Session Given The problems are open for submissions from 5pm on Sunday May 10 to 11:59pm on Thursday May 14. Youshould give yourself 1hr 50 minutes to complete the practice exam. During the days that the problem submissions are open,please do not discuss the problems or their solutions on Piazza.Starting on May 15, you can still submit the practice problems. But, feel free to also discuss and share your solutionsthrough Piazza.This exam is:open notes/books/any printed resourcesopen laptop (anything that you have on your own computer, not online storage)Online resources that you are allowed to access:Gradescopecourse websitelanguage documentation:Java: https://docs.oracle.com/javase/10/docs/api/C++: https://www.cplusplus.com/reference/ and/or https://en.cppreference.com/w/Instructions:Solve three out of the four problems given on the next pages. You will not get extra credit for solving all four problems. Ifyou do attempt four problems, we will pick the three with highest scores. For each problem, your last submission counts.Grading:Every exam problem is graded out of 10 points. The total exam grade is the weighted sum computed as follows (assumescoreN is a score for a particular problem with score1 >= score2 >= score3):exam = 5 * score1 + 3 * score2 + 2 * score3The total score for a problem is determined by the maximum between zero and the sum of scores for individual tests basedon their results. The maximum score for each test is determined by max_score = 10/number_of_tests.test outcome test scorepassed test max_scorewrong answer – 0.5 max_scoreruntime error – 0.5 max_scoretimeout error – 0.5 max_scorepresentation error 0.75 max_scorePage 1/2Jill’s BicycleJill likes to ride her bicycle around the city. But in the city of Carville where she lives some of the streets are not mostfriendly to the bicyclists. Over the years the bicycling club has rated all the streets’ safety on an integer scale: positivevalues indicate that the street is safe for a person on a bike, negative values indicate that it is unsafe to ride a bike on thatstreet. Jill wants to maximize the safety score along the streets that she is riding her bike. For other parts of her trip, she willjust take a bus.InputThe first line of input contains an integer, N, the number of streets along the route that Jill needs to take, 2 <= N<= 20,000Each of the next N lines contains a single integer. The i-th integer indicating the safety of the street i. The absolute value ofsafety for each road will not exceed 10^9.OutputThe program should identify the maximum positive safety score for a given route and print a line containing that value.If a non-negative score is not possible, the program should print“No safe streets along this route.”Example 1Input2-25Output5Example 2Input4-10-1-1OutputNo safe streets along this route.Example 3Input7-1312-251Output6Page 2/2Page 1/1Toy BlocksAyu is playing with toy blocks. Ayu decides to build two towers with those blocks. She wants to use up all of the blocks shehas and the number of blocks used in two towers should not differ by more than one. Besides, every block has a height andshe wants to minimize the height difference between two towers.InputThe first line of the input contains one integer N (1 <= N <= 100), the number of toy blocks. Each of the following N linescontains one integer indicating the height h (1 <= h <= 450) of that block.OutputPrint one line, containing two space separated integers, the heights of two towers. The smaller number goes first.Example 1Input:310090200Output:190 200Page 1/2Dejavu CenterWe call a positive integer a dejavu number if and only if it is only evenly divisible by 1 and itself (which is slightly differentfrom prime numbers since 1 is dejavu but not prime).Given integer N and C, let L be the list of dejavu numbers between 1 and N and the dejavu center isthe center part of L with length of 2C if |L| is even and 2C <= |L|the center part of L with length of 2C-1 if |L| is odd and 2C-1 <= |L|L itselfFor example, the dejavu center of N=10, C=2 is {2,3,5} (note L={1,2,3,5,7}). The dejavu center of N=11, C=2 is {2,3,5,7}(note L={1,2,3,5,7,11})InputThe input consists of a single line, containing two integers N (1 <= N <= 1000) and C (1 <= C <= N).OutputPrint one line N C: dejavu-center , where N and C is the input and dejavu-center is a space separated integerlist representing the dejavu center.Example 1Input:21 2Output:21 2: 5 7 11Example 2Input:18 2Output:18 2: 3 5 7 11Example 3Input:18 18Output:18 18: 1 2 3 5 7 11 13 17Example 4Input:100 7Output:100 7: 13 17 19 23 29 31 37 41 43 47 53 59 61 67Page 2/2Page 1/2It’s in The BagShirai Kuroko is moving out of her dormitory at the end of the semester. This is a big problem for Kuroko since she has waytoo many handbags.As a teleporter, she could use teleportation to transfer her bags back home. However, consecutive spatial manipulation isstill very tiring for her. She needs to minimize the number of teleportation trip to get all her bags back home.A bag can be packed within another empty bag if its size is strictly smaller than the outside one. And Kuroko can teleportone piece (the outside bag and all bags inside it) each time she makes a single trip.For example, given 4 bags with sizes of 4, 3, 2, 1, she can pack it up as shown below| || | | || | | | | || | | |_1_| | | || | |___2___| | || |_____3_____| ||_______4_______|(i.e., bag 1 goes into bag2, bag 2 goes into bag 3 and finally bag 3 goes into bag 4) and can teleport only once.Find the minimum number of teleportation trips necessary for Kuroko to teleport all bags back home.While maintaining the minimal number of teleportation, it will be hard to transfer too many bags in one teleportation, you arealso to minimize the total number of bags in any one piece that must be carried.Kuroko treasures her bags very much, so she won’t pack a bag into another bag if it already contains another bag in it. Thatis, two bags with sizes 1 and 2 cannot be placed into a bag of size 4.InputThe first line contains 1 integer n, the number of bags Kuroko has. 1<=n<=10000.In the next line, there are n integer smaller than 10^9 indicating the size of bags.OutputOutput one integer K, indicating the minimum number of teleportation trips necessary, followed by K lines, each containingthe details about bags for each trip.The 1st integer mi of those K lines will be the number of bags transported in that trip, then the following miintegers shouldindicate the sizes of the bags in that trip in the sorted order from smallest to largest.Each size in the input should appear exactly once in the output, and the bags in each piece must fit nested one withinanother.If there is more than one solution, any will do.Example 1Input:41 2 3 4Output:14 1 2 3 4Page 2/2Example 2Input:71 1 2 2 2 3 3Output:32 1 22 2 32 1 21

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