Consider an N-team tournament in which each team plays every other team once. If a tournament were to materialise, show (by example) that every team would be defeated by at least one other team.
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A: The question has been answered in step2
Consider an N-team tournament in which each team plays every other team once. If a tournament were to materialise, show (by example) that every team would be defeated by at least one other team.
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- Consider a tournament between N teams, each team playing each of the other teams. Show (by example) there is a tournament that might occur, where every team is beaten by some team.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.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|).
- Assume there are n = 2x players in a single elimination tournament with x rounds. How many single elimination tournaments should there be in order for the total number of matches to equal the number of matches in a round robin tournament?Let n be a natural number. Let's take the following 2 player game. We have .n matches. Player 1 takes one or two matches from the pile, then as long as there are still matches, player 2 takes one or two matches, and so on, alternating until there are no more matches left. The player who takes the last match loses. The losing player gets a benefit of -1 and the other player gets a benefit of 1. Represent this game for n=2 ,n=3 and n=4 and say how many strategies each player has.Assume we have two groups A and B of n cups each, where group A has n black cups while group B has n white cups. The cups in both groups have different shapes and hence a different amount of coffee per each cup. Given the following two facts: 1) All black cups hold different amounts of coffee, 2) Each black cup has a corresponding white cup that holds exactly the same amount of coffee, your task is to find a way to group the cups into pairs of black and white cups that hold the same amount of coffee. For example:
- We have 13 items in total. There are 6 guidebooks, and 7 towels. We pick two items, and among those, we must pick at least one guidebook and at least one towel. In how many ways can we do that?Solve it and provide the 100% correct answer with covering of all test cases.Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…
- Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you ll in the values is the correct one.Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Prove that the coin changing problem exhibits optimal substructure. Design a recursive backtracking (brute-force) algorithm that returns the minimum number of coins needed to make change for n cents for any set of k different coin denominations. Write down the pseudocode and prove that your algorithm is correct.The Josephus problem is the following game: N people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After M 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. Thus, if M = 0 and N = 5, players are eliminated in order, and player 5 wins. If M = 1 and N = 5, the order of elimination is 2, 4, 1, 5. Write a C program to solve the Josephus problem for general values of M and N. Try to make your program as efficient as possible. Make sure you dispose of cells. What is the running time of your program? If M = 1, what is the running time of your program? How is the actual speed affected by the delete routine for large values of N (N > 100,000)? ps. provide a screenshot of output, thankss