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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.
Explain the Arrays in Ruby Ruby arrays are dynamic arrays which expand automatically whenever a value is stored in a location beyond current end of the array. To the programmer
algorithm for multiple queue with example program
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
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
Add -75to+25 in 2s complement
In the last subsection, we have implemented a stack by using an array. While a stack is implemented by using arrays, it suffers from the basic restriction of an array - i.e., its s
You will write functions for both addition and subtraction of two numbers encoded in your data structure. These functions should not be hard to write. Remember how you add and subt
: Write an algorithm to evaluate a postfix expression. Execute your algorithm using the following postfix expression as your input: a b + c d +*f .
2. Write a note on i) devising ii) validating and iii) testing of algorithms.
algorithm and flow chart to find weather the given numbers are positive or negative or neutral
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