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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.
As part of an experiment, a school measured heights (in metres) of all its 500 students. Write an algorithm, using a flowchart that inputs the heights of all 500 students and ou
Surrounding of sub division method A polygon surrounds a viewport if it completely encloses or covers the viewport. This happens if none of its sides cuts any edge of the viewp
I am looking for assignment help on the topic Data Structures. It would be great if anyone help me.
i need help in java recursion assignment.
What is the time complexity of Merge sort and Heap sort algorithms? Time complexity of merge sort is O(N log2 N) Time complexity of heap sort is O(nlog2n)
Inorder traversal: The left sub tree is visited, then the node and then right sub-tree. Algorithm for inorder traversal is following: traverse left sub-tree visit node
Q. Write down an algorithm to add an element in the end of the circular linked list. A n s . Algo rithm to Add the Element at the End of Circular Linked Lists
AVL tree An AVL tree is a binary search tree in which the height of the left and right subtree of the root vary by at most 1 and in which the left and right subtrees are again
Red-Black trees have introduced a new property in the binary search tree that means an extra property of color (red, black). However, as these trees grow, in their operations such
Complexity : How do the resource needs of a program or algorithm scale (the growth of resource requirements as a function of input). In other words, what happens with the performan
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