Problem 2 (5 points) – B-Tree (1) (1 point) Explain how to f…

Problem 2 (5 points) – B-Tree (1) (1 point) Explain how to find the maximal key stored in a B-tree; (2) (2 points) Give the pseudo code of the successor function B-Succ(x, k) of a given key k stored in node x of a B-tree; (3) (2 points) Show the process of inserting the following keys into a B-tree with degree t = 2 in the given order using the algorithm in our Textbook: Your Family Name, FIU, SCIS, COP5407,  Final, Exam, and Fall2024 (you only need to show the relative positions of the keys without drawing the nodes).

Problem 3 (6 points) – Graph Algorithms (Searching and Minim…

Problem 3 (6 points) – Graph Algorithms (Searching and Minimum Spanning Tree) Given a directed weighted graph , in which , , and , , , , , , , . (1) (1 point) List the nodes visited in the order of using BFS(G,); (2) (1 point) List the nodes visited in the order of using DFS(G); (3) (1 point) Can topological sorting be performed on this graph? If yes, how it can be done? If no, what is the problem? (4) (1.5 points) Ignore the direction, list the edges in the order selected in the MST using Prim’s algorithm starting from root ; (5) (1.5 point) Ignore the direction, list the edges in the order selected in the MST using Kruskal’s algorithm.