numerous bouquet combinations, including two 5-rose bouquets (total profit of $70), and a 4-rose bouquet with three 2-rose bouquets (total profit of $75). Provide two different algorithms for calculatin
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Roses |
1 |
2 |
3 |
4 |
5 |
Profit |
$5 |
$15 |
$24 |
$30 |
$35 |
For each positive integer n, let f(n) be the maximum profit that Flora can make with n roses.
For example, if n = 10, Flora can make numerous bouquet combinations, including two 5-rose bouquets (total profit of $70), and a 4-rose bouquet with three 2-rose bouquets (total profit of $75).
Provide two different
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- A wrestling tournament has 256 players. Each match includes 2 players. The winner each match will play another winner in the next round. The tournament is single elimination, so no one will wrestle after they lose. The 2 players that are undefeated play in the final game, and the winner of this match wins the entire tournament. How would you determine the winner? Here is one algorithm to answer this question. Compute 256/2 = 128 to get the number of pairs (matches) in the first round, which results in 128 winners to go on to the second round. Compute 128/2 = 64, which results in 64 matches in the second round and 64 winners, to go on to the third round. For the third round compute 64/2 = 32, so the third round has 64 matches, and so on. The total number of matches is 128 + 64 + 32+ .... Finish this process to find the total number of matches.In a candy store, there are N different types of candies available and the prices of all the N different types of candies are provided to you. You are now provided with an attractive offer. You can buy a single candy from the store and get at most K other candies ( all are different types ) for free. Now you have to answer two questions. Firstly, you have to find what is the minimum amount of money you have to spend to buy all the N different candies. Secondly, you have to find what is the maximum amount of money you have to spend to buy all the N different candies. In both the cases you must utilize the offer i.e. you buy one candy and get K other candies for free. Example 1: Input: N = 4 K = 2 %3D candies[] = {3 2 1 4} Output: 3 7There 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…
- with n=6 and A=(3,5,4,1,3,2). Draw the corresponding walkthrough as shownGiven a rod of length n inches and an array of prices that contains prices of all pieces of size smaller than n. Determine the maximum value obtainable by cutting up the rod and selling the pieces. For example, if length of the rod is 8 and the values of different pieces are given as following, then the maximum obtainable value is 22 (by cutting in two pieces of lengths 2 and 6) length 1 2 3 4 5 6 7 8 price | 1 5 8 9 10 17 17 20 And if the prices are as following, then the maximum obtainable value is 24 (by cutting in eight pieces of length 1 Please provide the solution in the assembly programming language and please use both recursion and dynamic programing method to solve the problem.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
- 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.Generate random matrices of size n × n where n = 100, 200, . . . , 1000. Also generate a random b ∈ R n for each case. Each number must be of the form m.dddd (Example : 4.5444) which means it has 5 Significant digits in totalLet n E N be a natural number with a divisor d E N. If the sum of all of the positive divisors of n is equal to 2n + d, then we call n a near- perfect number. For example, if we have n = 12, then the divisors of n are 1, 2, 3, 4, 6 and 12. Therefore, the sum of the divisors of n is equal to 1+2+3+4+6+12=2*12+4, and 4|12. Hence, 12 is a near-perfect number. Write a function, near_perfect_number, which accepts any integer n as input, and returns True if n is a near-perfect number, and False otherwise.
- 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 [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 list of results mean Any combination of wins, losses and draws. You may wish to view this as a mapping from the set of distinct…A set of coins makes change for n if the sum of the values of the coins is n. For example, if you have 1- cent, 2-cent and 4-cent coins, the following sets make change for 7: • 7 1-cent coins . 51-cent, 1 2-cent coins 3 1-cent, 2 2-cent coins 3 1-cent, 1 4-cent coins . 11-cent, 3 2-cent coins . 1 1-cent, 1 2-cent, 1 4-cent coins Thus, there are 6 ways to make change for 7. Write a function count_change that takes a positive integer n and a list of the coin denominations and returns the number of ways to make change for n using these coins (Hint: You will need to use tree recursion): def count_change (amount, denominations): """Returns the number of ways to make change for amount. >>> denominations = [50, 25, 10, 5, 1] >>> count_change (7, denominations). 2 >>> count_change (100, denominations) 292 >>> denominations = [16, 8, 4, 2, 11 >>> count_change (7, denominations) 6 >>> count_change (10, denominations) 14 >>> count_change (20, denominations) 60 |||||| "*** YOUR CODE HERE ***" ĴDingyu 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.)