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a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by using potentials: i) Show there is a potential y* for the new costs for which the paths in the tree to each node v have cost y*v, and ii) explain why this proves it. What is the relationship between the shortest path distances of the modified problem and those of the original problem?
b) Can adding a constant k to the length of every arc coming out from a non-root node produce a change in the shortest path tree? Justify your answer.
Which sorting algorithm is best if the list is already sorted? Why? Insertion sort as there is no movement of data if the list is already sorted and complexity is of the order
1. A string s is said to be periodic with a period α, if s is α k for some k > 2. (Note that α k is the string formed by concatenating k times.) A DNA sequence s is called a tand
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Best Case: If the list is sorted already then A[i] T (n) = c1n + c2 (n -1) + c3(n -1) + c4 (n -1) = O (n), which indicates that the time complexity is linear. Worst Case:
In the book the following methods are presented: static void selectionSort(Comparable[] list) static void insertionSort(Comparable[] list) static boolean linearSearch(Comparable
Which sorting algorithm is easily adaptable to singly linked lists? Simple Insertion sor t is easily adabtable to singly linked list.
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What is AVL Tree? Describe the method of Deletion of a node from and AVL Tree ?
what is far and near procedures in system programming?
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