Here is the requirement: the input is a number which will divide an image into several equal part. For example, if the input is 4, it will return 3 parts: the values are the imgSize/4 imgSize/4 * 2 and imgSize/4 * 3.
If the input is n, then it will return n - 1 elements, as in the following implementation:
if (colorLevel == 8)
divide_thres = [ round(imgSize/8) round(imgSize/8)*2 round(imgSize/8)*3 round(imgSize/8)*4
round(imgSize/8)*5 round(imgSize/8)*6 round(imgSize/8)*7 ];
elseif (colorLevel == 4)
divide_thres = [ round(imgSize/4) round(imgSize/4)*2 round(imgSize/4)*3 ];
elseif (colorLevel == 3)
divide_thres = [ round(imgSize/3) round(imgSize/3)*2 ];
end
I want to allow the user to input a value between 2 and 255, and then automatically generate the divide_thres corresponding to that input. How can I re-write this code to be more efficient?
There are several problems with your code:
In each case, you unnecessarily divide imgSize by the same factor multiple times (instead of just once and for all).
You perform many "manual" scalar multiplications, but you could simply multiply the scalar value by a vector generated by the range 1 : colorLevel - 1.
Because the length of the resulting divide_thres vector can be easily computed from the value of colorLevel, there is no need to treat each case separately in an if statement.
Moreover, even if you had to compute the length in a different manner for the cases imgSize = 3, 4, and 8, you would be better off using a switch statement instead of an if statement, because the former would save you the trouble of writing imgSize == ... each time, which is prone to errors and a form of code duplication.
Here's a much simplified approach:
if 2 <= colorLevel && colorLevel <= 255
divide_thres = round(imgSize / colorLevel) * (1 : colorLevel - 1);
else
error('invalid colorLevel value') % (or some other informative message)
end
This should do it -
divide_thres = [1:colorLevel-1]*round(imgSize/colorLevel)
Related
Could someone explain to me the logic behind this hashMap algorithm? I'm getting confused about how the algorithm receives the total sum. I'm starting to learn about algorithms, so it's a little confusing for me. I made comments in my code to pinpoint each line code, but I'm not sure I'm grasping logic correctly. I'm just looking for an easier way to understand how the algorithm works to avoid confusing myself.
//**calculate Two Number Sum
func twoNumberSum(_ array: [Int], _ targetSum: Int) -> [Int] {
//1) initilize our Array to hold Integer Value: Boolean value to store value into hashTable
var numbersHashMap = [Int:Bool]()
//2) create placeHolder called number that iterates through our Array.
for number in array {
//3) variable = y - x
let match = targetSum - number
//4) ??
if let exists = numbersHashMap[match], exists {
//5) match = y / number = x
return [match, number] //
} else {
//6) Store number in HashTable and repeats
numbersHashMap[number] = true
}
}
return []
}
twoNumberSum([3,5,-4, 8, 11, 1, -1, -6], 10)
// x = Number
// y = Unknown *Solve for Y*
Sure, I can walk you through it. So we have a list of numbers, are we are trying to find two numbers that add together to make the specified target. To do this, for each number x, we check if (target - x) is in the list. If it is not, then we add x to the list. If it is, then we return x and (target - x).
Step 4 in your code is the part where we check if (target - x) is in the list. To see why this makes sense, let's walk through an example.
Say we have [2, 3, -1] and our target is 1. In this case, we first consider x = 2 and check our hashmap for (target - x) = (1 - 2) = -1. Since -1 is not in the hashmap, we add 2 to the hashmap. We then consider x = 3 and check for (1 - 3) = -2. Again, -2 is not in the hashmap, so we add it. Now we check x - -1. In this case, when we check (target - x) = (1 - (-1)) = 2, 2 is in the hashmap. Intuitively, we have already "seen" 2, and know that 2 and -1 can be added to get our value.
This is what provides the speed optimization over checking every two numbers in the list.
Let's say I want to generate a random number between 1 and 100, but I don't want to include 42. How would I do this without repeating the random method until it is not 42.
Updated for Swift 5.1
Excluding 1 value
var nums = [Int](1...100)
nums.remove(at: 42)
let random = Int(arc4random_uniform(UInt32(nums.count)))
print(nums[random])
Excluding multiple values
This extension of Range does provide a solution when you want to exclude more than 1 value.
extension ClosedRange where Element: Hashable {
func random(without excluded:[Element]) -> Element {
let valid = Set(self).subtracting(Set(excluded))
let random = Int(arc4random_uniform(UInt32(valid.count)))
return Array(valid)[random]
}
}
Example
(1...100).random(without: [40,50,60])
I believe the computation complexity of this second solution is O(n) where n is the number of elements included in the range.
The assumption here is the no more than n excluded values are provided by the caller.
appzYourLife has some great general purpose solutions, but I want to tackle the specific problem in a lightweight way.
Both of these approaches work roughly the same way: Narrow the range to the random number generator to remove the impossible answer (99 answers instead of 100), then map the result so it isn't the illegal value.
Neither approach increases the probability of an outcome relative to another outcome. That is, assuming your random number function is perfectly random the result will still be random (and no 2x chance of 43 relative to 5, for instance).
Approach 1: Addition.
Get a random number from 1 to 99. If it's greater than or equal to the number you want to avoid, add one to it.
func approach1()->Int {
var number = Int(arc4random_uniform(99)+1)
if number >= 42 {
number = number + 1
}
return number
}
As an example, trying to generate a random number from 1-5 that's not 3, take a random number from 1 to 4 and add one if it's greater than or equal to 3.
rand(1..4) produces 1, +0, = 1
rand(1..4) produces 2, +0, = 2
rand(1..4) produces 3, +1, = 4
rand(1..4) produces 4, +1, = 5
Approach 2: Avoidance.
Another simple way would be to get a number from 1 to 99. If it's exactly equal to the number you're trying to avoid, make it 100 instead.
func approach2()->Int {
var number = Int(arc4random_uniform(99)+1)
if number == 42 {
number = 100
}
return number
}
Using this algorithm and narrowing the range to 1-5 (while avoiding 3) again, we get these possible outcomes:
rand(1..4) produces 1; allowed, so Result = 1
rand(1..4) produces 2, allowed, so Result = 2
rand(1..4) produces 3; not allowed, so Result = 5
rand(1..4) produces 4, allowed, so Result = 4
i want a code to define the prompted number by user is prime or not . since it's an assignment
i'm not allowed to use ' isprime ' predefined code .
the following approach was not useful :
N = input( 'please enter a positive enteger value = ' ) ;
Quotient = floor(N - (mod(N,2)./2)) ;
for i = 1 : Quotient
if mod(N,i ) == 0
fprintf(' your prompted number is not prime ' ) ;
if mod(N,i) ~= 0
fprintf(' your prompted number is prime ' ) ;
end
end
end
for example if i enter a prime number like 13 it results in this :
your prompted number is prime
but if i enter a Non-prime num like 12 it repeats the ' your prompted number is prime ' message for 10 times .
for i = 1 : Quotient
if mod(N,i ) == 0
That will give you every number since x mod 1 is always zero. In other words, the remainder (when you divide any positive integer by one) is zero, since all of them divide perfectly.
You need to start at 2 rather than 1.
In addition, once you've found out the number is not prime, you should stop the loop since there's no possibility of it becoming prime again after that :-) And, for efficiency, you only need to go up to the square root of the number since, if it has a factor above that, you would have already found the equivalent factor below that.
The pseudo-code for such a beast would be:
set isprime to true
set chkval to 2
while chkval * chkval <= number:
if number mod chkval is zero:
set isprime to false
exit while
end if
increment chkval
end while
if isprime:
say number, " is prime"
else:
say number, " is composite"
Try to find factors and as soon as you find one you know it's not prime:
prime = true
for f = 2:ceil(sqrt(N)) %// Start from 2 as prime numbers DO have 1 as a factor. Anything larger than sqrt(N) will have to have a corresponding factor smaller than this so there is no point checking them
if mod(N,f) == 0
prime = false;
break;
end
end
There are 2 problems with your code. First, as already explained by paxdiablo, you need to start your loop from 2. Secondly you have nested your if statements, and since they are mutually exclusive conditions, the inner condition will never trigger.
for s=1:length(C_tem)
for w=1:length(C_tem{s})
if (abs(C_tem{s}{w}) >= 0)
C_tem{s}{w} = 1;
else
C_tem{s}{w} = 0;
end
end
end
I am trying to set the values larger than 0 to 1, and if less or equal to 0, but for some reason this doesn't work.
I'm new in matlab, and I really need the help if possible. Thank you in advance..
i havn't worked on matlab much but this part of code feels suspicious -
if (abs(C_tem{s}{w}) >= 0)
C_tem{s}{w} = 1;
else
C_tem{s}{w} = 0;
end
Why are you doing abs here? I think it will remove sign from number. Code should be something like this-
if (C_tem{s}{w} > 0) //I have removed abs and >= is replaced with >
C_tem{s}{w} = 1;
else
C_tem{s}{w} = 0;
end
abs(x)>=0 is true for all values of x. The simple answer is to remove the abs. The more complete answer follows up on Dan's comment. The cell array is unnecessary at the inner level. If you instead had a cell array of regular arrays, then you could do this for the entire block of code.
for s=1:length(C_tem)
C_tem{s} = (C_tem{s} >= 0);
end
Two things to notice: comparison operators are vectorized, meaning they return a matrix of the same size as the input, thus comparing all values at once. And, the output of the operator is 1 where true and 0 where false.
Also look at the builtin function sign to see if that's closer to what you want to do.
I am facing the problem of having several integers, and I have to generate one using them. For example.
Int 1: 14
Int 2: 4
Int 3: 8
Int 4: 4
Hash Sum: 43
I have some restriction in the values, the maximum value that and attribute can have is 30, the addition of all of them is always 30. And the attributes are always positive.
The key is that I want to generate the same hash sum for similar integers, for example if I have the integers, 14, 4, 10, 2 then I want to generate the same hash sum, in the case above 43. But of course if the integers are very different (4, 4, 2, 20) then I should have a different hash sum. Also it needs to be fast.
Ideally I would like that the output of the hash sum is between 0 and 512, and it should evenly distributed. With my restrictions I can have around 5K different possibilities, so what I would like to have is around 10 per bucket.
I am sure there are many algorithms that do this, but I could not find a way of googling this thing. Can anyone please post an algorithm to do this?.
Some more information
The whole thing with this is that those integers are attributes for a function. I want to store the values of the function in a table, but I do not have enough memory to store all the different options. That is why I want to generalize between similar attributes.
The reason why 10, 5, 15 are totally different from 5, 10, 15, it is because if you imagine this in 3d then both points are a totally different point
Some more information 2
Some answers try to solve the problem using hashing. But I do not think this is so complex. Thanks to one of the comments I have realized that this is a clustering algorithm problem. If we have only 3 attributes and we imagine the problem in 3d, what I just need is divide the space in blocks.
In fact this can be solved with rules of this type
if (att[0] < 5 && att[1] < 5 && att[2] < 5 && att[3] < 5)
Block = 21
if ( (5 < att[0] < 10) && (5 < att[1] < 10) && (5 < att[2] < 10) && (5 < att[3] < 10))
Block = 45
The problem is that I need a fast and a general way to generate those ifs I cannot write all the possibilities.
The simple solution:
Convert the integers to strings separated by commas, and hash the resulting string using a common hashing algorithm (md5, sha, etc).
If you really want to roll-your-own, I would do something like:
Generate large prime P
Generate random numbers 0 < a[i] < P (for each dimension you have)
To generate hash, calculate: sum(a[i] * x[i]) mod P
Given the inputs a, b, c, and d, each ranging in value from 0 to 30 (5 bits), the following will produce an number in the range of 0 to 255 (8 bits).
bucket = ((a & 0x18) << 3) | ((b & 0x18) << 1) | ((c & 0x18) >> 1) | ((d & 0x18) >> 3)
Whether the general approach is appropriate depends on how the question is interpreted. The 3 least significant bits are dropped, grouping 0-7 in the same set, 8-15 in the next, and so forth.
0-7,0-7,0-7,0-7 -> bucket 0
0-7,0-7,0-7,8-15 -> bucket 1
0-7,0-7,0-7,16-23 -> bucket 2
...
24-30,24-30,24-30,24-30 -> bucket 255
Trivially tested with:
for (int a = 0; a <= 30; a++)
for (int b = 0; b <= 30; b++)
for (int c = 0; c <= 30; c++)
for (int d = 0; d <= 30; d++) {
int bucket = ((a & 0x18) << 3) |
((b & 0x18) << 1) |
((c & 0x18) >> 1) |
((d & 0x18) >> 3);
printf("%d, %d, %d, %d -> %d\n",
a, b, c, d, bucket);
}
You want a hash function that depends on the order of inputs and where similar sets of numbers will generate the same hash? That is, you want 50 5 5 10 and 5 5 10 50 to generate different values, but you want 52 7 4 12 to generate the same hash as 50 5 5 10? A simple way to do something like this is:
long hash = 13;
for (int i = 0; i < array.length; i++) {
hash = hash * 37 + array[i] / 5;
}
This is imperfect, but should give you an idea of one way to implement what you want. It will treat the values 50 - 54 as the same value, but it will treat 49 and 50 as different values.
If you want the hash to be independent of the order of the inputs (so the hash of 5 10 20 and 20 10 5 are the same) then one way to do this is to sort the array of integers into ascending order before applying the hash. Another way would be to replace
hash = hash * 37 + array[i] / 5;
with
hash += array[i] / 5;
EDIT: Taking into account your comments in response to this answer, it sounds like my attempt above may serve your needs well enough. It won't be ideal, nor perfect. If you need high performance you have some research and experimentation to do.
To summarize, order is important, so 5 10 20 differs from 20 10 5. Also, you would ideally store each "vector" separately in your hash table, but to handle space limitations you want to store some groups of values in one table entry.
An ideal hash function would return a number evenly spread across the possible values based on your table size. Doing this right depends on the expected size of your table and on the number of and expected maximum value of the input vector values. If you can have negative values as "coordinate" values then this may affect how you compute your hash. If, given your range of input values and the hash function chosen, your maximum hash value is less than your hash table size, then you need to change the hash function to generate a larger hash value.
You might want to try using vectors to describe each number set as the hash value.
EDIT:
Since you're not describing why you want to not run the function itself, I'm guessing it's long running. Since you haven't described the breadth of the argument set.
If every value is expected then a full lookup table in a database might be faster.
If you're expecting repeated calls with the same arguments and little overall variation, then you could look at memoizing so only the first run for a argument set is expensive, and each additional request is fast, with less memory usage.
You would need to define what you mean by "similar". Hashes are generally designed to create unique results from unique input.
One approach would be to normalize your input and then generate a hash from the results.
Generating the same hash sum is called a collision, and is a bad thing for a hash to have. It makes it less useful.
If you want similar values to give the same output, you can divide the input by however close you want them to count. If the order makes a difference, use a different divisor for each number. The following function does what you describe:
int SqueezedSum( int a, int b, int c, int d )
{
return (a/11) + (b/7) + (c/5) + (d/3);
}
This is not a hash, but does what you describe.
You want to look into geometric hashing. In "standard" hashing you want
a short key
inverse resistance
collision resistance
With geometric hashing you susbtitute number 3 with something whihch is almost opposite; namely close initial values give close hash values.
Another way to view my problem is using the multidimesional scaling (MS). In MS we start with a matrix of items and what we want is assign a location of each item to an N dimensional space. Reducing in this way the number of dimensions.
http://en.wikipedia.org/wiki/Multidimensional_scaling