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Suppose we are comparing implementations of insertion sort and merge sort on the same machine. For inputs of size n, insertion sort runs in 8n2 steps, while merge sort runs in 64* nlog base 2 n steps. For which values of n odes insertion sort beat merge sort?
Your goal is to solve the following simple programming exercise. You have been asked by your accounting department to design an algorithm determining the annual profit for your company.
These numbers should be stored in an array. Use the sequential search algortithm to locate the number entered by the user. If the number is in the array, the program should display a message.
Create algorithm to calculate union of two input sets given as arrays, both of size O(n). The output must be array of distinct elements that form union of the sets.
The Viterbi algorithm is a deterministic algorithm for solving the Decoding problem. Design a randomized algorithm for solving the Decoding problem.
As queries are expensive, you would like to calculate median using as few queries as possible. Provide the algorithm which finds median value using at most O(log n) queries.
Calculate the worst-case run-time complexity of your algorithm and prove optimality of the solution it gives. Suppose that the road is a straight line with a western end and an eastern end.
Assume we use hash function h to hash n distinct keys into the array T of length m. Suppose simple uniform hashing, determine the expected number of collisions?
Data Structures and Algorithm Design
Addition and Subtraction of numbers in binary and round to the nearest decimal number with three significant decimal digits
If this message is encrypted with DES by using a random 56-bit key, determine encrypted message's entropy?
Determine hash value of modified file look like, as compared with original hash value?
Expalin the search algorithm that results from each of the following special cases. How does it relate to other algorithms we have discussed.
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