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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
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What is Space complexity of an algorithm? Explain.
write a c++ program to find out the area of a curve y=f(x) between x=a and x=b
Q. Write down an algorithm to evaluate an expression given to you in postfix notation. Show the execution of your algorithm for the following given expression. AB^CD-EF/GH+/+*
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Q. Define the graph, adjacency matrix, adjacency list, hash function, adjacency matrix, sparse matrix, reachability matrix.
1) Why space complexity is comparatively more critical than time complexity? 2) Determine the space complexity of Euclid Algorithm?
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