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Let G(V,E) be a directed graph, with source s∈V , sink t∈V , and nonnegative edge capacities {ce}. Provide a polynomial-time algorithm to decide whether G has a unique minimum s - t cut (i.e., an s - t cut of capacity strictly less than that of all other s - t cuts).
Divide 16 digit value N by six digit integer D obtaining quotient Q and remainder (or sign of the remainder) R by division algorithms.
The recent discovery of the following fragment of uncommented procedural C code in the Sunlab has caused a big scandal. What is the worst-case time complexity of foo(a,1,N,k), and for which inputsdoes it occur?
Suppose you need to sort a relation of 40 gigabytes, with 4 kilobyte blocks, using a memory size of 40 megabytes. Find the cost of sorting the relation, in seconds, with bb = 1 and with bb = 100.
Write an implementation of a data structure S that supports the following operations: Insert(S, x): insert the key x into S only if it is not already there.
Describe a sorting algorithm to be parsimonious if it never compares same pair of input values twice. (Supose that all the values being sorted are distinct.).
Consider the following algorithm for finding the smallest element in an unsorted array: RANDOMMIN(A[1 .. n]). What is the exact expected number of executions of line ( )?
Illustrate all your work. Use modular approach to solving this problem. Give the following submodule. Calculations - module to compute gross pay. Using the Program Development Cycle, develop an algorithm using pseudocode for the following task.
Design an O(n) algorithm that decides (schedules) for each node at which time slot to start sending data such that the total number of time (slots) is minimized.
Consider T be augmented red-black tree, where each node x has attribute x.size, which is number of internal nodes in subtree rooted at x. Given such augmented red-black tree T.
For instance, the constraints x1 = x2, x2 = x3, x3 = x4, and x1 6= x4 cannot be satis fied. Give an efficient algorithm that takes as input m constraints over n variables and decides whether the constraints can be satis fied.
Using only asymmetric encryption algorithms write down any steps taken by Bob which permit him to read the message.
Consider adaptive playout delay algorithm. Demonstrate through simple example which adjusting playout delay at beginning of each talk spurt results in compressing
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