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Tree is a special type of graph, in which there is exactly one path between every pair of nodes. By removing nodes from a tree, we separate it into many small subtrees. Given a tree T=(V,E) consisting of n nodes and m edges and an integer k<n , find the minimum number of nodes in tree to remove so that the tree is separated into subtrees of sizes at most k. Provide the algorithm, the correctness proof and the time complexity.
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 ( )?
Suppose now there are three users. Find the probability that at a given time, all three users are transmitting simultaneously. Find the fraction of time during which the queue grows.
Give a linear-time algorithm to find an odd-length cycle in a directed graph. You may not suppose that graph is strongly connected.
Write down algorithm, using pseudocode, to perform the following task, Given a string of numbers, recognize all of the substrings that form numbers that are divisible by 3.
Algorithm that will receive two integer items from a terminal operator, and display to the screen their sum, difference, product and quotient.
Design an algorithm to solve the Spectral Assembly problem under the above conditions. Does the problem have a unique solution?
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.
Explain the following sorting techniques using appropriate algorithms- (i) selection sort (ii) bubble sort
Implement the following algorithm for the evaluation of arithmetic expressions. Each operator has a precedence. The + and - operators have the lowest precedence.
Running time of quicksort can be enhanced in practice by taking advantage of fast running time of insertion sort when its input is "nearly" sorted.
Let the adaptive playout delay algorithm. Show through simple example that adjusting playout delay at beginning of each talk.
Create an algorithm to produce list of customers from Glad Rags Clothing Company's customer master file. Each record on customer master file contains the customer's number
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