There are six runners in the 100-yard dash. How many ways are there for three medals gold, silver and bronze to be awarded if ties are possible
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DISCRETE STRUCTURE
a)There are six runners in the 100-yard dash. How many ways are there for three medals
gold, silver and bronze to be awarded if ties are possible.
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- Single Lane Highway Problem Description Certain number of cars are passing a single lane road. Speeds of all cars vary. It is easy to see, that depending on the speeds of the cars various groups will be formed. Being a single lane road passing/overtaking is not allowed. Given speeds of cars, calculate how many groups can be formed if all possible permutations are taken into account. Refer example1 for better understanding. Print number of groups divided by the number of permutations. Constraints 0 <= N < 10 ^ 5 0 <= speed of individual vehicle < 10 ^ 9 Input First line contains an integer N, which denotes the number of vehicles Second line contains N space separated integers which denotes the speed of individual vehicle. Output Print number of groups divided by the number of permutations rounded upto 6 decimal places. Time Limit 1 Examples Example 1 Input 3 10 20 30 Output 1.833333 Explanation: So all possible permutations are: {10 20 30} {10 30 20} {20} {10 30} {20 30}…(Heat transfer) The formula developed in Exercise 5 can be used to determine the cooling time, t, caused only by radiation, of each planet in the solar system. For convenience, this formula is repeated here (see Exercise 5 for a definition of each symbol): t=Nk2eAT3fin A=surfaceareaofasphere=4r2 N=numberofatoms=volumeofthespherevolumeofanatom Volume of a sphere sphere=43radius3 The volume of a single atom is approximately 11029m3 . Using this information and the current temperatures and radii listed in the following chart, determine the time it took each planet to cool to its current temperature, caused only by radiation.Subject / Operation Research You need to visit a city you have never been to before and you want to reach that city by the shortest route. That's why you work on the map to determine the shortest path. Depending on the route you choose, you have to pass through different cities (cities that can be passed: A, B, C, D, E). Table 3 shows the distance (kilometers) between adjacent cities. Answer the following questions regarding this shortest path problem. a)Create the network representation b) Write the mathematical model. c) Solve with Dijkstra's algorithm.
- Sequential Money Problem (Coin Row)• Suppose there are n coins lined up side by side on a table; Let the values of these coins be c₁, c₂, ..., cn (the valuesthey do not have to be different from each other, there may be more than one coin of the same value on the table; but all positive).• The goal is not to take two adjacent coins on the table side by side.collecting the largest total valuable coins from the table, provided that The algorithm that solves the Ordered Money problem;a. By using the brute-force method, evaluating all possible valid alternatives and reaching the result (with the "exhaustive search" method),b. Write the "recurrence" equation that describes the problem directly (without using the dynamic programming technique). Describe the time complexity of each of your algorithms for both of the above spelling.Celebrity problem A celebrity among a group of n people is a person who knows nobody but is known by everybody else. The task is to identify a celebrity by only asking questions to people of the form: ”Do you know him/her?” Solution Select two people from the group given, say, A and B, and ask A whether A knows B. If A knows B, remove A from the remaining people who can be a celebrity; if A doesn’t know B, remove B from this group. Solve the problem recursively for the remaining group of people who can be a celebrity Which design strategy does the following solution use? A-)Decrease-by-a-constant factor algorithm B-)Variable-size-decrease algorithm C-)Decrease-by-a-constant algorithm D-)Divide-and-ConquerDISCRETE STRUCTURE How many ways are there to choose a dozen of donuts from 20 veritiesa) If there are no two donuts of the same varietyb) If there is no restrictionc) If there must be at least six kaya-filled donuts.
- Question 4 - Algorithm Design Imagine you are a treasure hunter standing at one side of the river. There are n (a positive integer) stones on the river. They are aligned on a straight line and at the nth stone, there is treasure waiting for you. Your target is to reach the nth stone. For each move, you have the choice of either walking (move one stone ahead) or leaping (move two stones ahead). Also, you are not allowed to travel backwards. Design an algorithm that calculates the number of ways (sequences of walks/leaps) that get you to the treasure stone. You should clearly explain the algorithm and demonstrate the correctness of the algorithm with a complete proof. Here is an example. For n = 1 5, there are 8 ways: Method 1: walk → walk → walk → walk → walk Method 2: walk → walk → walk → leap Method 3: walk → walk → leap → walk Method 4: walk → leap → walk → walk walk Method 5: leap → walk → walk → Method 6: leap → leap walk Method 7: leap → walk → leap Method 8: walk → leap leapTranscribed Image Text A student took four quizzes in a term and would like to compute their average. He also would like to know what will be the remarks. Follow the range of grades and its equivalent remarks, and then fill-up the table below: 100-95 - Excellent 94-90 – Very Satisfactory 89-85 - Satisfactory 84-80 - Fine 79-75 - Fair 74 and below - PoorThe Philosophers' Dinner Problem Five philosophers sit around a table and spend their lives dining and thinking. Each philosopher has a bowl of noodles and a fork to the left of your plate. To eat the noodles you need two forks and each philosopher you can only take the ones to your left and right. If any philosopher takes a fork and the other is busy, he will wait, fork in hand, until pick up the other fork, so you can start eating later. If two adjacent philosophers try to pick up the same fork at the same time, a race condition: they both compete to take the same fork, and one of them left without eating. If all the philosophers take the fork to their right at the same time, then everyone will be waiting forever, because someone must release the fork that is lack. No one will because everyone is in the same situation (hoping that someone put down their forks). Then the philosophers will starve. This lock mutual is called deadlock or deadlock. The problem is to find an algorithm that…
- 10 - In an examination, 500 students appeared. Out of these students, 38 % got A+ grade, 45 % got B+ and the remaining just passed. Assuming that no student failed, find the number of students who got A+, B+ and the number of students who just passed.(Python code)50 40 30 20 10 4 6 8 10 12 14 Time (s) The diagram above shows the journey of a train plotted as a velocity-time graph. Find: a) The acceleration on the first part of the journey b) The total distance covered in the first 10 seconds c) The amount of time that the train is travelling at constant velocityGoal Seek function in Excel - Select the incorrect answer a. The changing cell in Goal Seek should have a formula b. Allows the user to determine the desired INPUT value for the formula, where the OUTPUT value is already known c. Goal Seek finds out one variable, Solver can find out more variables d. It gets the answer immediately, it does not use the trial and error approach until it gets an answer
