I'm trying to make an algorithm in Lua to find the optimal combination of items to meet multiple ordered criteria.
Constraints are :
Finding the closest to criteria (sum of same variable for each slot) combination of items with exactly 1 item per slot
15 slots
Maximum 5 criteria, minimum 1 criteria
All values are positive integers
Criteria are prioritized such as A > B > C ...
Number of possible items per slot is theoretically between 0 and 15
For example I have a list of :
{slot: 1, valueA: 10, valueB: 20, valueC: 0}
{slot: 1, valueA: 10, valueB: 20, valueC: 16}
{slot: 2, valueA: 10, valueB: 40, valueD: 29}
{slot: 2, valueA: 30, valueB: 460, valueK: 47}
{slot: 2, valueA: 40, valueB: 50, valueC: 32}
{slot: 3, valueA: 55, valueB: 0, valueJ: 50}
With criteria such as : TotalA = 50, TotalB = 20, TotalC = 90
I want to get the best combination of items to meet TotalA and then TotalB and finally TotalC.
I tried to brute force this using loops but it takes too much time to solve this.
I've found a few discussion about the Knapsack problem and how to solve using dynamic programming or ILP solver (didn't found one in Lua however) but I'm not good enough in mathematics to figure out a working solution.
There's also a missing dimension in the Knapsack problem, the ordering of the criteria.
If someone can guide me with some simple words, pseudo code or Lua it would be awesome.
I already posted a related question (Create a new vector by appending elements between them in R).
I would like to know whether it's possible to increment a vector with a specified number of elements (like accumulate() from purr package).
In fact, I'm working with a vector of 16000 genes. I'm trying to write a for loop where at each iteration, 100 genes should be knocked out from the data set and proceed some clustering analysis (clustering with 16000 genes, clustering with 15900 genes, clustering with 15800 genes, etc.) My idea is to make a list from the vector where each element of it is a vector of genes incremented by 100 (first element 100 genes, second element 200 genes, third element 300 genes and the 160th element, the total 16000 genes).
With accumulate (), I can increment one by one only between two following elements. Is there a way to make it increment 100 by 100?
Thank you all once again for your help!
Instead of a for loop, you could use a while loop and build a new list every time. It's not the most efficient way of doing this, but considering your dataset size, it should do the trick.
Here is some code to help you get started:
# Create a list of values
my_list <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23)
# Get the length of your list
max_len <- length(my_list)
# While [max_len] is positive, create a new list of [max_len] elements and decrement [max_len] by some value (here, 10) for the next list
while (max_len > 0) {
new_list = my_list[1:max_len]
print(new_list)
max_len <- max_len - 10
}
Hope that helps !
I am trying to find out the numbers between 1 and 1,000 that the sum of their digits is equal to 3. I am just looking for any formula that can help me calculate this. For e.g. 111, or 12 equals to 3, the ones, tens, and hundreds added up together will equal 3.
any help will be appreciated.
think of all numbers having 3 digits: 001 and 002
We can start to iterate on this quickly. You cannot have a number in that sequence greater than 3.
So immediately we rule out all numbers >= 400
We can also rule out,within each group of hundred, any number that is greater than ?40 (eg 140 340)
Then we can start to just press into the numbers a bit.
We only have to dig into ?01 - ?39 for 0, 1, 2 and 3.
Start with 00?. We know that there is only one number works here : 0 + 0 + x =3 solve : 003
So we have 0, moving up to the next set of 10 : 01? we know there is only one number that will work. 012.
We have logic, each leading two digit combination leads to only one solution. We know we only have 0?? 1?? 2?? and 3?? for the leading digit. We have ?0? ?1? ?2? and ?3? for the second digit.
We can be comfortable listing : 3, 12, 21, 30, 102, 111, 120, x13?, 201, 210, x22?, 300
If you don't want to use math, use python:
a=[]
for x in range(10):
for y in range(10):
for z in range(10):
if x+y+z==3:
a.append('%r%r%r'%(x,y,z))
a = ['003','012','021','030','102','111','120','201','210','300]
Context
This question concerns sequence analysis using TraMineR package. The package offers automatic transformation of temporal sequences (statuses in time) to event sequences (changes between statuses in time). One of the recurrent issues in my analyses concerns the options to distinguish events of change between equal statuses.
Question-specific example
Suppose we have sequences of employment statuses, e.g. work, unemployment, inactivity, retirement. The analysis is focused on career transitions, distinguishing between stable and transitional careers. All kinds of transitions are relevant, from work to unemployment, inactivity to work, but also (and most importantly) from work to work!
Question
For TraMineR an event takes place when a status in a sequence is changed. For instance, the respondent had 3 years of work and then 1 in unemployment: Work-Work-Work-Unemployment (assuming annual interval). This is the STS format, representing statuses in time. However, in SPELL format we have additional information, e.g:
Status Time1 Time2
Work 1 2
Work 2 3
Work 3 3
Unemployment 3 4
From the table above we can clearly see that two work-to-work transition events have occurred (otherwise there would be just one line: Work from 1 to 3). The question is whether there is any convenient way to extract an event object from the sequence object based on these data.
Data
My data contains work-related respondent statuses in the SPELL format (status, begin & end time), like this:
to.SO <- structure(list(ID = c(10, 11, 11, 12, 13, 13, 13, 13, 14, 14,
14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15), status = c(1,
1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 3, 2, 3, 1, 1, 1, 3, 1, 3, 3,
1, 3), time1 = c(1, 1, 104, 1, 1, 60, 109, 121, 1, 42, 47, 54,
64, 72, 78, 85, 116, 1, 29, 39, 69, 74, 78, 88), time2 = c(125,
104, 125, 125, 60, 109, 121, 125, 42, 47, 54, 64, 72, 78, 85,
116, 125, 29, 39, 69, 74, 78, 88, 125)), .Names = c("ID", "status",
"time1", "time2"), row.names = 10:33, class = "data.frame")
What I have tried
As per this post I must convert SPELL to STS first, then define sequences:
sts.data <- seqformat(data=to.SO,from="SPELL",to="STS",
id="ID",begin="time1",end="time2",status="status",
limit=125,process=FALSE)
sts.seq <- seqdef(sts.data,right="DEL")
alphabed <- c("Work","Study","Unemployed")
alphabet(sts.seq) <- alphabed
The information I require is already lost at this step, but until the bug (see link) is resolved there is no other way. It still shows what I want to achieve:
sts.seqe <- seqecreate(sts.seq) # creating events
sts.seqe
My results
Here, the first four event sequences are identical. If you look at the SPELL data (to.SO), it is apparent that there are multiple work-to-work transitions involved for respondents with id 11 and 13. In my other article I solve this by ascribing different statuses to job-1, job-2 and so forth. It is a less desirable strategy however, since it (1) explodes the number of statuses making subsequent dissimilarity analysis difficult and (2) is not theoretically important which job in career it is, the status of employment alone should cover it.
Thanks
I imagine this goes beyond the existing package capabilities, but perhaps I am missing something. Thanks in advance for reading this long post (at least) and for having any suggestions.
We could indeed imagine a solution which creates the event sequences from the spell data as you suggest. TraMineR does not offer this for now (but see Matthias' solution).
A work around, which you have already given in your question, is to distinguish the successive jobs as job1, job2, ...
I understand that this is less desirable, but you can use this strategy just for defining the event sequences assigning the same event, e.g. "start new job" to each transition from job i to job i+1. To do so you will need to specify a matrix (tmat) of size a x a where a is the size of your state alphabet, which lists in each cell(i, j), the events occurring when transiting from state i to state j. For example at the intersection of the row job1 and column job2, you would give "start new job", and since switching from job2 to job1 should not be possible you would just leave the corresponding cell empty. The cells tmat(i,i) on the diagonal define the start event when the state sequence starts in the corresponding state i.
Once you have defined the matrix (tmat) giving the events assigned to each possible transition, you create the event sequence object as
seqe <- seqecreate(sts2.seq, tevent=tmat)
And you can still use your original sts.seq for state sequence analysis with a single work status.
Hope this helps.
'seqecreate' accepts different kinds of input. One of them is a state sequences object (as produced by seqdef). But you can also build an event sequences objects by providing data in TSE format. For this, you should specify three vectors: id, timestamp, and event.
The spell format can be viewed as data in the TSE format (if you ignore the end of period). The begin column gives the time the event in the status column occured.
Therefore, we can use the following code:
## Start by giving some labels to the status vector
to.SO$event <- factor(to.SO$status, levels=1:3, labels=c("Work","Study","Unemployed"))
## Now, we can build the event sequences using seqecreate
## You may want to use timestamp=(to.SO$time1-1) instead. Events sequences start at time=0
seqe <- seqecreate(id=to.SO$ID, timestamp=to.SO$time1, event=to.SO$event)
seqe
Now the fourth indiviudal has the correct event sequences
If you want to analyze the "Work>work" transition, then you need to recode your data.
## New vector holding our recoded events
event2 <- as.character(to.SO$event)
## For each row in the TSE data
for(i in 2:nrow(to.SO)){
if(to.SO[i-1, "ID"]==to.SO[i, "ID"]) {## If we have the same ID (individual)
if(to.SO[i-1, "event"]=="Work"&& to.SO[i, "event"]=="Work"){ ##Check
event2[i] <- "Work>Work"
}
}
}
## More general case
event3 <- as.character(to.SO$event)
## For each row in the TSE data
for(i in 2:nrow(to.SO)){
if(to.SO[i-1, "ID"]==to.SO[i, "ID"]) {## If we have the same ID (individual)
event3[i] <- paste(to.SO[i-1, "event"], to.SO[i, "event"], sep=">")
}
}
By adapting this code, you can specify the transitions your are interested in.
seqe2 <- seqecreate(id=to.SO$ID, timestamp=to.SO$time1-1, event=event2)
seqe2
OR
seqe3 <- seqecreate(id=to.SO$ID, timestamp=to.SO$time1-1, event=event3)
seqe3
How many positive two-digits integers are factors of (2^24 - 1)?
Can anyone tell me the formula or some shortcuts to find positive integers?
There is no easy way to find factors of a number except calculating them. You have to iterate over the two-digits integers and make mod calculation.
There appear to be 12 divisors in all: 13, 15, 17, 21, 35, 39, 45, 51, 63, 65, 85 and 91.
See: http://www.wolframalpha.com/input/?i=factorize+2%5E24+-+1
There actually is a trick that I know! First you need to prime factorize the number, lets say that my number is 56. My remaining prime numbers would be 7, 2, 2, 2. Since I have three 2s, I would write 2^3. Since there is only one 7, I will write 7^1. Then, add one to each of the powers: 1+1 3+1, and then multiply them. 1+1=2 3+1=4
4*2=8
So your for this example, the answer is 8!! Have fun!
from a fifth grader