(a) Explain, and give pseudo-code for, Dijkstra's algorithm to find the shortest path in an undirected graph when the distances for edges are given and all are non-negative. Your answer should include a brief explanation of why it always gives an optimal (shortest) path (if one exists). Then use Dijkstra's algorithm to find the shortest path from node B to node E in the graph below. Show your working, including the open and closed lists at each stage. 4a | 4 14 (10 marks) (b) Explain, and give pseudo-code for, the Floyd-Warshall algorithm to find the lengths of the shortest paths between each pair of vertices in a graph. The graph can have a mix of directed and bidirectional edges, but you can assume the distances are such that there are no negative cycles. Your answer should include a brief explanation of why it always gives an optimal path for each pair of vertices. Then use the algorithm on the graph below to find the matrix of all-pairs of shortest paths. Show your working. no n2 n1 (10 marks)