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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.
Determine the class invariants- Ruby Ruby has many predefined exceptions classes (like ArgumentError) and new ones can be created easily by sub-classing StandardError, so it's
A significant aspect of Abstract Data Types is that they explain the properties of a data structure without specifying the details of its implementation. The properties might be im
A full binary tree with n leaves have:- 2n -1 nodes.
In-order Traversal This process when executed iteratively also needs a stack and a Boolean to prevent the implementation from traversing any portion of a tree twice. The gener
Pre-order Traversal The method of doing a pre-order traversal iteratively then has the several steps(suppose that a stack is available to hold pointers to the appropriate nodes
Q. The degree of a node is defined as the number of children it has. Shear show that in any binary tree, the total number of leaves is one more than the number of nodes of degree 2
what is the difference between data type and abstract data type
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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.
what are the characteristies of good algorithm
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