One can manually count path lengths in a graph using adjacency matrices. Using the simple example below, produces the following adjacency matrix: A B A 1 1 B 1 0 This matrix means that given two vertices A and B in the graph above, there is a connection from A back to itself, and a two-way connection from A to B. To count the number of paths of length one, or direct connections in the graph, all one must do is count the number of 1s in the graph, three in this case, represented in letter notation as AA, AB, and BA. AA means that the connection starts and ends at A, AB means it starts at A and ends at B, and so on. However, counting the number of two-hop paths is a little more involved. The possibilities are AAA, ABA, and BAB, AAB, and BAA, making a total of five 2-hop paths. The 3-hop paths starting from A would be AAAA, AAAB, AABA, ABAA, and ABAB. Starting from B, the 3-hop paths are BAAA, BAAB, and BABA. Altogether, that would be eight 3-hop paths within this graph. Write a program taking any graph with at least two, but no more than five vertices, and count the number of paths of any length from 1 to 4 hops. Input from the keyboard two integers consisting of an integer N, indicating a graph with N nodes, followed by an integer P, the path length to calculate. Next, enter N strings, each of length N, containing 0s and 1s, indicating the adjacency matrix for the graph, separated by a space. Output the number of P length paths in the given matrix and the actual paths. The program must use a Graph data structure. Refer to the sample output below. Sample Run: How many nodes in the graph: 2 Path length to calculate: 1 Enter (0 or 1) the string for the adjacency matrix: 11 10 There are 3 1-length paths in the matrix: AA AB BA
One can manually count path lengths in a graph using adjacency matrices. Using the simple example
below, produces the following adjacency matrix:
A B
A 1 1
B 1 0
This matrix means that given two vertices A and B in the graph above, there is a connection from A back to
itself, and a two-way connection from A to B. To count the number of paths of length one, or direct
connections in the graph, all one must do is count the number of 1s in the graph, three in this case,
represented in letter notation as AA, AB, and BA. AA means that the connection starts and ends at A, AB
means it starts at A and ends at B, and so on. However, counting the number of two-hop paths is a little
more involved. The possibilities are AAA, ABA, and BAB, AAB, and BAA, making a total of five 2-hop paths.
The 3-hop paths starting from A would be AAAA, AAAB, AABA, ABAA, and ABAB. Starting from B, the 3-hop
paths are BAAA, BAAB, and BABA. Altogether, that would be eight 3-hop paths within this graph. Write a
program taking any graph with at least two, but no more than five vertices, and count the number of paths
of any length from 1 to 4 hops.
Input from the keyboard two integers consisting of an integer N, indicating a graph with N nodes,
followed by an integer P, the path length to calculate. Next, enter N strings, each of length N, containing 0s
and 1s, indicating the adjacency matrix for the graph, separated by a space. Output the number of P length
paths in the given matrix and the actual paths. The program must use a Graph data structure. Refer to the
sample output below.
Sample Run:
How many nodes in the graph: 2
Path length to calculate: 1
Enter (0 or 1) the string for the adjacency matrix: 11 10
There are 3 1-length paths in the matrix: AA AB BA
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