如何计算 R 中向量中有序序列的数量

Question

I have the following data set as an example.

Data<-c("a","d","c","b","d","a","d","b","c","b","a","b","d","c","b","a","c","d","d","c")

I need to find out how many times a < b < c < d, all possible combinations.

I have created a loop (using 4 IF functions) but it takes long time when we have large data set. With this loop the answer is 47 times.

Is there any efficient way to do so in R.

Here is my attempt, but it is very slow when say we have more than 4 letters and large data set.

Data<-c("a","d","c","b","d","a","d","b","c","b","a","b","d","c","b","a","c","d","d","c")
set.seed(123)
Data0<-sort(sample(1:100,20))

df<-data.frame(Data,Data0)

A<-df[Data=="a",2]
B<-df[Data=="b",2]
C<-df[Data=="c",2]
D<-df[Data=="d",2]


myfun<-function(A,B,C,D){
b0<-0
f0<-0
for (i in 1:length(A)){
for (j in 1:length(B)){
for (k in 1:length(C)){
for (l in 1:length(D)){

f0<-f0+sum(A[i]<B[j])*sum(B[j]<C[k])*sum(C[k]<D[l])

}}}}

return(f0)
}


myfun(A,B,C,D)

---

Many Thanks

Answer 1

You could use split to divide Data0 based on groups ie Data , create all possible combinations using expand.grid and count number of times a < b < c < d .

temp <- do.call(expand.grid, split(df$Data0, df$Data))
sum(with(temp, a < b & b < c & c < d))
#[1] 47

If there are many columns and we do not want to check it manually, we can use apply and for every row check the difference between consecutive elements with diff and count number of occurrences when all the values are higher than the previous values.

sum(apply(temp, 1, function(x) all(diff(x) > 0)))
#[1] 47