Source file: | graduate.{c, cpp, java} |

Input file: | graduate.in |

A prospective CS student is investigating how many semesters it will take to graduate from a variety of different universities. Each university provides a list of required courses, their prerequisites, and when each course is offered. Given this information, determine the minimum number of semesters to graduate.

Consider the following example. A student is required to take 4
courses, mt42, cs123, cs456, and cs789. mt42 is only offered in the fall
semester and has no prerequisites. Similarly, cs123 is only offered in the
spring semester and has no prerequisites. cs456 is only offered in the
spring semester and has both cs123 and mt42 as prerequisites. Finally, cs789 is offered in both fall and
spring and has cs456 as its
only prerequisite. The shortest time to graduate is 5 semesters, by
taking mt42 in the fall, cs123 in the next spring, cs456 the following spring (since
it is not offered in the fall) and finally cs789 the following fall.

For this problem, there are only two semesters, fall and spring.
Always start counting semesters from the fall.

In addition to the fall/spring scheduling issues, there is one
slight complication. In order to keep the dormitories full, each
university limits the number of courses that can be taken in any
semester. This limit appears as part of the input data. The third
example below illustrates this issue.

Output: The output contains one line for each data set, formatted as shown in the sample output.

Example input: |
Example output: |

4 6 |
The minimum number of semesters required to graduate is 5. |

*Last modified on October 29, 2005 at 11:04 PM.*