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How did you even do it? The best I could do so far is using this QCQP
minimize 2 d r + d^2
s.t.
d >= 0
r >= 0
for each point x,y:
(x-cx)^2 + (y-cy)^2 >= r
(x-cx)^2 + (y-cy)^2 <= r+d
The point constraints work out to something like cx^2 + cy^2 - 2xcx - 2ycy - r + x^2 + y^2 >= 0 (with all the squared terms on the left, linear variables in the middle and finally some constants). The square terms are all non-negative so the matrixes that define them are positive semi-definite, so it can be solved with SDP.
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Hey im having trouble in finishing this algo:
A robot engine warms up with his trip and cooled down by a fan.
The robot required to ensure that the engine is not overheating.
Given that the temperature versus time engine is
1.2t=Tm
Temperature of the enviroment is 15=Te
Constant k=0.8
It i1s known that the rate of the cooling is define by
dT/dt = -k(T-Te)+Tm
Also known that the speed of the robot is 25m/s And the starting temparture of the engine is 35.
We need to find the Differential Equations for the road founded in the last question for Each Δt=0.1
This is the answers that i dont know how to get to.
temp is:
Time Temp[degC]
0.0 35.00
0.0 33.40
0.1 31.94
0.2 30.61
0.3 29.40
0.4 28.29
0.5 27.29
0.6 26.38
0.7 25.55
0.8 24.80
0.9 24.13
1.0 23.52
And when its getting warmer:
2.7 19.44
2.8 19.42
2.9 19.42
3.0 19.42
3.1 19.44
3.2 19.47
3.3 19.51
3.4 19.56
3.5 19.61
3.6 19.68
3.7 19.75
And the Path from the last question:
0 0
24 11
7 34
78 196
218 308
289 461
344 412
380 451
516 451
543 554
605 591
600 600
Thank you alot in advence!
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============ REPEAT QUESTION FROM C# FORUM
Hello there. We take the example of Bubble Sort Algo.
Time Complexity
Best O(n)
Worst O(n^2)
Space Complexity
Worst O(1)
Let us suppose a simple array contains 25 elements. What does above information mean and how should I visualize it?? Thanks for clearing some basics.
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An algorithm presents a method to do something which ideally works for all manner of inputs. As you know, there are lots of different sorting algorithms, but bearing in mind they are all meant to do the same thing, why so many?
It's to do with the starting condition. If a list is sorted already when you give it to a sorting algorithm, it doesn't have to do any sorting but merely determine that it is already sorted and nothing needs to be done. You can do this by making sure each item is bigger (or equal) to the last. This would be a best case scenario, but each of your N items in the list need to be checked so you end up with O(n) - this means linear performance. A list twice as long takes twice as long.
The worst possible case is when the list is sorted the wrong way around. In this case there are more items, and each item has to bubble up further so you end up with something like n * (n/2) required ops which becomes O(n*n). Each operation takes time so number of ops/time are the same thing here. Double the size and it takes 4 times as long.
In the space complexity O(1) means constant. No new space is required as the sort is contained within the datastructure.
In your case with 25 elements, best case means checking those 25 elements are in order. Worse case is bubbling each the furthest possible distance. A randomized list will be somewhere in between the extremes.
Regards,
Rob Philpott.
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Just look up the definition.
f(n) ∈ O(g(n)) iff there exists an n0 and c such that for all n > n0, f(n) < c g(n)
This quite technical definition means the whole big O deal is really a statement about membership of a function in some set of functions that, informally, all "grow about the same". But they only have to start growing about the same after some point n0 (which you don't know) and an arbitrary constant is hidden.
For time complexity that function we make statements about is the function that counts how many "elementary operations" some algorithm takes a function of the size of its input. In order to do that, one must agree about what kind of operations are elementary. There are several models for that, the "usual one" has the at first sight odd property that mathematical operations on integers of size O(log n) run in constant time. This is necessary to prevent the following problem: suppose you could only do operations on constant-length integers in constant time, and you want to manipulate an index into an array. That array has length n, so the index must have size (you guessed it) log n. It would therefore take non-constant space to even just have an index, and non-constant time to do anything with an index, which usually no one wants.
It should be clear from the n0 that big O notation explicitly says nothing about the behaviour of the function at any particular constant. It also says nothing about what happens when you double that constant, a mistake that is commonly made, leading to questions such as "it took x milliseconds for an input of size 10, how long will it take for an input of size 20" - you cannot know based on some big O.
Django_Untaken wrote: Let us suppose a simple array contains 25 elements
So it should be clear by now that you can't say much about that situation. Bubble sort (and literally anything else) is going to take some constant number of elementary operations (aka "time") on that input, because there is no variable to vary. You cannot compute the number of operations based on the big O (but based on detailed knowledge of the algorithm, you can).
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Django_Untaken wrote: Let us suppose a simple array contains 25 elements. What does above information mean and how should I visualize it??
Nothing ! it don't work that way.
Say that you just measured runtime it takes for 25 elements for best case and worst case.
The Big O notation allow you to evaluate what it takes for 250 elements or 2500 elements.
Best case is O(n) means that 10 times the data will take 10 time the runtime and 100 times the data will take 100 time the runtime.
Worst case is O(n^2) means that 10 times the data will take 100 time the runtime and 100 times the data will take 10000 time the runtime.
See these links:
Big O notation - Wikipedia, the free encyclopedia[^]
Analysis of algorithms - Wikipedia, the free encyclopedia[^]
Patrice
“Everything should be made as simple as possible, but no simpler.” Albert Einstein
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ppolymorphe wrote: Best case is O(n)
Surely the best case would be O(1)? 
And both O(log n) and O(log log n) would be better than O(n).
"These people looked deep within my soul and assigned me a number based on the order in which I joined."
- Homer
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Richard Deeming wrote: Surely the best case would be O(1)?
And both O(log n) and O(log log n) would be better than O(n).
Sure, but not for bubble sort.
But Bubble Sort best case is O(n).
Patrice
“Everything should be made as simple as possible, but no simpler.” Albert Einstein
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I have this Insertion Sort algorithm analysis:
[^]
And here is the function in best and worst case scenarios
http://s32.postimg.org/gjgb7n5s5/Untitled2.png[^]
My question would be, how did they get these functions? What is a, what is b? Why in the worst case scenario a is powered by two?
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'a' and 'b' are the standard names of the constants used in the standard representation of a linear function.
Linear Functions[^]
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I am currently working on a procedurally generated game, and vaguely remember having read a book/paper/article in which it was said that there exists a published algorithm which can generate high quality game board games with a random set of rules, which are as good as human designed game board games. The algorithm was NOT limited to a single game such as Sudoku or Crossword puzzles, it rather would generate a set of rules for the players to play by, so it could potentially generate tic tac toe, checkers or 4 in-a-row wins and variations of all 3 games.
I think the article was published between 1980's and 2006ish
and that it was published in a journal.
Sadly I cannot remember where I read the article, only that it must've been in the last 8 months. If you know about this algorithm or something similar to it, please post.
Thanks a bundle,
Mark io
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Hi i have this Algorithm, could anyone help me figure out the answer to it, and how?
Create a recurrence function to represent the following algorithm's time complexity and use the master method to analyse the following algorithm:
/* The function f(x) is unimodal over the range [min, max] and can be evaluated in Θ(1) time
* ε > 0 is the precision of the algorithm, typically ε is very small
* max > min
* n = (max - min)/ε, n > 0, where n is the problem size */
Algorithm(max, min)
{
if ((max - min) < ε)
{
return (max - min)/2 // return the answer
}
leftThird = (2 * min + max) / 3 // represents the point which is 1/3 of the way from min to max
rightThird = (min + 2 * max) / 3 // represents the point which is 2/3 of the way from min to max
if (f(leftThird) < f(rightThird))
{
return Algorithm(leftThird, max) // look for the answer in the interval between leftThird and max
}
else
{
return Algorithm(min, rightThird) // look for the answer in the interval between min and rightThird
}
}
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Your homework is set to test what you know, not how good you are at convincing strangers to do your work for you!
The questions will be based on the material you have covered in your course. If you really don't know where to start, then you need to talk to your teacher.
"These people looked deep within my soul and assigned me a number based on the order in which I joined."
- Homer
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This is your HomeWork. You are the one that have to work, not us.
Patrice
“Everything should be made as simple as possible, but no simpler.” Albert Einstein
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If you are familiar with idle game or incremental games like Adventure Capitalist or Clicker Heroes you know that after a while you are dealing with very large numbers. If you are not aware basically you earn points in these games which you invest so that you can earn more points even quicker, rinse and repeat.
I wrote a small game of this style myself but didn't leave the range that a double couldn't handle but it did get me thinking on how to deal with extraordinarily large numbers.
Just to play around I figured a quick and easy way was to just keep a list with ints, each index represents a higher power and you can easily go higher if needed. index zero keeps numbers between 0-999 and index 1 then starts at 10^3. So index 5 would be ^7 etc.
Except for numbers 0-999 if you want to increase the number I have a function where you specify what number 1-9 you want to add and to which power. If you add say 9^5 to 3^5 it sorts this out by becoming 2^5 and 1^6.
So far I haven't accounted for subtraction yet in my little project but that should be fairly easy in a similar manner.
I think this shouldn't be too computationally heavy unless if used to run addition between several large lists.
Should I want to use this in a game I think it could also be easily adapted to use some approximation to reduce unnecessary work. For example if you have an entity in the game which adds 10^15 points per second and one that adds 10^3 and you show 5 decimals instead of doing all the background computations of adding those smaller numbers every second you just approximate how many seconds before they add as much so that it shows and then go from there if I made myself clear.
public void AddNumber(int value, int power)
{
if (power == 0)
{
NumberContainer[0] += value;
while (NumberContainer[0] >= 1000)
{
NumberContainer[0] -= 1000;
AddNumber(1, 1);
}
} else if(power < mPower)
{
NumberContainer[power] += value;
while( NumberContainer[power] >= 10)
{
NumberContainer[power] -= 10;
AddNumber(1, power + 1);
}
}else
{
}
}
public static NumberControl operator +(NumberControl c1, NumberControl c2)
{
int mMaxp = c1.mPower;
if (c2.mPower > mMaxp) mMaxp = c2.mPower;
NumberControl nc = new NumberControl(mMaxp);
for(int i = 0;i < c1.NumberContainer.Count;i++)
{
nc.AddNumber(c1.NumberContainer[i], i);
}
for (int i = 0; i < c2.NumberContainer.Count; i++)
{
nc.AddNumber(c2.NumberContainer[i], i);
}
return nc;
}
Here is how I add numbers. Thinking about this really got me wondering about how others would choose to solve it instead.
Number container is just a list<int>.
I'm planning on profile how well it handles a few different scenarios, for example if you have a list that goes to the power of 100 and have say 80 "generators" which adds a number at different power levels each second how will it will hold out compared to if I approximate those that are smaller than a certain range from the biggest number.
Reading the numbers is done by specifying how many decimals I want shown and then just walk backwards in the list and adding to a string so unless I want full precision it also works fairly well.
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This forum is for asking questions. What you've got there looks more like a Tip.
Submit a new Article - CodeProject[^]
You might also want to see how your code compares to the built-in BigInteger structure[^].
Eric Lippert did a series of blog posts[^] covering how you could implement integer operations without using the built-in number types, which is also worth a read.
"These people looked deep within my soul and assigned me a number based on the order in which I joined."
- Homer
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Maybe but then it would need a bit more polish and I'm not sure it would fit, maybe a small blog post and carry with it some test results and discussion around it.
When I started thinking about how to solve this I had a nagging suspicion that there already was something readily available but I couldn't figure out what search terms to use to find it so I turned it in to code instead. That blog post was interesting I admire how some people can go so in-depth in a subject.
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Member 11683251 wrote: Thinking about this really got me wondering about how others would choose to solve it instead.
My solution here[^].
Not the most efficient way
Bastard Programmer from Hell 
If you can't read my code, try converting it here[^]
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It may be a good idea to create a struct or class I'll call it LN which has a private vector with intergers VEC in the range of 0 to 9. The class has functions for Algebraic operations (+,-,*,/) to add two LN together. These functions must:
- determine the sizes of both VEC and resize accordingly.
- iterate though both VEC and execute the operation digit by digit.
Since vectors are dynamically allocated, you have virtually no cap on how many digits the number has (accept for RAM).
You'll have to replace all score related constant values in your code with LN's
I'm not sure how your game mechanics are designed, but if you have many hundreds of entities which add some constant value per second, it might be a good idea to have a single variable X which is added to the game score S every second, instead of iterating through all entities and adding the constant value to S. That is, when an entity is created, it adds it value per second constant E to X and when the entity is destroyed it subtracts E from X.
In every game step you then add X to S. This therefore only requires a single addition operation per game step and of course an addition operation when creating or destroying an entity.
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Concerning the situation that might arise if you have hundreds of entities I figured that I could just do some approximations. The most important parts would be those entities that's closest to the current largest number in the bank so to speak.
If you have one entity that adds say 10^70 you it I could just go over everything below say 10^60 to calculate what to add per second for all those entities instead of doing 60 different calculations.
So far I'm not working on creating a game but this kinda grew from curiosity but I did some testing and 100 different entities, one for each level up to 10^100 was just a few ms. No graphics or anything else but even if I kept increasing it would be a while before there would be a performance hit. For a mobile app it might me more important but my home computer doesn't have a high end cpu so I was quite happy with the current performance.
There is a game called clicker heroes and the highest I ever came in that game was in the span of 10^130.
There are so many of these games out there and they mainly target mobile with in game purchases which costs exorbitant amounts of money. While I see the allure of these games where the amount of in game points you accumulate while you are idle and can just pop in every once in a while to spend and increase the gathering rate I find it hard to comprehend how people can justify dropping 100$ > for in game credits.
I'll see if I make an implementation of your suggestion of vectors if I got the time but it's always interesting to compare different solutions. If I do I'll make a comparison with one of the string based methods too.
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It sounds like you need arbitrary-precision numbers.
With C-1999 or C++2011, you are guaranteed to have a 64-bit built-in type. If you limit yourself to "digits" containing 9 decimal digits (they fit into 32 bits), you can perform the four basic arithmetic operations with "digits" that are easily converted to decimal notation.
The following article (printed in Dr. Dobb's Journal in August 1992; includes source code) should get you started: Multiple-Precision Arithmetic in C | Dr Dobb's[^]
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack.
--Winston Churchill
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