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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.
Define about the inheritance hierarchy Languages Eiffel and D provide constructs in language for invariants and pre- and post conditions which are compiled into the code and ar
Comp are two functions n 2 and 2 n / 4 for distinct values of n. Determine When s ec on d function b ec om es l a r g er th an f i r st functi
red black tree construction for 4,5,6,7,8,9
For the following graph find the adjacency matrix and adjacency list representation of the graph.
explain quick sort algorithm
what is circular doubly link list?write down the algorithm for insertion of elements in circular doubly link list
Write an algorithm, using a flowchart, which inputs the heights of all 500 students and outputs the height of the tallest person and the shortest p erson in the school.
I =PR/12 Numbers of years .Interest rate up to 1yrs . 5.50 up to 5yrs . 6.50 More than 5 yrs . 6.75 design an algorithm based on the above information
In any singly linked list, each of the elements contains a pointer to the next element. We have illustrated this before. In single linked list, traversing is probable only in one d
Preconditions assertion A precondition is an assertion which should be true at the initiation of an operation. For instance, a square root operation can't accept a negative a
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