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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.
An algorithm is a sequence of steps to solve a problem; there may be more than one algorithm to solve a problem. The choice of a particular algorithm depends upon following cons
In this unit, the following four advanced data structures have been practically emphasized. These may be considered as alternative to a height balanced tree, i.e., AVL tree.
For preorder traversal, in the worst case, the stack will rise to size n/2, where n refer to number of nodes in the tree. Another method of traversing binary tree non-recursively t
Give an algorithm to find both the maximum and minimum of 380 distinct numbers that uses at most 568 comparisons.
Handout 15 COMP 264: Introduction to Computer Systems (Section 001) Spring 2013 R. I. Greenberg Computer Science Department Loyola University Water TowerCampus, Lewis Towers 524 82
c++ To calculate the amount to be paid by a customer buying yummy cupcakes for his birth day party
Multilist Representation of graph
Double ended queues are implemented along doubly linked lists. A doubly link list can traverse in both of the directions as it contain two pointers namely left pointers and righ
#question. merging 4 sorted files containing 50,10,25,15 records will take time?
Question 1 Describe the following- Well known Sorting Algorithms Divide and Conquer Techniques Question 2 Describe in your own words the different asymptotic func
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