by calculating r for a range of values of θ and then converting r and θ to Cartesian coordinates using the standard equations x = r cosθ, y = r sinθ. Use this method to make a plot of the function r = ecosθ – 2 cos(4θ) + sin5 (θ/12) in the range 0 <= θ <= 24π. use python code to answer the highlight one
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 English. PLease give the total time complexity.
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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.
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