answer all the 3 questions

[Repen en fiesturing and from the ple+ Code Ency Set Set 1 Ipar Cathering Survetes vingtes by the same alphabetical, were by bine-cunhada e compendio the blood when her yes, tad pagal mother Ing. 5. [10 points List the following functions according to their order of growth from the lowest to the highest. (n-2) 1. 10 log (n+100), In n, 200, 3", 0.005n" + 3m* + m2 + 1, 0.5, 1000 n + 50, n. 6 6. [12 points) Fill in the following: Algorithms Best Case Condition Efficieny Worst Case Condition Efficiency Selection Sort Bubble Sort Insertion Sort 7. 110 points] Considering the following graph: ch (a) Starting at vertex a and resolving ties by the vertex alphabetical order, traverse the graph by breath-first-search and construct the corresponding breath-first search tree. (5 points) (b) Is the graph a DAG (Directed Acyclic Graph)? If yes, find topological sort of the graph, If no, explain why. (5 points) 8 16 points). For Quicksort for the sequence {45, 29, 71, 90, 12, 31, 103, the last swap is the first swap is the number of swaps is the number of comparisons is Justify you answer. 1. [12 points| True or False T F (a) An algorithm is a sequence of instructions for solving a problem in a finite amount of time. TF (b) Algorithms can be specified in a natural language. TF (c) logan e 2(vn). TF (d) If t(n) 0(g(n)), then g(n) E (t(n)). TF (e) (). TF (1) An algorithm's time efficiency is principally measured as a function of its input size by counting the number of times its basic operation is executed. TF (g) Apply exhaustive search to solve traveling salesman problem, the time complexity is (2"). TF (h) Russian peasant multiplication is an algorithm applied decrease-by-variable-size technique TF (1) Selection sort is a direct application of the brute force technique to the sorting problem TF) Selection sort is a direct application of the brute force technique to the sorting problem TF 6) The recurrence for worst case of QuickSort is T(n) = T(n-1)+O(n). TF (k) Merge Sort is not a stable sorting algorithm TF (1) The worst case time complexity of merge sort is in logn)