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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.
B i n a ry Search Algorithm is given as follows 1. if (low > high) 2. return (-1) 3. mid = (low +high)/2; 4. if ( X = = a [mid]) 5. return (mid); 6.
Best Case: If the list is sorted already then A[i] T (n) = c1n + c2 (n -1) + c3(n -1) + c4 (n -1) = O (n), which indicates that the time complexity is linear. Worst Case:
What are the Dynamic arrays Dynamic arrays are convenient for programmers since they can never be too small-whenever more space is needed in a dynamic array, it can simply be e
A graph is a mathematical structure giving of a set of vertexes (v1, v2, v3) and a group of edges (e1, e2, e3). An edge is a set of vertexes. The two vertexes are named the edge en
Q. Let a binary tree 'T' be in memory. Write a procedure to delete all terminal nodes of the tree. A n s . fun ction to Delete Terminal Nodes from Binary Tree
By changing the NULL lines in a binary tree to the special links called threads, it is possible to execute traversal, insertion and deletion without using either a stack or recursi
Q. Assume that we have separated n elements in to m sorted lists. Explain how to generate a single sorted list of all n elements in time O (n log m )?
Which data structure is used for implementing recursion Stack.
boundary tag system in data structure?
WRITE AN ALGORITHM TO READ TWO NUMBERS AND PRINT THE LOWER VALUE
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