I have been searching for long but unable to find a solution for this.
My question is "Suppose you have n street lights(cannot be moved) and if you get any m from them then it should have atleast k working.Now in how many ways can this be done"
This seems to be a combination problem, but the problem here is "m" must be sequential.
Eg:
1 2 3 4 5 6 7 (Street lamps)
Let m=3
Then the valid sets are,
1 2 32 3 43 4 54 5 65 6 7Whereas,1 2 4 and so are invalid selections.
So every set must have atleast 2 working lights. I have figured how to find the minimum lamps required to satisfy the condition but how can I find the number of ways in it can be done ?
There should certainly some formula to do this but I am unable to find it.. :(
Should always be (n-m)+1.
E.g., 10 lights (n = 10), 5 in set (m = 5):
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
5 6 7 8 9
6 7 8 9 10
Gives (10-5)+1 = 6 sets.
The answer should always be m choose k for all values of n where n > m > k. I'll try to explain why;
Given, for example, the values m = 10, n = 4, k = 2, you can start by generating all possible permutations of 1s and 0s for sets of 4 lights, with exactly 2 lights on;
1100
0110
0011
1001
0101
1010
As you can see, there are 6 permutations, because 4 choose 2 = 6. You can choose any of these 6 permutations to be the first 4 lights. You then continue the sequence until you get n (in this case 10) lights, ensuring that you only ever add a zero if you must in order to keep the condition true of having 2 lights on for every 4. What you will find is that the sequence simply repeats; for example:
1100 -> next can be 1, so 11001
Next can still be 1 and meet the condition, so 110011.
The next must now be a zero, giving 1100110, and then again -> 11001100. This simply continues until the length is n : 1100110011. Given that the starting four can only be one of the above set, you will only get 6 different permutations.
Now, since the sequence will repeat exactly the same for any value of n, it means that the answer will always be m choose k.
For your example in your comment of 6,3,2, I can only find the following permutations:
011011
110110
101101
Which works, because 3 choose 2 = 3. If you can find more, then I guess I'm wrong and I've probably misunderstood again :D but from my understanding of this problem, I'm certain that the answer will always be m choose k.
Related
I realize this is a topic that's covered somewhat well but I couldn't find anything that approaches this specific concern:
I have a df with 800 columns, 10 iterations of 80 columns (each column represents an item) - Each column is named something like: 1_BL_PRE.1 1_FU_PRE.1 1_BL_PRE.1 1_BL_POST.1
Where the first '1' indicates the item number and the second '1' indicates the iteration number.
What I'm trying to figure out is how to get the sums of specific groups of items from all 10 iterations.
As a short example let's say I want to take the 1st and 3rd item of BL_PRE and get the sum of all 10 iterations for those 2 items - how would I do this?
subject 1_BL_PRE.1 2_BL_PRE.1 3_BL_PRE.1 1_BL_PRE.2 2_BL_PRE.2
1 40002 3 4 3 1 2
2 40004 1 2 3 4 4
3 40006 4 3 3 3 1
4 40008 2 3 1 2 3
5 40009 3 4 1 2 3
Expected output (where A represents the sum of 1_BL_PRE.1, 3_BL_PRE.1, 1_BL_PRE.2 and so on):
subject BL_PRE_A
1 40002 12
2 40004 14
3 40006 15
4 40008 20
5 40009 12
My hunch is the solution is related to a for-loop or lappy (and I'm not familiar at all with either). I'm trying to work with apply(finaldata,1,function(x) {sum(x ...)}) but I haven't been able to figure out the conditional statement for the function of sum.
If there's an implementation with plyr I'd be really curious to see what that looks like. (and if there's a thread that answers this, apologies and just re-direct!)
**Edited to include small example + code I'm trying to get to work
Thanks!
I have a sequence dataset like below:
customerid flag 0 1 2 3 4 5 6 7 8 9 10 11
abc234 1 3 4 3 4 5 8 4 3 3 2 14 14
abc233 0 4 4 4 4 4 4 4 4 4 4 4 4
qpr81 0 9 8 7 8 8 7 8 8 7 8 8 7
qnr94 0 14 14 14 2 14 14 14 14 14 14 14 14
Values in column 0 to 11 are the sequences. There are two sets of customers with flag=1 and flag=0, I have differentiating event sequences for both sets. ( Only frequencies and residuals for 2 groups are shown here)
Subsequence Freq.0 Freq.1 Resid.0 Resid.1
(3>4) 0.19208177 0.0753386 5.540793 -21.43304
(4>5) 0.15752553 0.059960497 5.115241 -19.78691
(5>4) 0.15950556 0.062782167 5.037413 -19.48586
I want to find the customer ids and the flags for which the event sequences match.
Should I write a python script to traverse the transactions or is there some direct method in R to do this?
`
CODE
--------------
library(TraMineR)
custid=c(a1,a2,a3,b4,b5,c6,c7,d8,d9)#sample customer ids
flag=c(0,0,0,1,0,1,1,0,1)#flag
col1=c(14,14,14,14,14,5,14,14,2)
col2=c(14,14,3,14,3,14,6,3,3)
col3=c(14,2,2,14,2,14,2,2,2)
col4=c(14,2,2,14,2,14,2,2,14)
df=data.frame(custid,flag,col1,col2,col3,col4)#dataframe generation
print(df)
#Defining sequence from col1 to col4
df.s<-seqdef(df,3:6)
print(df.s)
#finding the transitions
transition<-seqetm(df.s,method='transition')
print(transition)
#converting to TSE format
df.tse=seqformat(df.s,from='SPS',to='TSE',tevent = transition)
print(df.tse)
#Event sequence generation
df.seqe=seqecreate(id=df.tse$id,timestamp=df.tse$time,event=df.tse$event)
print(df.seqe)
#subsequences
fsubseq <- seqefsub(df.seqe, pMinSupport = 0.01)
print(fsubseq)
groups <- factor(df$flag>0,labels=c(1,0))
#finding differentiating event sequences based on flag using ChiSquare test
diff <- seqecmpgroup(fsubseq, group = df$flag, method = "chisq")
#Using seqeapplysub for finding the presence of subsequences?
presence=seqeapplysub(fsubseq,method="presence")
print(presence[1:3,3:1])
`
Thanks
From what I understand, you have state sequences and have transformed them into event sequences using the seqecreate function of TraMineR. The events you are considering are the state changes. Thus (3>4) stands for a subsequence with only one event, namely the event 3>4 (switching from 3 to 4). Then, you identify the event subsequences that best discriminate your two flags using the seqefsub and seqecmpgroup functions.
If this is correct, then you can identify the sequences containing each subsequence with the seqeapplysub function. I cannot illustrate here because you do not provide any code in your question. Look at the online help of the seqeapplysub function.
======= update referring to your added code =======
Here is how you get the ids of the sequences that contain the most discriminating subsequence.
First we extract the first three most discriminating sequences from your diff object. Second, we compute the presence matrix that provides a column for each extracted subsequence with a 1 in regard of the sequences that contain the subsequence and 0 otherwise.
diffseq <- seqefsub(df.seqe, strsubseq = paste(diff$subseq[1:3]))
(presence=seqeapplysub(diffseq, method="presence"))
Now you get the ids for the first subsequence with
custid[presence[,1]==1]
For the second it would be custid[presence[,2]==1] etc.
Likewise you get the flag with
flag[presence[,1]==1]
Hope this helps.
I am having a hard time figuring how to program this in R: Given a number of X and Y pairs, such as
X Y
9 1
1 2
12 3
8 4
9 4
4 5
16 6
18 7
5 8
11 9
4 10
6 11
6 12
14 13
18 13
20 13
13 14
20 15
20 16
I need to sample randomly n pairs that fulfil the condition that Xs and Ys are unique. For instance, if n=3 and using the data above, the following combinations (9,1) (4,5) (4,10) or (1,2) (14,13) (20,13) will be invalid because X=4 or Y=13 are duplicated in each of the solutions. However, (9,1) (1,2) and (8,4) will be a valid solution because the Xs and Ys are unique. Any help will be moooooost welcome.
If you start by sampling (randomizing) the rows of your original data, then subset only those rows where X or Y are not duplicated and then select the first, last or any n (=3) number of rows (you could use sample again), you should be fine, I think.
set.seed(1) # for reproducibility
head(subset(df[sample(nrow(df)),], !duplicated(X) & !duplicated(Y)), 3)
# X Y
#6 4 5
#7 16 6
#10 11 9
In response to the comment by #Richo64, saying that this approach will not randomly select the pairs:
It does sample the pairs randomly because the first (inner most) thing I do is
df[sample(nrow(df)),]
which samples the rows of the data randomly. Now, once we have done that, it's a random process which, say 4, in column X will come first and therefore will remain in the data because the other 4 is removed since it is a duplicated entry in X.
The same applies to values in Y.
It's obvious then, that after the sampling and subsetting, you are free to choose any 3 rows of the remaining data and even if you always selected the first 3 rows, you would still get a random selection that will differ every time you run it (except when it coincidently samples the same rows again).
Lets say I have the following data.frame in R
df <- data.frame(order=(1:10),value=c(1,7,3,5,9,2,9,10,2,3))
Other than looping through data an testing whether value exceeds previous high value how can I get successive high values so that I can end up with a table like this
order value
1 1
2 7
5 9
8 10
TIA
Here's one option, if I understood the question correct:
df[df$value > cummax(c(-Inf, head(df$value, -1))),]
# order value
#1 1 1
#2 2 7
#5 5 9
#8 8 10
I use cummax to keep track of the maximum of column "value" and compare it (the previous row's cummax) to each "value" entry. To make sure the first entry is also selected, I start by "-Inf".
"get successive high values (of value?)" is unclear.
It seems you want to filter only rows whose value is higher than previous max.
First, we reorder your df in increasing order of value... (not clear but I think that's what you wanted)
Then we use logical indexing with diff()>0 to only include strictly-increasing rows:
rdf <- df[order(df$value),]
rdf[ diff(rdf$value)>0, ]
order value
1 1 1
9 9 2
10 10 3
4 4 5
2 2 7
7 7 9
8 8 10
I am working with a large dataset and I am trying to first identify clusters of values that meet specific threshold values. My aim then is to only keep clusters of a minimum length. Below is some example data and my progress thus far:
Test = c("A","A","A","A","A","A","A","A","A","A","B","B","B","B","B","B","B","B","B","B")
Sequence = c(1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10)
Value = c(3,2,3,4,3,4,4,5,5,2,2,4,5,6,4,4,6,2,3,2)
Data <- data.frame(Test, Sequence, Value)
Using package evd, I have identified clusters of values >3
C1 <- clusters(Data$Value, u = 3, r = 1, cmax = F, plot = T)
Which produces
C1
$cluster1
4
4
$cluster2
6 7 8 9
4 4 5 5
$cluster3
12 13 14 15 16 17
4 5 6 4 4 6
My problem is twofold:
1) I don't know how to relate this back to the original dataframe (for example to Test A & B)
2) How can I only keep clusters with a minimum size of 3 (thus excluding Cluster 1)
I have looked into various filtering options etc. however they do not cluster data according to a desired threshold, with no options for the minimum size of the cluster either.
Any help is much appreciated.
Q1: relate back to original dataframe: Have a look at Carl Witthoft's answer. He wrote a variant of rle() (seqle() because it allows one to look for integer sequences rather than repetitions): detect intervals of the consequent integer sequences
Q2: only keep clusters of certain length:
C1[sapply(C1, length) > 3]
yields the 2 clusters that are long enough:
$cluster2
6 7 8 9
4 4 5 5
$cluster3
12 13 14 15 16 17
4 5 6 4 4 6