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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.
Evaluate the frequency counts for all statements in the following given program segment. for (i=1; i ≤ n; i ++) for (j = 1; j ≤ i; j++) for (k =1; k ≤ j; k++) y ++;
State the ways to construct container taxonomy There are several ways that we could construct our container taxonomy from here; one way that works well is to make a fundamental
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Worst Fit method:- In this method the system always allocate a portion of the largest free block in memory. The philosophy behind this method is that by using small number of a ve
Acyclic Graphs In a directed graph a path is said to form a cycle is there exists a path (A,B,C,.....P) such that A = P. A graph is called acyclic graph if there is no cycle in
Conversion of Forest into Tree A binary tree may be used to show an entire forest, since the next pointer in the root of a tree can be used to point to the next tree of the for
Q. Take an array A[20, 10] of your own. Suppose 4 words per memory cell and the base address of array A is 100. Find the address of A[11, 5] supposed row major storage.
write an algorithm to find the average number of occurances of MECHANIL in an english passage
A spanning tree of any graph is only a subgraph that keeps all the vertices and is a tree (having no cycle). A graph might have many spanning trees. Figure: A Graph
The following are several operations on a AA-tree: 1. Searching: Searching is done using an algorithm which is similar to the search algorithm of a binary search tree. 2. Ins
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