**Assigned**: Tuesday, January 20, 1998

**Due**: Thursday, January 22, 1998

**Turn in problems 1, 3, and 5**.

**Summary**. In this assignment, you will be working on a few
problems related to computing values based on a table and on writing descriptions
of the processes by which someone else might solve similar problems.

**Intent**. This assignment is intended to give you some
experience thinking about and writing up *algorithms*, formal sets
of instructions for completing tasks.

**Note**. Some of these are fairly difficult problems. Work
hard on them, but don't be disappointed if you can't get a "perfect" answer
(or even a correct answer).

For the first few parts of this assignment, you will be computing the costs of flying between cities. For those computations, you should use the following completely fictitious table of costs. Starting cities run along the left column, destinations along the top. For example, according to this table, it costs $150 to fly directly from Boston to Des Moines.

BOS | NYC | ORD | DSM | CIN | LAX | |
---|---|---|---|---|---|---|

Boston (BOS) | X | 10 | 30 | 150 | 50 | 1000 |

New York (NYC) | 5 | X | 15 | 400 | 50 | 400 |

Chicago (ORD) | 25 | 10 | X | 300 | 20 | 600 |

Des Moines (DSM) | 50 | 50 | 50 | X | 50 | 200 |

Cincinnati (CIN) | 200 | 75 | 100 | 150 | X | 500 |

Los Angeles (LAX) | 600 | 800 | 300 | 500 | 200 | X |

**1. Cheapest Flights**. Suppose Sarah and Steven Starr need to fly
from Boston to Los Angeles and that their funds are relatively tight. What is the
cheapest way to get from Boston to Los Angeles?

**2. Cheapest Tour**. Suppose Peter and Penelope Prospective live
in Boston and would like to visit schools in NY, Chicago, Des Moines, Cincinatti,
and LA (and return home). They don't care which order they visit the cities.
What is the cheapest *tour* that starts in Boston, ends in Boston, and
includes all of the other cities, and visits each city exactly one (e.g., no
one wants to go through O'Hare more than once).

Unfortunately (or fortunately, as the case may be), airlines change their rates frequently. Hence, a solution you work out today may not work the next day. For these questions, you need to think about more general solutions.

**3. Cheapest Flights, Revisited**. Suppose the airlines have
published a table of costs of flying between cities (similar to my table above).
Sarah and Steven Starr need to fly from city X (one of the cities, but you don't
know which one) to city Y (one of the cities, but you don't know which one) and
want the cheapest possible series of flights. How could they figure out which
is the cheapest?

**4. Cheapest Tour, Revisited**. Suppose the airlines have published
a table of costs of flying between cities (similar to my table above). Peter and
Penelope Prospective want to visit all the cities, beginning and ending at city
X. How might they determine the cheapest series of flights that visits all cities
exactly once?

As you may have noted for problems three and four above, sometimes problem solving involves writing down instructions. Sometimes, instructions will be very precise. Sometimes, they can be more general. Many tasks require instructions. For this problem, you'll consider more practical tasks.

**5. Freshling Instructions**
Suppose Grinnell were to compile a list of "How to XXX" for new students and
hired you to work on it. For your first assignment, you are to pick two tasks
that you think new students should know about (e.g., registering, picking a
tutorial, choosing their first classes, escaping campus) and write up clear
instructions that "anyone" (even a faculty member) could understand.

**Disclaimer** Often, these pages were created "on the fly" with little, if any, proofreading. Any or all of the information on the pages may be incorrect. Please contact me if you notice errors.

Source text last modified Tue Jan 20 16:42:10 1998.

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