# Naive Rainbow Baseball

Today, the buggles decided to play a baseball game, but they are rather out of luck, actually. First, kinda forgot the rules, and ... well ... they cannot find the ball and bats again. So they decided to "adapt a bit" the rules. As the are no ball, the buggles can only running around the field, what they do happily: for a while, all attending buggle run at full speed in all directions around the field.

But after a few collisions, they decide to invent new rules to organize a bit the game: They make one team per base and two players per team. One of the teams has only one player so that its base has an empty location. Then, the players are dispatched randomly around the bases, and the game for them is to reach their home base. The whole game stops when all players are home. There is no winning team: either all players win, or they all lose. Actually, this game is very different from the original baseball. The only rule that remains is that you can only run around the field, from one base to the next one, without crossing middle of the field.

Now, they are asking you to help them deciding who and when should move so that each player returns to its base. Only one buggle can move at each round, from its position to the empty spot. The maximal distance that a buggle can cover in one round is of one base.

So, at each round, the empty spot is on one base (say `B`), and you should decide which buggle enters that empty spot. There is four candidates (two from base `B-1` and two from base `B+1`). Actually, there is a fifth candidate since the buggle that is on the same base than the empty spot can change its position, but that's not really helping.

### The Naïve algorithm

In this exercise, we will first explore a very simple algorithm. To decide which of the four candidate buggles should enter the empty spot, we first restrict ourselves and decide that buggles can only turn clockwise. Then, from the two remaining candidates, we pick the one that has the largest distance to cover to reach its base (turning clockwise). Click on the demo button: this works rather well in practice.

It's hard to find a simpler algorithm for this problem: While it's not sorted, search for the base containing the candidate buggles: if the hole is in base `B`, it's the base `B+1`, modulo the amount of bases. Then, compute the distance that each buggle of that base still has to run to reach its base (0 if it's already home). Once you found the buggle that should enter the empty spot, just use the `move` method on it, and iterate.

The main difficulty should be to get the few equations right: determining the base next to the hole should be easy, but determining the distance that a player has to cover may reveal a bit more challenging. Don't hesitate to draw pictures on a paper to cover all possible cases. It should not be that difficult either: there is not that many cases after all.