# Programming

1. (10 points) Given a string of characters, count the number of substrings that start with an A and end with a B. For example, there are four such substrings in CABAAXBYA, i.e. AB, ABAAXB, AAXB, AXB. Write a program that uses the brute-force approach to count the number of such substrings in a given string.

A sample dialogue might look like as follows:

*Please enter a string: ADABCBA*

*The number of substrings that start with an A and end with a B is 4*

2. (10 points) Given a graph (with 6 vertices) represented in adjacency matrix, write a program that uses the brute-force approach to determine whether the graph is a star as follows (i.e., there is a center vertex in the graph, and the other 5 vertices are connected to this vertex, but there is no edge between any of these 5 vertices)

3. (10 points) Write a program that uses the decrease-and-conquer algorithm as discussed in class to generate the power set of a set of *n*unique elements. The power set of a set *S* is the set of all the subsets of *S*, including the empty set and *S* itself. For example, if *S* is {4, 9, 5}, the power set your program should output is {}, {4}, {9}, {4, 9}, {5}, {4, 5}, {9, 5}, {4, 9, 5}.

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**Category**: Coursework