Numbering path
Given the intersections connected by one-way streets in a city, you are to write a program that determines the number of different routes between each intersection. A route is a sequence of one-way streets connecting two intersections.
Intersections are identified by non-negative integers. A one-way street is specified by a pair of intersections. For example, j k indicates that there is a one-way street from intersection j to intersection k. Note that two-way streets can be modeled by specifying two one-way streets: j k and k j.
Consider a city of four intersections connected by the following one-way streets:
0 1
0 2
1 2
2 3
There is one route from intersection 0 to 1, two routes from 0 to 2 (the routes are 0 → 1 → 2 and 0 → 2), two routes from 0 to 3, one route from 1 to 2, one route from 1 to 3, one route from 2 to 3, and no other routes.
It is possible for an infinite number of different routes to exist. For example if the intersections above are augmented by the street 3 2, there is still only one route from 0 to 1, but there are infinitely many different routes from 0 to 2. This is because the street from 2 to 3 and back to 2 can be repeated yielding a different sequence of streets and hence a different route. Thus the route 0 → 2 → 3 → 2 → 3 → 2 is a different route than 0 → 2 → 3 → 2.
Input
Contains a sequence of city specifications. Each specification begins with the number of one-way streets in the city. The first number describes the amount of one-way streets in the city. It is followed by one-way streets given as pairs of intersections. Each pair j k represents a one-way street from intersection j to intersection k. In all cities, intersections are numbered sequentially from 0 to the "largest" intersection. All integers in the input are separated by whitespace.
There will never be a one-way street from an intersection to itself. No city will have more than 30 intersections.
Output
A square matrix of the number of different routes from intersection j to intersection k is printed. If the matrix is denoted M, then M[j][k] is the number of different routes from intersection j to intersection k. The matrix M should be printed in row-major order, one row per line.
If there are an infinite number of different paths between two intersections -1 should be printed. DO NOT worry about justifying and aligning the output of each matrix. All entries in a row should be separated by whitespace.