longest common substring in R finding non-contiguo

Question

I have a question regarding finding the longest common substring in R. While searching through a few posts on StackOverflow, I got to know about the qualV package. However, I see that the LCS function in this package actually finds all characters from string1 which are present in string2, even if they are not contiguous.

To explain, if the strings are string1 : "hello" string2 : "hel12345lo" I expect the output to be hel, however I get the output as hello. I must be doing something wrong. Please see my code below.

library(qualV)
a= "hello"
b="hel123l5678o" 
sapply(seq_along(a), function(i)
    paste(LCS(substring(a[i], seq(1, nchar(a[i])), seq(1, nchar(a[i]))),
              substring(b[i], seq(1, nchar(b[i])), seq(1, nchar(b[i]))))$LCS,
          collapse = ""))

I have also tried the Rlibstree method but I still get substrings which are not contiguous. Also, the length of the substring is also off from my expectation.s Please see below.

> a = "hello"
> b = "h1e2l3l4o5"

> ll <- list(a,b)
> lapply(data.frame(do.call(rbind, ll), stringsAsFactors=FALSE), function(x) getLongestCommonSubstring(x))
$do.call.rbind..ll.
[1] "h" "e" "l" "o"

> nchar(lapply(data.frame(do.call(rbind, ll), stringsAsFactors=FALSE), function(x) getLongestCommonSubstring(x)))
do.call.rbind..ll.
                21

Answer 1

Here are three possible solutions.

library(stringi)
library(stringdist)

a <- "hello"
b <- "hel123l5678o"

## get all forward substrings of 'b'
sb <- stri_sub(b, 1, 1:nchar(b))
## extract them from 'a' if they exist
sstr <- na.omit(stri_extract_all_coll(a, sb, simplify=TRUE))
## match the longest one
sstr[which.max(nchar(sstr))]
# [1] "hel"

There are also adist() and agrep() in base R, and the stringdist package has a few functions that run the LCS method. Here's a look at stringsidt. It returns the number of unpaired characters.

stringdist(a, b, method="lcs")
# [1] 7

Filter("!", mapply(
    stringdist, 
    stri_sub(b, 1, 1:nchar(b)),
    stri_sub(a, 1, 1:nchar(b)),
    MoreArgs = list(method = "lcs")
))
#  h  he hel 
#  0   0   0 

Now that I've explored this a bit more, I think adist() might be the way to go. If we set counts=TRUE we get a sequence of Matches, Insertions, etc. So if you give that to stri_locate() we can use that matrix to get the matches from a to b.

ta <- drop(attr(adist(a, b, counts=TRUE), "trafos")))
# [1] "MMMIIIMIIIIM"

So the M values denote straight across matches. We can go and get the substrings with stri_sub()

stri_sub(b, stri_locate_all_regex(ta, "M+")[[1]])
# [1] "hel" "l"   "o" 

Sorry I haven't explained that very well as I'm not well versed in string distance algorithms.

Answer 2

Leveraging @RichardScriven's insight that adist could be used, but this function combines it all,

EDIT This was tricky because we needed to get the longest_string in two contexts, so I made this function:

longest_string <- function(s){return(s[which.max(nchar(s))])}

This combines @RichardSriven's work using the library...

library(stringi)
library(stringdist)
lcsbstr <- function(a,b) { 
  sbstr_locations<- stri_locate_all_regex(drop(attr(adist(a, b, counts=TRUE), "trafos")), "M+")[[1]]
  cmn_sbstr<-stri_sub(longest_string(c(a,b)), sbstr_locations)
  longest_cmn_sbstr <- longest_string(cmn_sbstr)
   return(longest_cmn_sbstr) 
}

We can rewrite it to avoid the use of any external libraries (but still using the adist)...

lcsbstr_no_lib <- function(a,b) { 
    matches <- gregexpr("M+", drop(attr(adist(a, b, counts=TRUE), "trafos")))[[1]];
    lengths<- attr(matches, 'match.length')
    which_longest <- which.max(lengths)
    index_longest <- matches[which_longest]
    length_longest <- lengths[which_longest]
    longest_cmn_sbstr  <- substring(longest_string(c(a,b)), index_longest , index_longest + length_longest - 1)
    return(longest_cmn_sbstr ) 
}

All of identify only 'hello ' as the longest common substring, instead of 'hello r':

identical('hello ', 
    lcsbstr_no_lib('hello world', 'hello there'), 
    lcsbstr(       'hello world', 'hello there'))

EDIT And since the edit, works regardless of which argument is the longer of the two:

identical('hello',
    lcsbstr_no_lib('hello', 'hello there'), 
    lcsbstr(       'hello', 'hello there'),
    lcsbstr_no_lib('hello there', 'hello'), 
    lcsbstr(       'hello there', 'hello'))

LAST EDIT But this is only good if you accept this behavior. Notice this result:

lcsbstr('hello world', 'hello')
#[1] 'hell'

I was expecting 'hello', but since the transformation actually moves (via deletion) the world to become the hello, so only the hell part is considered a match according to the M:

drop(attr(adist('hello world', 'hello', counts=TRUE), "trafos"))
#[1] "MMMMDDDMDDD"
#[1]  vvvv   v
#[1] "hello world"

This behavior is observed using [this Levenstein tool] -- it gives two possible solutions, equivalent to these two transforms; can we tell adist which one we prefer? (the one with the greater number of consecutive M)

#[1] "MMMMDDDMDDD"
#[1] "MMMMMDDDDDD"

Finally, don't forget adist allows you to pass in ignore.case = TRUE (FALSE is the default)

Answer 3

I'm not sure what you did to get your output of "hello". Based on trial-and-error experiments below, it appears that the LCS function will (a) not regard a string as an LCS if a character follows what would otherwise be an LCS; (b) find multiple, equally-long LCS's (unlike sub() that finds just the first); (c) the order of the elements in the strings doesn't matter -- which has no illustration below; and (b) the order of the string in the LCS call doesn't matter -- also not shown.

So, your "hello" of a had no LCS in b since the "hel" of b was followed by a character. Well, that's my current hypothesis.

Point A above:

a= c("hello", "hel", "abcd")
b= c("hello123l5678o", "abcd") 
print(LCS(a, b)[4]) # "abcd" - perhaps because it has nothing afterwards, unlike hello123...

a= c("hello", "hel", "abcd1") # added 1 to abcd
b= c("hello123l5678o", "abcd") 
print(LCS(a, b)[4]) # no LCS!, as if anything beyond an otherwise LCS invalidates it

a= c("hello", "hel", "abcd") 
b= c("hello1", "abcd") # added 1 to hello
print(LCS(a, b)[4]) # abcd only, since the b hello1 has a character

Point B above:

a= c("hello", "hel", "abcd") 
b= c("hello", "abcd") 
print(LCS(a, b)[4]) # found both, so not like sub vs gsub of finding first or all

Answer 4

df <- data.frame(A. = c("Australia", "Network"),
                 B. = c("Austria", "Netconnect"), stringsAsFactors = FALSE)

 auxFun <- function(x) {

   a <- strsplit(x[[1]], "")[[1]]
   b  <- strsplit(x[[2]], "")[[1]]
   lastchar <- suppressWarnings(which(!(a == b)))[1] - 1

   if(lastchar > 0){
     out <- paste0(a[1:lastchar], collapse = "")
   } else {
     out <- ""
   }

   return(out)
 }

 df$C. <- apply(df, 1, auxFun)

 df
 A.         B.    C.
 1 Australia    Austria Austr
 2   Network Netconnect   Net