IOI'95 Task: Street Race
Task: Street Race
Figure 1 gives an example of a course for a street race.
You see some points, labeled from 0 to N (here N=9),
and some arrows connecting them.
Point 0 is the start of the race;
point N is the finish.
The arrows represent one-way streets.
The participants of the race move from point to point via the streets,
in the direction of the arrows only.
At each point, a participant may choose any outgoing arrow.
Figure 1: A street course with 10 points
A well-formed course has the following properties:
A participant does not have to visit every point of the course
to reach the finish.
Some points, however, are unavoidable.
In the example, these are points 0, 3, 6, and 9.
Given a well-formed course,
your program has to determine
the set of unavoidable points
that all participants have to visit,
excluding start and finish (Subtask A).
- Every point in the course can be reached from the start.
- The finish can be reached from each point in the course.
- The finish has no outgoing arrows.
Suppose the race has to be held on two consecutive days.
For that purpose the course has to be split into two courses, one for each day.
On the first day, the start is at point 0,
and the finish at some `splitting point'.
On the second day, the start is at this splitting point and
the finish is at point N.
Given a well-formed course, your program has to determine
the set of splitting points (Subtask B).
A point S is a splitting point for the well-formed course C
if S differs from the start and the finish of C,
and the course can be split into two well-formed courses
that have no common arrows and that have S as only common point.
In the example, only point 3 is a splitting point.
The file INPUT.TXT describes a well-formed course with
at most 50 points and at most 100 arrows.
There are N+1 lines in the file.
The first N lines contain the endpoints of the arrows
that leave from the points 0 through N-1 respectively.
Each of these lines ends with the number -2.
The last line contains the number -1.
Your program should write two lines to the file OUTPUT.TXT.
The first line should contain
the number of unavoidable points in the input course,
followed by the labels of these points, in any order (Subtask A).
The second line should contain
the number of splitting points of the input course, followed by
the labels of all these points, in any order (Subtask B).
Example Input and Output
Figure 2 gives
possible input and output files for the example of Figure 1.
| INPUT.TXT | | OUTPUT.TXT |
| 1 2 -2 | | 2 3 6 |
| 3 -2 | | 1 3 |
| 3 -2 | |____________|
| 5 4 -2 |
| 6 4 -2 |
| 6 -2 |
| 7 8 -2 |
| 9 -2 |
| 5 9 -2 |
| -1 |
Figure 2: Example input and output