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Give a linear-time algorithm to find an odd-length cycle in a directed graph. You may NOT assume that the graph is strongly connected. (Hint: First solve this problem under the assumption that the graph is strongly connected. Then show that every directed graph is a DAG of its strongly connected components.)
Our goal is to plan this trip so that we minimize the maximum amount of walking done in a single day. Your algorithm should be based on dynamic programming and run efficiently.
How does he calculate the signature on each of m1j mod n (for positive integer j), m1-1 mod n, m1*m2 mod n, and in general m1j*m2k mod n (for arbitrary integers j and k)?
Suppose the cost of seek is 5milliseconds, while the disk transfer rate is 40 mgbytes per second. Find the cost of sorting the relation , in seconds, w/bb = 1 & w/ bb= 100.
You should build enough new roads such that if City A was reachable from City B via some old roads, City A must be reachable from City B via some new roads.
storage pool and that there is a special null value. Write an algorithm to count the nodes in a linked list with first node pointed to by first."
Solve the following recurrence relations by the method of your choiceT(n) = 1 for n = 4 and T(n) =pnT(pn) + n for n > 4. Argue that the solution to the recurrence T(n) = T(n=3) + T(2n=3) + cn is (n lg n) by appealing to the recursion tree.
Data Structures and Algorithm Design
Write a program to simulate a grocery store checkout counter. Construct one long queue from which customers dequeue to the next available counter.
Write down the suitable example of best use of Encryption, Virus, VPN, Firewall securities, when and explain why?
Provide an O(n) algorithm which ?nds xbest such that distbest:= ∑i=1 to n|xbest - xi| is as small as possible.
Consider a simple symmetric encryption algorithm as follows:Is it a problem if the first block of input happens to be the same as the key? Explain why?
Implement a queue as a circular array as follows: Use two index variables head and tail that contain the index of the next element to be removed and the next element to be added.
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