Tower Bloxx Download
Juliana Ellerbe
There is a game called "Tower Bloxx" recently released on xbox. One part of the game is to place different colored towers on a field in a most optimal way in order to maximize number of most valuable towers. I wrote an algorithm that would determine the most efficient tower placement but it is not very efficient and pretty much just brute forcing all possible combinations. For 4x4 field with 4 tower types it solves it in about 1 hr, 5 tower types would take about 40 hours which is too much.
Here are the rules:There are 5 types of towers that could be placed on a field. There are several types of fields, the easiest one is just 4x4 matrix, others fields have some "blanks" where you can't build. Your aim is to put as many the most valuable towers on a field as possible to maximize total tower value on a field (lets assume that all towers are built at once, there is no turns).
Which means that for example green tower should have at least 1 red and 1 blue towers at either north, south, west or east neighbor cells (diagonals don't count). White tower should be surrounded with all other colors.
After adding more illegal states (yellow cannot be built in the corners, white cannot be built in corners and on the edges, field should contain at least one tower of each type), realizing that only 1 white tower could be possibly built on 4x4 field and optimizing java code the total time was brought down from 40 to 16 hours. Maybe threading would bring it down to 10 hrs but that's probably brute forcing limit.
My algorithm works by starting with an "empty" board. It places each possible color of tower in the first empty slot and in each case (each color) then recursively calls itself. The recursed calls try each color in the second slot, recursing again, until the board is full.
As each tower is placed, I check the just-placed tower and all of it's neighbors to verify that they're obeying the rules, treating any empty neighbors as wild cards. So if a white tower has four empty neighbors, I consider it valid. If a placement is invalid, I do not recurse on that placement, effectively pruning the entire tree of possibilities under it.
My first approach was to estimate the upper bound of a partially-filled board by assuming every empty cell is filled with a white tower. I then modified the 'solution' function to track the best score seen and to ignore any board whose upper bound is less than than that best score.
That helped some, reducing a 4x4x5 board from 23s to 15s. To improve it further, I modified the upper bound function to assume that each Empty is filled with the best tower possible, consistent with the existing non-empty cell contents. That helped a great deal, reducing the 4x4x5 time to 2s.
One easy way to improve the brute force method is to explore only legal states. For example, if you are trying all possible states, you will be testing many states where the top right corner is a white tower. All of these states will be illegal. It doesn't make sense to generate and test all of those states. So you want to generate your states one block at a time, and only go deeper into the tree when you are actually at a potentially valid state. This will cut down your search tree by many orders of magnitude.
It seems like a good approach would be to start with a white tower and then build a set of towers around it based on the requirements, trying to find the smallest possible colored set of shapes which can act as interlocking tiles.
Linear programming, for this kind of problem, essentially amounts to having a lot of variables (for example, the number of red towers present in cell (M, N)) and relationships among the variables (for example, the number of white towers in cell (M, N) must be less than or equal to the number of towers of the non-white color that has the smallest such number, among all its neighbors). It's kind of a pain to write up a linear program, but if you want a solution that runs in seconds, it's probably your best bet.
This skyscraper construction game tests your balancing skills as you try to build the biggest towers you can. You do this simply by tapping the screen to drop a block that's hanging from a crane. You'll need to drop this block as close to the center of the top level of the building underneath to keep your tower as straight as possible, or you'll end up in all sorts of trouble as the whole structure swings from side to side the more unbalanced it becomes.
This free version of Tower Bloxx Deluxe 3D consists of three different game modes, all based around this same concept. In the first, 'Build City' mode you need to create your own virtual city using different types of building blocks to make different styles of towers. The bigger the towers are that you build, the higher the population your city will be.
'Quick Game' is the second game option in Tower Bloxx Deluxe 3D, where the object is just to build a 50-story apartment block that reaches Space. The other game mode is the insanely fun 'Party Game', where you race a friend in split-screen mode to see who can build the highest tower in the quickest time.
A combo system lets you rack up a high score by dropping pieces at the dead center of the block below. Tower Bloxx isn't too strict with its physics, allowing you to build a wavy tower that would never stand in the real world. The more lopsided your building is, however, the more it will sway in the wind as you gain height. A moving tower is a tough target for a swinging crane.
Use a metronome. I never managed to put the pretty roof on the red towers, so I went to , set it to 2 beats per cycle at 46 beats per minute and voila, the second try got me a 13x combo and a shiny golden roof for my new favourite building. I'm not sure this qualifies as cheating, but then again I'm not sure I care.
Interesting and fun game. :) The tactical aspect keeps you thinking to prevent wasting a lot of time on towers you won't need later on, and the unlockables make building previous towers more interesting again too, while also encouraging more precise building.
Fire the floors out every time the crane passes over the tower (in either swing direction), rather than waiting for the best shot or waiting for the swing to reset. The more floors you get on during the bonus peroid, the more points you get.
So, using regular old MS Paint and some ingenuity, I've come up with two different ways of making the same pattern of 13 yellow towers and 4 each of the other 4 towers, which makes me thing that that's the optimal city. I'm slowly playing through trying to actually build the city that way and it's working okay so far.
The two plans I came up with have the same arrangement of yellow towers, but the 4 blue, 4 red, and 4 green towers were in different places between the two plans. Interestingly, the plans were symmetric in the same ways, and there was a noticeable pattern of the colors, which is why I think it's the optimal layout.
Careful, guys. Your "optimal" plans require you to destroy towers that other towers are dependent on. So that may hamper you in the long run. For example, if you have greens in the corners and are now bounded by two yellows, and you unlock the special green roof, you're going to have to demolish those two yellows and insert a red and a blue tower in their place before you can replace the regular-roofed green tower in the corner with your special-roofed green tower.
It got me 11th place when I finished it, but now it's in 13 and I'm rebuilding almost all of the buildings to try to get higher. My highest combo was 23 on a yellow building, which gave a +1467 bonus (the tower ended up with 1964 people). Not as good as some other people's here.
I don't keep a yellow tower unless i get 1700+ citizens in it, but i got several 2k yellows, and i managed to do a 26combo with 2500 citizens, which is my record. I guess this city is gonna hit aprox 35k+ citizens, im gonna post the layout soon.
Case B:
Then tower X is blue and since X was the last tower placed, there remains a blue tower on the board.
Case R, G, Y:
Then one of tower X's neighbors is blue, and since X was the last tower placed, there remains a blue tower on the board.
I unlocked the towers but how do I use them!by the way!if you want a real cheat in the corner when you build a tower before putting it where you want it says how many guys live there and put it over annother tower and its population will be at the bottom number in the corner!remember that its the top right corner!
found out how to make speacial roofs happen! do your towers perfect man! well not perfect but like really strait like one straight and another straight right after and keep that up! they let one miss slip but not two!
i think this is a very good and i got addicted to this as soon as i put down the first block!although i havent even managed to put a normal roof on a yellow tower i still play this games after school.
I'm playing TB3D on the iPhone, and I'm stumped as to how to unlock the "Keys to the City." I have #1 rated buildings in every slot in every town, generally with much higher than the minimum tower population required for a #1 rating. All 3 cities are down to 1 blue tower, with 9 yellows in Seller's Market and 10 in Richmond Business. My populations are:
BUT, I can't find out what the box in the upper left shows. It has a tower with "XX/20" and two people there. I would assume the goal of the game is to get this number to be "20/20" but what is it then? Any clues?
Here is a way to get 13y, 4g, 6r, 1b building 42 towers in all (assuming you build them all perfect first time). As noted above, it means you have limited options later in the game so other layouts may let you get higher scores as your skill improves. I used this on the Nokia phone version.
Thinking over the weekend about the best you can do with all towers rebuildable to improve your score while you practise I came up with this. It won't beat high scores possible with the other layout but is OK if you don't want to got to all the trouble of starting again and having to build at least 42 towers improve your personal best.
760c119bf3