21. Let us say that a graph G = (V, E) is a near-tree if it is connected and has at most n +8 edges, where n IVI. Give an algorithm with running time O(n) that takes a near-tree G with costs on its edges, and returns a minimum spanning tree of G. You may assume that all the edge costs are distinct. 2. (25) IMST: near-tree Textbook Exercise 21 in Chapter 4. An edge cost means an edge weight. Assume a graph is represented using an adjacency list. In your answer, (a) describe the algorithm (a precisely implementable outline is adequate) and state (b) why the algorithm works (that is, correct) and (c) why the running time is O(n). Hints: BFS and the following optimality principle of a greedy MST algorithm: "An algorithm that builds a spanning tree by repeatedly deleting edges (in any order) when justified by the cycle property ends up with a minimum spanning tree