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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 easily adaptable to singly linked lists? Simple Insertion sor t is easily adabtable to singly linked list.
The time needed to delete a node x from a doubly linked list having n nodes is O (1)
Give example of assertion and abstract data type For illustration, consider Natural ADT whose carrier set is the set of non-negative integers and whose operations are the usual
how to define the size of array
#include #include int sumFact(int numb); int calculateFactorial(int digit); main() { int numb, sumfact; do{ printf ("Enter a number 1 to 9999\n"); scanf("%
What do you understand by tree traversal? The algorithm walks by the tree data structure and performs some computation at everynode in the tree. This process of walking by the
The number of different directed trees with 3 nodes are ?? The number of disimilar directed trees with three nodes are 3
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The Linked list is a chain of structures wherein each structure contains data in addition to pointer, which stores the address (link) of the next logical structure in the list.
important points on asymptotic notation to remember
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