Mathematica Random Integer Function - wolfram-mathematica

Is there any way to use the RandomInteger function in Mathematica such that once an integer has been drawn, it cannot be drawn again. For example, I am looking to use the RandomInteger to draw 12 integers, between 1 & 12, such that each number is only drawn once. Thanks.

When applied to a list, RandomSample produces a random permutation.
RandomSample#Range[12]

Related

Fastest way to find a 3X3 square of intigers in a string

I have a string with the length of 480000 , it represents a 800x600 frame.
meaning 600 rows and 800 columns. i need to find a square of 3X3 were all the 9 values are in a specific range. i have the range itself. and return the index of the middle.
this is what i am doing right now:
# find 3x3 minValue < square < maxVlaue
for row in range(598):
for col in range(798):
if checkRow(frame,row,col,minValue,maxValue):
if checkRow(frame,row+1,col,minValue,maxValue):
if checkRow(frame,row+2,col,minValue,maxValue):
string = str(row+1),str(col+1)
print string
return
def checkRow(Frame,row,col,minValue,maxValue):
if (Frame[row*800+col])>minValue) and (Frame[row*800+col])<maxValue):
if (Frame[row*800+col+1])>minValue) and (Frame[row*800+col+1])<maxValue):
if (Frame[row*800+col+2])>minValue) and (Frame[row*800+col+2])<maxValue):
return True
return False
this way i check each "pixel" until the square is found.
is there some kind of special function in python for this job?
or maybe a faster and more efficient algorithm?
i thought about checking a pixel every 2 columns and skipping 2 rows. this way i can make sure i wont miss the 3x3 square, but this way when i hit a pixel , i need to check 9 different options for the square itself. so i am not sure how much faster it will be.
thanks

d3.js using d3.scale.sqrt()

What does the d3.scale.sqrt() scale do? As per the documentation it is similar to d3.scale.pow().exponent(.5), so the returned scale is equivalent to the sqrt function for numbers; for example:
sqrt(0.25) returns 0.5.
so when we apply a domain similar to this:
d3.scale.sqrt().domain([1, 100]).range([10, 39])
does it signify it takes the value between 1-100 and return the sqrt function which ranges between 10-39? Could anybody clarify and provide more details on how this scale works?
The way scales work in D3 is that they map input values (defined by .domain()) to output values (defined by .range()). So
d3.scale.sqrt().domain([1, 100]).range([10, 39])
maps values from 1 to 100 to the 10 to 39 range. That is, 1 corresponds to 10 and 100 to 39. This has nothing to do with the transformation the scale applies, which only affects the distribution of values within the range. For the sqrt function, the growth is sub-linear, which means that more of the input values will fall into the latter part of the output range.

count and average certain pixels in image with MATLAB

I have one image in bmp format, with size of 512*512. I want to count the number of pixels with values more than 11 and then find the average of these pixels. Here is my code. I don't know what is the problem but the sum of pixel values is wrong and it is always 255. I tried with different images.
Could you please help me to figure it out?
A=imread('....bmp');
sum=0; count=0;
for i=1:512
for j=1:512
if (A(i,j)>=11)
sum=sum+A(i,j);
count=count+1;
end
end
end
disp('Number of pixels grater than or equal to 11')
disp(count)
disp('sum')
disp(sum)
disp('Average')
Avrg=sum/count;
disp(Avrg)
Why doesn't your code work
Difficult to tell, could you display a portion of your matrix and the size using something like
disp(A(1:10,1:10))
disp(size(A))
% possibly also the min and max...
disp(min(A(:))
disp(max(A(:))
just to be sure the format of A is as you expect - imread could have given you a 512x512x3 matrix if the image was read in color, or the image may be in the interval [0,1].
Better approach
Once you're sure that the matrix is indeed 512x512, and has values above 11, you're best off by generating a mask, i.e.
mask = A > 11;
numabove11 = sum(mask(:));
avabove11 = mean(A(mask));
Also in your code you use >= i.e. greater than or equal to, but you say 'greater than' - pick which you want and be consistent.
Explanation
So what do these 3 lines do?
Generate a logical matrix, same size as A that is true wherever A > 11, else false.
Sum the logical matrix, which means sum values that are 1 everywhere that A > 11, else 0 (boolean values are converted to floats for this summation).
Index in to matrix A using logical indexing, and take the mean of those values.
Avoid shadowing builtins
In your code you use the variable sum - this is bad practice as there is a builtin matlab function with the same name, which becomes unusable if you use a variable of the same name.
I also faced a similar problem and actually the solution lies in the fact that matlab stores A(i,j) in uint8 format whose maximum value is 255, so, just change the statement:
sum=sum+A(i,j);
to
sum=sum+double(A(i,j));
I hope this helps.

Traversing a 2D array in an angle

Generally we traverse the array by row or column but here I want to traverse it in an angle.
I will try and explain what I mean,
So lets say if the angle is 45 degree then rather than row by col it would search as (0,0) then (0,1) (1,0) then (0,2) , (1,1) ,(2,0) and so on.. .(sorry could not upload an image as I am new user and not allowed to do so, may be try and imagine/draw an array that would help get what I am trying to say)
But what will happen if the user inputs an angle like 20 degree how can we determine how to search the array.
i just wanted to know if there is any algorithm which does something similar to this? Programming language is not an issue i guess the issue is more of algoritham sort.
Any ideas would be welcome.
Please feel free to ask if I am not able to explain clearly what I am looking for.
Thanks guys.
Easy. Take an angle (let's say 45). This corresponds to a vector v=(1, 1) in your case. (This can be normalized to a unitary vector (sqrt(2)/2, sqrt(2)/2), but this is not necessary)
For every single point in your array, you have their coordinates (x, y). Simply do the scalar product of these coordinates with the vector. Let's call f(x, y) = scalarProduct((x, y), v)
Sort the values of f(x, y) and you've got the "traversing" you're looking for!
A real example.
Your matrix is 3x3
The scalar products are :
(0,0).(1,1) = 0
(0,1).(1,1) = 1
(0,2).(1,1) = 2
(1,0).(1,1) = 1
(1,1).(1,1) = 2
(1,2).(1,1) = 3
(2,0).(1,1) = 2
(2,1).(1,1) = 3
(2,2).(1,1) = 4
If you order these scalar products by ascending order, you obtain the ordering (0,0), (1,0), (1,0), (2,0), (1,1), (0,2), (2,1)...
And if you want to do it with the angle 20, replace all occurences of v=(1, 1) with v=(cos(20), sin(20))
Here's an illustration of a geometrical interpretation. The scalar products correspond to the intersections of the vector v (in red) with the blue lines.
For every starting point (the leftmost point of every row), use trigonometry to determine an ending point for the given angle. The tan(angle) is defined as (height difference / width of the array), so your height differece is tan(angle)*(witdh of the array). You only have to calculate the height difference once. If y+height difference is greater than the height of the array, just subtract the height (or use the modulo operator).
Now that you have a starting point and an ending point you could use Bresenham's Algorithm to determine the points in between: http://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm
You want to look for a space-filling-curve for example a morton curve or z-curve. If you want to subdivide the array in 4 tiles you may want to look for a hilbert curve or a moore curve.

An algorithm to solve a simple(?) array problem

For this problem speed is pretty crucial. I've drawn a nice image to explain the problem better. The algorithm needs to calculate if edges of a rectangle continue within the confines of the canvas, will the edge intersect another rectangle?
We know:
The size of the canvas
The size of each rectangle
The position of each rectangle
The faster the solution is the better! I'm pretty stuck on this one and don't really know where to start.
alt text http://www.freeimagehosting.net/uploads/8a457f2925.gif
Cheers
Just create the set of intervals for each of the X and the Y axis. Then for each new rectangle, see if there are intersecting intervals in the X or the Y axis. See here for one way of implementing the interval sets.
In your first example, the interval set on the horizontal axis would be { [0-8], [0-8], [9-10] }, and on the vertical: { [0-3], [4-6], [0-4] }
This is only a sketch, I abstracted many details here (e.g. usually one would ask an interval set/tree "which intervals overlap this one", instead of "intersect this one", but nothing not doable).
Edit
Please watch this related MIT lecture (it's a bit long, but absolutely worths it).
Even if you find simpler solutions (than implementing an augmented red-black tree), it's good to know the ideas behind these things.
Lines that are not parallel to each other are going to intersect at some point. Calculate the slopes of each line and then determine what lines they won't intersect with.
Start with that, and then let's see how to optimize it. I'm not sure how your data is represented and I can't see your image.
Using slopes is a simple equality check which probably means you can take advantage of sorting the data. In fact, you can probably just create a set of distinct slopes. You'll have to figure out how to represent the data such that the two slopes of the same rectangle are not counted as intersecting.
EDIT: Wait.. how can two rectangles whose edges go to infinity not intersect? Rectangles are basically two lines that are perpendicular to each other. shouldn't that mean it always intersects with another if those lines are extended to infinity?
as long as you didn't mention the language you chose to solve the problem, i will use some kind of pseudo code
the idea is that if everything is ok, then a sorted collection of rectangle edges along one axis should be a sequence of non-overlapping intervals.
number all your rectangles, assigning them individual ids
create an empty binary tree collection (btc). this collection should have a method to insert an integer node with info btc::insert(key, value)
for all rectangles, do:
foreach rect in rects do
btc.insert(rect.top, rect.id)
btc.insert(rect.bottom, rect.id)
now iterate through the btc (this will give you a sorted order)
btc_item = btc.first()
do
id = btc_item.id
btc_item = btc.next()
if(id != btc_item.id)
then report_invalid_placement(id, btc_item.id)
btc_item = btc.next()
while btc_item is valid
5,7,8 - repeat steps 2,3,4 for rect.left and rect.right coordinates
I like this question. Here is my try to get on it:
If possible:
Create a polygon from each rectangle. Treat each edge as an line of maximum length that must be clipped. Use a clipping algorithm to check weather or not a line intersects with another. For example this one: Line Clipping
But keep in mind: If you find an intersection which is at the vertex position, its a valid one.
Here's an idea. Instead of creating each rectangle with (x, y, width, height), instantiate them with (x1, y1, x2, y2), or at least have it interpret these values given the width and height.
That way, you can check which rectangles have a similar x or y value and make sure the corresponding rectangle has the same secondary value.
Example:
The rectangles you have given have the following values:
Square 1: [0, 0, 8, 3]
Square 3: [0, 4, 8, 6]
Square 4: [9, 0, 10, 4]
First, we compare Square 1 to Square 3 (no collision):
Compare the x values
[0, 8] to [0, 8] These are exactly the same, so there's no crossover.
Compare the y values
[0, 4] to [3, 6] None of these numbers are similar, so they're not a factor
Next, we compare Square 3 to Square 4 (collision):
Compare the x values
[0, 8] to [9, 10] None of these numbers are similar, so they're not a factor
Compare the y values
[4, 6] to [0, 4] The rectangles have the number 4 in common, but 0 != 6, therefore, there is a collision
By know we know that a collision will occur, so the method will end, but lets evaluate Square 1 and Square 4 for some extra clarity.
Compare the x values
[0, 8] to [9, 10] None of these numbers are similar, so they're not a factor
Compare the y values
[0, 3] to [0, 4] The rectangles have the number 0 in common, but 3 != 4, therefore, there is a collision
Let me know if you need any extra details :)
Heh, taking the overlapping intervals answer to the extreme, you simply determine all distinct intervals along the x and y axis. For each cutting line, do an upper bound search along the axis it will cut based on the interval's starting value. If you don't find an interval or the interval does not intersect the line, then it's a valid line.
The slightly tricky part is to realize that valid cutting lines will not intersect a rectangle's bounds along an axis, so you can combine overlapping intervals into a single interval. You end up with a simple sorted array (which you fill in O(n) time) and a O(log n) search for each cutting line.

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