In a tournament chart from the bottom to the top where there is a winner I've been told that it is somehow connected with the gray-code. I know that the grey code is an alternative code, it's recursive and is useful to find the best solution in various games, space-filling-curves, error correction codes, harddisk positioning and is a shorthand for the piano player but how is this code is related with a tournament chart?
Parsed the following from here:
A tournament is really a node in a binary tree. The value in each
node contains the ranking of the best ranking team contained in the
tournament tree. It turns out that the gray code of the ranking-1 has
a bit pattern that conveniently helps us descend the binary tree to
the appropriate place at which to put the team. When descending the
three, the bits in the gray code of the ranking from least-significant
to most-significant indicate which branch to take.
Related
I was asked the following question in an interview
You are given a 4 X 4 grid. Some locations on the grid contain
treasure. Your task is the visit all the locations that contain the
treasure and collect it. You are allowed to move on the four adjacent
cells (up, down, left, right). Each movement and the action of
"treasure collection" is of a single unit cost. You need to traverse
the entire grid, and collect all the treasure on the grid, minimizing
the cost taken.
If I can recall properly, here is a sample graph that was given:
U..X
..X.
X..X
..X.
Where, U is my current position and X marks the position of the treasure.
The solution that I presented was to use breadth first search traversing the graph and "collecting the treasure" while doing so. However, the interviewer insisted that there was a better way to minimize the cost. I hope you could help me in figuring it out.
You should have recognized that this is a Traveling Salesman Problem in a small disguise. Using breadth-first, you can determine the shortest way between the different vertices you have to visit which gives you a derived graph containing just those ways as weighted edges between the vertices. From then on, it's a classic TSP.
BFS alone is not going to solve it for you, because you cannot move in all directions at the same time. It is not a single-source shortest path problem, because once you collect the treasure, you start your path to the next one from your current spot, not from the original spot.
The time that it takes to collect all treasure depends on the order in which you visit the boxes with X. Since there are only five of them, you can try all 120 orderings, compute the cost, and pick the best one.
Note that if the order is fixed, the solution is trivial: you add up manhattan distances between the cells in order, and pick the smallest result.
I have data which is related to movement of players in a game. Each player reports back the distance, speed, current coords and a TimeStamp.
This game may have 1/2k players playing at any given moment in time, so plotting this on a may would just be blurry... I was wondering what useful (if any) data can be extracted and visualized from this data? I attempted to create a line graph of average speed and running total of movement (two different graphs), but these don't seem to be what the user wants. The user isn't sure what they want, but they "know" that a line graph is the wrong way to go!
Any information you could give me on what data might be useful to extract or how best this data could be visualized would be greatly appreciated!
There are a TON of options I think. I am not a data-visualization expert but it sounds basically like the players could be shown separately, all at once, totaled, averaged, etc. And then their actual stats (distance, velocity, duration, time, location) can be shown individually or in relation/proportion to each other (totaled, averaged, you know). That would probably produce a large number of possible perspectives right there? And then you would have options for how to visually present these perspectives. Plain text, icons/colors, graphs/contours 1D, 2D, 3D. Do you see what I mean?
What are some path finding algorithms used in games of all types? (Of all types where characters move, anyway) Is Dijkstra's ever used? I'm not really looking to code anything; just doing some research, though if you paste pseudocode or something, that would be fine (I can understand Java and C++).
I know A* is like THE algorithm to use in 2D games. That's great and all, but what about 2D games that are not grid-based? Things like Age of Empires, or Link's Awakening. There aren't distinct square spaces to navigate to, so what do they do?
What do 3D games do? I've read this thingy http://www.ai-blog.net/archives/000152.html, which I hear is a great authority on the subject, but it doesn't really explain HOW, once the meshes are set, the path finding is done. IF A* is what they use, then how is something like that done in a 3D environment? And how exactly do the splines work for rounding corners?
Dijkstra's algorithm calculates the shortest path to all nodes in a graph that are reachable from the starting position. For your average modern game, that would be both unnecessary and incredibly expensive.
You make a distinction between 2D and 3D, but it's worth noting that for any graph-based algorithm, the number of dimensions of your search space doesn't make a difference. The web page you linked to discusses waypoint graphs and navigation meshes; both are graph-based and could in principle work in any number of dimensions. Although there are no "distinct square spaces to move to", there are discrete "slots" in the space that the AI can move to and which have been carefully layed out by the game designers.
Concluding, A* is actually THE algorithm to use in 3D games just as much as in 2D games. Let's see how A* works:
At the start, you know the coordinates of your current position and
your target position. You make an optimistic estimate of the
distance to your destination, for example the length of the straight
line between the start position and the target.
Consider the adjacent nodes in the graph. If one of them is your
target (or contains it, in case of a navigation mesh), you're done.
For each adjacent node (in the case of a navigation mesh, this could
be the geometric center of the polygon or some other kind of
midpoint), estimate the associated cost of traveling along there as the
sum of two measures: the length of the path you'd have traveled so
far, and another optimistic estimate of the distance that would still
have to be covered.
Sort your options from the previous step by their estimated cost
together with all options that you've considered before, and pick
the option with the lowest estimated cost. Repeat from step 2.
There are some details I haven't discussed here, but this should be enough to see how A* is basically independent of the number of dimensions of your space. You should also be able to see why this works for continous spaces.
There are some closely related algorithms that deal with certain problems in the standard A* search. For example recursive best-first search (RBFS) and simplified memory-bounded A* (SMA*) require less memory, while learning real-time A* (LRTA*) allows the agent to move before a full path has been computed. I don't know whether these algorithms are actually used in current games.
As for the rounding of corners, this can be done either with distance lines (where corners are replaced by circular arcs), or with any kind of spline function for full-path smoothing.
In addition, algorithms are possible that rely on a gradient over the search space (where each point in space is associated with a value), rather than a graph. These are probably not applied in most games because they take more time and memory, but might be interesting to know about anyway. Examples include various hill-climbing algorithms (which are real-time by default) and potential field methods.
Methods to procedurally obtain a graph from a continuous space exist as well, for example cell decomposition, Voronoi skeletonization and probabilistic roadmap skeletonization. The former would produce something compatible with a navigation mesh (though it might be hard to make it equally efficient as a hand-crafted navigation mesh) while the latter two produce results that will be more like waypoint graphs. All of these, as well as potential field methods and A* search, are relevant to robotics.
Sources:
Artificial Intelligence: A Modern Approach, 2nd edition
Introduction to The Design and Analysis of Algorithms, 2nd edition
Input:
I have created and filled an array/table in velocity. This array currently contains 3 things:
(note that this example is pure fiction)
Top level community name (e.g. Stack Overflow USA, Stack Overflow BEL)
Subcommunity (e.g. stackOverflow.com/r/USA/CSS and stackOverflow.com/r/BEL/JSON)
Owner(s) of the subcommunity (e.g. Frank)
Depending on the situation and the point in time, the amount of top level communities, that have a variable number of subcommunities are each owned by a variable number of owners. And, each top level community can also have one or more owners.
(input) table example:
SO USA, , Phil
SO USA, CSS, Frank
SO USA, JSON, Marc
SO BEL, CSS, Marieke
SO BEL, CSS, Francis
SO BEL, JSON, Patrick
SO FRA, , Francois
output:
I now want to position these communities and sub communities graphically on a webpage like this
Depending on the amount of subcommunities, the top level community will have a different size, and should therefore be parsed where it fits best on the page (e.g on a 600pxx800px canvas).
Here are my questions:
does somebody know code that has already been written to solve this kind of problem?
if not, how would I best tackle this?
I work for game development company which makes casual games. One of the main casual genres is match-3: there is a field and chips of different colors. One should move chips so that they make lines of at least three chips of the same color. If the move leads to making a line the chips in the line disappear.
Chips on field can be located differently: there may be a lot of chips of the same color gouped in one place or there may be a situation when a player can't make a move - all the neighbour chips are of the different colors.
So, I want to express the situation on the field mathematically with a factor of order (disorder). If the factor is high a player can make a lot of matches and the lines made by the player are long. If the factor is low, the field is in complete disorder and one can't make a single match. This may be helpful for generating field of different difficulty.
The question is: what branch of math can help me to do this. Where should I start my research. Any suggestions for keywords to google?
Thanks in advace.
Entropy.
I would look into graph theory. You can for example make a graph, where nodes would be positions on the board, and two nodes would be connected with an edge if they are neighbours and have a chip of the same color. If you have large components with nodes of large degree, you have less disorder. If all your components are small, you have high disorder.
First thing that comes to mind is that you're looking at the distribution of n populations (one for each color), which I would approach with Poisson sampling,. You can use that to calculate the probability of finding two adjacent units of the same population (color), which will give you a measure of the difficulty of your puzzle.