Design a dynamic programming algorithm for the bigger-is-smarter elephant problem by comparing it, as done previously, with the problem of finding the longest weighted path within a directed level graph problem.

Run a programme to calculate the average length of the paths identified and the empirical likelihood that BreadthFirstPaths will identify a path between two randomly picked vertices for various graph models.

Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 3 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm   (Would anything change if B to C weight was changed from 3 to 4? To 1? What about 5?)

design an algorithmthat given a directed graph g = (v e) and a distinguished vertex s v determines for each v v the shortest path from s to v. if g has n vertices and e edges then your algorithmmust run in time o(n + e).

Write a function in a directed graph represented by adjacency lists that returns true (1) if an edge exists between two provided vertices u and v and false (0) otherwise.

An undirected graph G = (V,E) is said to be k-colorable if all the vertices of G can be colored using k different colors such that no two adjacent vertices have the same color. Design an algorithm that runs in time O(n + e) to color a graph with two colors or determine that the graph is not 2-colorable.

Hello, i have this Dijkstra’s exercise. could you help me to solve it?

Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). ... Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.

Run a programme to compute the average length of the routes identified for several graph models and to empirically evaluate the chance that BreadthFirstPaths discovers a path between two randomly selected vertices.

Q/ Write a java program to implement Warshall’s algorithm for transitive closure of a Directed Graph.