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1. The following is a recursive algorithm to calculate the k-th power of 2.
Input k a natural numberOutput kth power of 2Algorithem:If k =0then return 1Else return 2* power _of_2(k-1)
Please review the decomposition of a recursive algorithm described in slide #17 (week 1, 3-Recursion-IterativeAlgorithms.pdf). Please show the decomposition whne k = 5.
2. Please write an iterative algorithm to calculate the k-th power of 2. This iterative algorithm should be equivalent to the recursive algorithm in question 1.
3. Reorder the following time efficiencies from largest to smallest:
a) nlog n
b) 52
c) n + n2 + n3 + n4
d) n3
e) n5 log n
4. Determine the big-O notations for the following time efficiencies and reorder them from largest to smallest:
a) 50n3 + n2 + log n + n +10000
b) 2n5 +100n2 +1000log n
c) 200n + n2 log n
d) 10log n + n2 log n +10n4
5. Describe the information flow among DNAs, RNAs, and proteins
Implementations of Kruskal's algorithm for Minimum Spanning Tree. You are implementing Kruskal's algorithm here. Please implement the array-based Union-Find data structure.
(i) Consider a system using flooding with hop counter. Suppose that the hop counter is originally set to the "diameter" (number of hops in the longest path without traversing any
Explain Floyd's algorithm It is convenient to record the lengths of shortest paths in an n by n matrix D known as the distance matrix: the element d ij in the i th row an
Data array A has data series from 1,000,000 to 1 with step size 1, which is in perfect decreasing order. Data array B has data series from 1 to 1,000,000, which is in random order.
Q. How can we free the memory by using Boundary tag method in the context of Dynamic memory management?
what is cardinality
what is folding method?
Q. Explain the result of inserting the keys given. F, S, Q, K, C, L, H, T, V, W, M, R, N, P, A, B, X, Y, D, Z, E in an order to an empty B-tree of degree-3.
A linear collection of data elements where the linear node is given by means of pointer is known as Linked list
Which sorting algorithm is easily adaptable to singly linked lists? Simple Insertion sor t is easily adabtable to singly linked list.
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