Note: Use 18290796

1. (30p) Employ your id to get a directed graph as follows (114290504' will be used here as an example to show you how the number is calculated): multiply your id with 987654321 14290504 987654321 = 14114078024867784 remove all the zeros from the resulting number 14114078024867784 - 141147824867784 consider each consecutive two numbers as an edge in the directed graph 1-4-1-1-4-7--8-2-4-8-6-7--7--8-4 remove the reflexive edges (having same starting and ending nodes) from the graph 1-4-1-4-7-8-2-4-8-6-7-8-4 Note that for the duplicate edges, your consider only one of them for the graph. For the duplicate 1 - 4-1+4, we used only one of them in the graph. a) Show the adjacency list of your graph. b) Does the graph contain a Hamilton cycle? If your answer is YES, provide one such Hamilton cycle. If NO, explain the reason. Employ your id to calculate a specific number that will be used in the further questions as follows (14290504' will be used here as an example to show you how the number is calculated): multiply your id with 987654321 14290504 . 987654321 = 14114078024867784 remove all the zeros and ones from the resulting number 14114078024867784 447824867784 cut out the last 3 digits and assign them to the letters A, B, C, respectively. 77 A, 8 B. put the numbers in place of the corresponding red letters to solve the following questions. 2. (20p) Solve the recurrence relation a, = Aan-2 where a, = Banda, = C 3. (30p) For the functions f(x) = x4 + 2x ve g(x)=x" a) Determine whether f(x) = 0(g(x)) or not. Justify your answer. b) Determine whether g(x) = 0(f(x)) or not. Justify your answer 4. (20p) How many ways are there to distribute A x B x C blue balls to 4 people Muslum, Orhan, Ferdi, and Bergen if Ferdi and Bergen together get no more than A+B and Orhan gets at least C