Homework Assignment 4
                               CS 378h
                         Unique Number: 53455
                             Spring, 2026

                      Given:  February 23, 2026
                         Due:  March 5, 2026


This homework assignment concerns the calculation of reachability
using matrices.

Consider a square matrix that has all zero elements below the diagonal
and zero elements on the diagonal.  Above the diagonal are only
entries with 1 or 0.  Given a matrix element (i, j) where j > i, this
matrix has a 1 if element i is connected to element j.

By repeated "multiplication", one can calculate the connectivity of
all nodes.  Our original initial square matrix only contains a 1 where
element i is connected to element j.  We can calculate the
reachability of i to all elements by repeatedly "multiplying" the
original matrix with an evolving solution that first computes the
two-step reachability, and then the three-step reachability, ... by
repeatedly "multiplying" the original, one-step matrix by the evolving
matrix.

Apply the methods you learned to transpose a matrix to the problem of
calculating the reachability of a matrix; that is, think about how to
compute the reachability of a matrix by repeated "multiplication".

Turn-in a C-language program that computes the reachability of a
matrix described in the second paragraph of this assignment.  Include
some tests that show your program works correctly for matrices as
large as 2^15 distinct elements; thus, your result array will contain
2^30 entries, with approximately 2^29 i,j pairs that will indicate whether
element i is connected to element j.

Think carefully about how to perform the "multiplication" efficiently.

Your homework should include a one-page, C-language-style comment at
the beginning of your program that explains your approach and how to
test your program.