Problem 1: (page limit: 2 pages) Sometimes there are multiple shortest paths between pairs of nodes in a graph. Develop an algorithm for the following task: given an undirected graph G = (V, E) with unit edge lengths and nodes v and w, output the number of distinct shortest paths from v to w. For example, for the graph below, on input v and w your algorithm should output 2. Your algorithm's running time should be linear in n = IV and m= El. (a) Describe your algorithm in pseudocode. (b) Give a formal proof of correctness. (c) Show that your algorithm runs in O(n + m) time. Problem 1: (page limit: 2 pages) Sometimes there are multiple shortest paths between pairs of nodes in a graph. Develop an algorithm for the following task: given an undirected graph G = (V, E) with unit edge lengths and nodes v and w, output the number of distinct shortest paths from v to w. For example, for the graph below, on input v and w your algorithm should output 2. Your algorithm's running time should be linear in n = IV and m= El. (a) Describe your algorithm in pseudocode. (b) Give a formal proof of correctness. (c) Show that your algorithm runs in O(n + m) time