Thread: Problem with task

Hi, I have a problem with my task. I have 2-dimensional board and in the middle are 3 numbers (1,1,1) - in vertical rotation. They make one segment. The „next step” will be one distinction of that segment. It is growing in the way that to each end, added are the next numbers (one greater than the previously added) with changing rotation (vertical- horizontal -vertical etc.)
On that 2-dimensional board I put point (x,y) in some place, which in case of meeting with growing segments will stop their growth. My job is to put for giving points (x,y) if growing segments
will ever meet with the points (if yes after how many steps ),if not then I have to write never.

I think I need to look for solution in moving diagonal. For main diagonal (0x0, 1x1, 2x2 etc.) Results are next power of number 2. Every next power of the number 2 they make ,,almost squares" with dimensions (2^¡)- 1 x 2^¡. At the end of that squares ( in middle of the bigger square) (1x2,3x4,7x8 etc.)....(each smaller is a half of the bigger one )) I am able to turn in any another diagonal and in her middle I am able to turn in another one (just how many times I need), but unfortunately there are a certain shifts (resulting probably from that the ,,almost squares" are not the real squares (3x4 instead of 4x4)). I m going to show it in the examples below for better understanding. I am adding also a link to the picture of the board (32x32) and few examples correct and invalid.
Board (-1- will never meet, 0x0 in the bottom left corner): img27.imageshack.us/img27/3600/planszad.png

Example 1. (Correct)
1). Preliminary result: 8 (4x4)
2). Preliminary result: 12 (6x2)
3). Preliminary result: 10 (5x3) (half dimensional of quadrangle 4x4 6x2)
4). End result: 12 (4x2)

Example 2 (correct)
x =2 y=10
1) preliminary result: 16 (8x8)
2) preliminary result: 24 (4x12)
4) end result: 28 (2x10)

Example 3 (invalid)
X=9. Y=3 (the result is number even and is placed UNDER dimensional)
1) preliminary result: 16 (8x8)
2) preliminary result: 24 (12x4)
Preliminary result: 28 (10x2)
4) end result: 30 (9x3)

Explanation: in the end result the result should be reduced by 2 not increased but I don't know what I am doing wrong. Please help me with this task, I need to finish it till the end of the week.

P.S. Coordinates x and y they fit in interval (-100000;100000) but growing segments are ,,quarters" symmetric so in case of negative coordinates we can make them into positive (x=|x|, y=|y|). I put a link to oryginal content of the task: img51.imageshack.us/img51/462/tresc.png

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So when you say "have a problem", does this mean you've got as far as writing any code at all?

If you have code, you should post it.
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I'm afraid I don't understand what that task is from your description.

Your post of the original content says to draw line segments on a grid to simulate the development of one of the pathogens. This seems simple and straightforward. You could write a program that accepts input for a given age then draws the shape of the colony. Since the colony can only grow in one way the shape will always be the same at any given age.

You then proceed to describe a program that has nearly nothing in common with the "original" description. From the best I can gather you are giving it a set of coordinayes and seeing if line segments ever meet in that coordinate?

Still seems very unclear. What if the given coordinates are at 0,0 then it is the center (midpoint) of a singular line segment therefor not really a meeting of line segments. Would this then qualify as false? If the point 0, 1 was given does this qualify as true since the next line segment will draw rotated with this at its midpoint or are we only talking about points such as -1, 0 where two parallel line segments meet at an endpoint?

Try to be more concise in a description of the objective before telling us the logic behind what didn't work. I think you would have gotten an answer by now if it had been clear.

Seems pretty strait forward. Build the table in planszad.png, big enough to enclose all input bacteriostats, and then some. Then look up the coordinate of each bacteriostat on the table, and that'll give you the result for each trial.

Build the table in planszad.png, big enough to enclose all input bacteriostats, and then some

His description said -1,000,000 <= x <= 1,000,000.

So that would be storing 1,000,000,000,000 sets of coordinates in a map. Seems excessive.

It definitely seems like there is a simplier pattern here. Its full of symmetry and rotation.

First thing I notice is on the Y axis is it counts upward in 2s (with the exception of coordinate (0, 1)) and only the powers of 2 are in white, all other numbers are -1.

The X axis is counting upward in 2s but in odd numbers, and only the ((powers of 2)-1) are in white, all other numbers are -1.
So all valid coordinates could be represented as the number set

Where N is any whole number and the equation represents as
X Coordinate = AGE

(2^N) - 1 = (2^(N+1))-1

If you just save the picture put it a image editing program.
(change coordinate (16, 25) to white as it is improperly colored and change coordinate (2, 12) to that tanish grey color as it is also colored wrong)

Then look at the picture itself and you can see that smaller segments can be copied, pasted and then rotated to the right or the left by 90 in order to create the exact same pattern based on if you translate upward or towards the right.

Translating up seems to be a rotation to the left by 90 degrees while translating right seems to be a rotation to the right by 90 degrees.

It seems that other than the X and Y axis being a different pattern the rest of it is just a rotation of the pattern performed by (1, 1), (15, 16).

The things that concern me about the assumption is.
1. The picture's colors were wrong so logically the picture's numbers could be wrong.
2. The Pattern's reptition seems to change by powers of 2 so (32, 32) could represent a new point in the sequence with a few new "special cases" that are only relected into its larger counterparts rather than smaller.

I am guessing there is a fractal algorithym at work here, but I never managed to finish that book so I'm at a loss for spotting it yet. I do enjoy this puzzle though so I will probably keep thinking about it until a solution is presented.

Though it looks like the modulus of 16 is going to be significant.

Originally Posted by algo00

I put a link to oryginal content of the task: img51.imageshack.us/img51/462/tresc.png

o_O

Original content?
I think this is the original one: High School Programming League 2012/13 - Problem HS12BAPE

This is not the way to win a contest.

You guys are ninjas on finding this stuff.

I am slightly dissapointed I won't find the solution to this. The best I could tell it is a differential equation. I started learning trajectories and fractal complex plane graphing to see if I could solve this from that information and while I have found equations to represent each axis value individually I haven't found one to represent the entire problem.

I always love a good problem. Kinda scary to think a highschooler somewhere has already solved this.