Confusion on Quantifiers? [duplicate] - java

I found this tutorial on regular expressions and while I intuitively understand what "greedy", "reluctant" and "possessive" qualifiers do, there seems to be a serious hole in my understanding.
Specifically, in the following example:
Enter your regex: .*foo // Greedy qualifier
Enter input string to search: xfooxxxxxxfoo
I found the text "xfooxxxxxxfoo" starting at index 0 and ending at index 13.
Enter your regex: .*?foo // Reluctant qualifier
Enter input string to search: xfooxxxxxxfoo
I found the text "xfoo" starting at index 0 and ending at index 4.
I found the text "xxxxxxfoo" starting at index 4 and ending at index 13.
Enter your regex: .*+foo // Possessive qualifier
Enter input string to search: xfooxxxxxxfoo
No match found.
The explanation mentions eating the entire input string, letters been consumed, matcher backing off, rightmost occurrence of "foo" has been regurgitated, etc.
Unfortunately, despite the nice metaphors, I still don't understand what is eaten by whom... Do you know of another tutorial that explains (concisely) how regular expression engines work?
Alternatively, if someone can explain in somewhat different phrasing the following paragraph, that would be much appreciated:
The first example uses the greedy quantifier .* to find "anything", zero or more times, followed by the letters "f", "o", "o". Because the quantifier is greedy, the .* portion of the expression first eats the entire input string. At this point, the overall expression cannot succeed, because the last three letters ("f", "o", "o") have already been consumed [by whom?]. So the matcher slowly backs off [from right-to-left?] one letter at a time until the rightmost occurrence of "foo" has been regurgitated [what does this mean?], at which point the match succeeds and the search ends.
The second example, however, is reluctant, so it starts by first consuming [by whom?] "nothing". Because "foo" doesn't appear at the beginning of the string, it's forced to swallow [who swallows?] the first letter (an "x"), which triggers the first match at 0 and 4. Our test harness continues the process until the input string is exhausted. It finds another match at 4 and 13.
The third example fails to find a match because the quantifier is possessive. In this case, the entire input string is consumed by .*+ [how?], leaving nothing left over to satisfy the "foo" at the end of the expression. Use a possessive quantifier for situations where you want to seize all of something without ever backing off [what does back off mean?]; it will outperform the equivalent greedy quantifier in cases where the match is not immediately found.

I'll give it a shot.
A greedy quantifier first matches as much as possible. So the .* matches the entire string. Then the matcher tries to match the f following, but there are no characters left. So it "backtracks", making the greedy quantifier match one less character (leaving the "o" at the end of the string unmatched). That still doesn't match the f in the regex, so it backtracks one more step, making the greedy quantifier match one less character again (leaving the "oo" at the end of the string unmatched). That still doesn't match the f in the regex, so it backtracks one more step (leaving the "foo" at the end of the string unmatched). Now, the matcher finally matches the f in the regex, and the o and the next o are matched too. Success!
A reluctant or "non-greedy" quantifier first matches as little as possible. So the .* matches nothing at first, leaving the entire string unmatched. Then the matcher tries to match the f following, but the unmatched portion of the string starts with "x" so that doesn't work. So the matcher backtracks, making the non-greedy quantifier match one more character (now it matches the "x", leaving "fooxxxxxxfoo" unmatched). Then it tries to match the f, which succeeds, and the o and the next o in the regex match too. Success!
In your example, it then starts the process over with the remaining unmatched portion of the string, "xxxxxxfoo", following the same process.
A possessive quantifier is just like the greedy quantifier, but it doesn't backtrack. So it starts out with .* matching the entire string, leaving nothing unmatched. Then there is nothing left for it to match with the f in the regex. Since the possessive quantifier doesn't backtrack, the match fails there.

It is just my practice output to visualise the scene-

I haven't heard the exact terms 'regurgitate' or 'backing off' before; the phrase that would replace these is "backtracking", but 'regurgitate' seems like as good a phrase as any for "the content that had been tentatively accepted before backtracking threw it away again".
The important thing to realize about most regex engines is that they are backtracking: they will tentatively accept a potential, partial match, while trying to match the entire contents of the regex. If the regex cannot be completely matched at the first attempt, then the regex engine will backtrack on one of its matches. It will try matching *, +, ?, alternation, or {n,m} repetition differently, and try again. (And yes, this process can take a long time.)
The first example uses the greedy
quantifier .* to find "anything", zero
or more times, followed by the letters
"f" "o" "o". Because the quantifier is
greedy, the .* portion of the
expression first eats the entire input
string. At this point, the overall
expression cannot succeed, because the
last three letters ("f" "o" "o") have
already been consumed (by whom?).
The last three letters, f, o, and o were already consumed by the initial .* portion of the rule. However, the next element in the regex, f, has nothing left in the input string. The engine will be forced to backtrack on its initial .* match, and try matching all-but-the-last character. (It might be smart and backtrack to all-but-the-last-three, because it has three literal terms, but I'm unaware of implementation details at this level.)
So the matcher
slowly backs off (from right-to-left?) one letter at a time
until the rightmost occurrence of
"foo" has been regurgitated (what does this mean?), at which
This means the foo had tentatively been including when matching .*. Because that attempt failed, the regex engine tries accepting one fewer character in .*. If there had been a successful match before the .* in this example, then the engine would probably try shortening the .* match (from right-to-left, as you pointed out, because it is a greedy qualifier), and if it was unable to match the entire inputs, then it might be forced to re-evaluate what it had matched before the .* in my hypothetical example.
point the match succeeds and the
search ends.
The second example, however, is
reluctant, so it starts by first
consuming (by whom?) "nothing". Because "foo"
The initial nothing is consumed by .?*, which will consume the shortest possible amount of anything that allows the rest of the regex to match.
doesn't appear at the beginning of the
string, it's forced to swallow (who swallows?) the
Again the .?* consumes the first character, after backtracking on the initial failure to match the entire regex with the shortest possible match. (In this case, the regex engine is extending the match for .*? from left-to-right, because .*? is reluctant.)
first letter (an "x"), which triggers
the first match at 0 and 4. Our test
harness continues the process until
the input string is exhausted. It
finds another match at 4 and 13.
The third example fails to find a
match because the quantifier is
possessive. In this case, the entire
input string is consumed by .*+, (how?)
A .*+ will consume as much as possible, and will not backtrack to find new matches when the regex as a whole fails to find a match. Because the possessive form does not perform backtracking, you probably won't see many uses with .*+, but rather with character classes or similar restrictions: account: [[:digit:]]*+ phone: [[:digit:]]*+.
This can drastically speed up regex matching, because you're telling the regex engine that it should never backtrack over potential matches if an input doesn't match. (If you had to write all the matching code by hand, this would be similar to never using putc(3) to 'push back' an input character. It would be very similar to the naive code one might write on a first try. Except regex engines are way better than a single character of push-back, they can rewind all the back to zero and try again. :)
But more than potential speed ups, this also can let you write regexs that match exactly what you need to match. I'm having trouble coming up with an easy example :) but writing a regex using possessive vs greedy quantifiers can give you different matches, and one or the other may be more appropriate.
leaving nothing left over to satisfy
the "foo" at the end of the
expression. Use a possessive
quantifier for situations where you
want to seize all of something without
ever backing off (what does back off mean?); it will outperform
"Backing off" in this context means "backtracking" -- throwing away a tentative partial match to try another partial match, which may or may not succeed.
the equivalent greedy quantifier in
cases where the match is not
immediately found.

http://swtch.com/~rsc/regexp/regexp1.html
I'm not sure that's the best explanation on the internet, but it's reasonably well written and appropriately detailed, and I keep coming back to it. You might want to check it out.
If you want a higher-level (less detailed explanation), for simple regular expressions such as the one you're looking at, a regular expression engine works by backtracking. Essentially, it chooses ("eats") a section of the string and tries to match the regular expression against that section. If it matches, great. If not, the engine alters its choice of the section of the string and tries to match the regexp against that section, and so on, until it's tried every possible choice.
This process is used recursively: in its attempt to match a string with a given regular expression, the engine will split the regular expression into pieces and apply the algorithm to each piece individually.
The difference between greedy, reluctant, and possessive quantifiers enters when the engine is making its choices of what part of the string to try to match against, and how to modify that choice if it doesn't work the first time. The rules are as follows:
A greedy quantifier tells the engine to start with the entire string (or at least, all of it that hasn't already been matched by previous parts of the regular expression) and check whether it matches the regexp. If so, great; the engine can continue with the rest of the regexp. If not, it tries again, but trimming one character (the last one) off the section of the string to be checked. If that doesn't work, it trims off another character, etc. So a greedy quantifier checks possible matches in order from longest to shortest.
A reluctant quantifier tells the engine to start with the shortest possible piece of the string. If it matches, the engine can continue; if not, it adds one character to the section of the string being checked and tries that, and so on until it finds a match or the entire string has been used up. So a reluctant quantifier checks possible matches in order from shortest to longest.
A possessive quantifier is like a greedy quantifier on the first attempt: it tells the engine to start by checking the entire string. The difference is that if it doesn't work, the possessive quantifier reports that the match failed right then and there. The engine doesn't change the section of the string being looked at, and it doesn't make any more attempts.
This is why the possessive quantifier match fails in your example: the .*+ gets checked against the entire string, which it matches, but then the engine goes on to look for additional characters foo after that - but of course it doesn't find them, because you're already at the end of the string. If it were a greedy quantifier, it would backtrack and try making the .* only match up to the next-to-last character, then up to the third to last character, then up to the fourth to last character, which succeeds because only then is there a foo left after the .* has "eaten" the earlier part of the string.

Here is my take using Cell and Index positions (See the diagram here to distinguish a Cell from an Index).
Greedy - Match as much as possible to the greedy quantifier and the entire regex. If there is no match, backtrack on the greedy quantifier.
Input String: xfooxxxxxxfoo
Regex: .*foo
The above Regex has two parts:
(i)'.*' and
(ii)'foo'
Each of the steps below will analyze the two parts. Additional comments for a match to 'Pass' or 'Fail' is explained within braces.
Step 1:
(i) .* = xfooxxxxxxfoo - PASS ('.*' is a greedy quantifier and will use the entire Input String)
(ii) foo = No character left to match after index 13 - FAIL
Match failed.
Step 2:
(i) .* = xfooxxxxxxfo - PASS (Backtracking on the greedy quantifier '.*')
(ii) foo = o - FAIL
Match failed.
Step 3:
(i) .* = xfooxxxxxxf - PASS (Backtracking on the greedy quantifier '.*')
(ii) foo = oo - FAIL
Match failed.
Step 4:
(i) .* = xfooxxxxxx - PASS (Backtracking on the greedy quantifier '.*')
(ii) foo = foo - PASS
Report MATCH
Result: 1 match(es)
I found the text "xfooxxxxxxfoo" starting at index 0 and ending at index 13.
Reluctant - Match as little as possible to the reluctant quantifier and match the entire regex. if there is no match, add characters to the reluctant quantifier.
Input String: xfooxxxxxxfoo
Regex: .*?foo
The above regex has two parts:
(i) '.*?' and
(ii) 'foo'
Step 1:
.*? = '' (blank) - PASS (Match as little as possible to the reluctant quantifier '.*?'. Index 0 having '' is a match.)
foo = xfo - FAIL (Cell 0,1,2 - i.e index between 0 and 3)
Match failed.
Step 2:
.*? = x - PASS (Add characters to the reluctant quantifier '.*?'. Cell 0 having 'x' is a match.)
foo = foo - PASS
Report MATCH
Step 3:
.*? = '' (blank) - PASS (Match as little as possible to the reluctant quantifier '.*?'. Index 4 having '' is a match.)
foo = xxx - FAIL (Cell 4,5,6 - i.e index between 4 and 7)
Match failed.
Step 4:
.*? = x - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4.)
foo = xxx - FAIL (Cell 5,6,7 - i.e index between 5 and 8)
Match failed.
Step 5:
.*? = xx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 5.)
foo = xxx - FAIL (Cell 6,7,8 - i.e index between 6 and 9)
Match failed.
Step 6:
.*? = xxx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 6.)
foo = xxx - FAIL (Cell 7,8,9 - i.e index between 7 and 10)
Match failed.
Step 7:
.*? = xxxx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 7.)
foo = xxf - FAIL (Cell 8,9,10 - i.e index between 8 and 11)
Match failed.
Step 8:
.*? = xxxxx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 8.)
foo = xfo - FAIL (Cell 9,10,11 - i.e index between 9 and 12)
Match failed.
Step 9:
.*? = xxxxxx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 9.)
foo = foo - PASS (Cell 10,11,12 - i.e index between 10 and 13)
Report MATCH
Step 10:
.*? = '' (blank) - PASS (Match as little as possible to the reluctant quantifier '.*?'. Index 13 is blank.)
foo = No character left to match - FAIL (There is nothing after index 13 to match)
Match failed.
Result: 2 match(es)
I found the text "xfoo" starting at index 0 and ending at index 4.
I found the text "xxxxxxfoo" starting at index 4 and ending at index 13.
Possessive - Match as much as possible to the possessive quantifer and match the entire regex. Do NOT backtrack.
Input String: xfooxxxxxxfoo
Regex: .*+foo
The above regex has two parts: '.*+' and 'foo'.
Step 1:
.*+ = xfooxxxxxxfoo - PASS (Match as much as possible to the possessive quantifier '.*')
foo = No character left to match - FAIL (Nothing to match after index 13)
Match failed.
Note: Backtracking is not allowed.
Result: 0 match(es)

Greedy: "match the longest possible sequence of characters"
Reluctant: "match the shortest possible sequence of characters"
Possessive: This is a bit strange as it does NOT (in contrast to greedy and reluctant) try to find a match for the whole regex.
By the way: No regex pattern matcher implementation will ever use backtracking. All real-life pattern matcher are extremely fast - nearly independent of the complexity of the regular expression!

Greedy Quantification involves pattern matching using all of the remaining unvalidated characters of a string during an iteration. Unvalidated characters start in the active sequence. Every time a match does not occur, the character at the end is quarantined and the check is performed again.
When only leading conditions of the regex pattern are satisfied by the active sequence, an attempt is made to validate the remaining conditions against the quarantine. If this validation is successful, matched characters in the quarantine are validated and residual unmatched characters remain unvalidated and will be used when the process begins anew in the next iteration.
The flow of characters is from the active sequence into the quarantine. The resulting behavior is that as much of the original sequence is included in a match as possible.
Reluctant Quantification is mostly the same as greedy qualification except the flow of characters is the opposite--that is, they start in the quarantine and flow into the active sequence. The resulting behavior is that as little of the original sequence is included in a match as possible.
Possessive Quantification does not have a quarantine and includes everything in a fixed active sequence.

Related

Regular expression not extracting correctly (Java Pattern / Matcher) [duplicate]

I found this tutorial on regular expressions and while I intuitively understand what "greedy", "reluctant" and "possessive" qualifiers do, there seems to be a serious hole in my understanding.
Specifically, in the following example:
Enter your regex: .*foo // Greedy qualifier
Enter input string to search: xfooxxxxxxfoo
I found the text "xfooxxxxxxfoo" starting at index 0 and ending at index 13.
Enter your regex: .*?foo // Reluctant qualifier
Enter input string to search: xfooxxxxxxfoo
I found the text "xfoo" starting at index 0 and ending at index 4.
I found the text "xxxxxxfoo" starting at index 4 and ending at index 13.
Enter your regex: .*+foo // Possessive qualifier
Enter input string to search: xfooxxxxxxfoo
No match found.
The explanation mentions eating the entire input string, letters been consumed, matcher backing off, rightmost occurrence of "foo" has been regurgitated, etc.
Unfortunately, despite the nice metaphors, I still don't understand what is eaten by whom... Do you know of another tutorial that explains (concisely) how regular expression engines work?
Alternatively, if someone can explain in somewhat different phrasing the following paragraph, that would be much appreciated:
The first example uses the greedy quantifier .* to find "anything", zero or more times, followed by the letters "f", "o", "o". Because the quantifier is greedy, the .* portion of the expression first eats the entire input string. At this point, the overall expression cannot succeed, because the last three letters ("f", "o", "o") have already been consumed [by whom?]. So the matcher slowly backs off [from right-to-left?] one letter at a time until the rightmost occurrence of "foo" has been regurgitated [what does this mean?], at which point the match succeeds and the search ends.
The second example, however, is reluctant, so it starts by first consuming [by whom?] "nothing". Because "foo" doesn't appear at the beginning of the string, it's forced to swallow [who swallows?] the first letter (an "x"), which triggers the first match at 0 and 4. Our test harness continues the process until the input string is exhausted. It finds another match at 4 and 13.
The third example fails to find a match because the quantifier is possessive. In this case, the entire input string is consumed by .*+ [how?], leaving nothing left over to satisfy the "foo" at the end of the expression. Use a possessive quantifier for situations where you want to seize all of something without ever backing off [what does back off mean?]; it will outperform the equivalent greedy quantifier in cases where the match is not immediately found.
I'll give it a shot.
A greedy quantifier first matches as much as possible. So the .* matches the entire string. Then the matcher tries to match the f following, but there are no characters left. So it "backtracks", making the greedy quantifier match one less character (leaving the "o" at the end of the string unmatched). That still doesn't match the f in the regex, so it backtracks one more step, making the greedy quantifier match one less character again (leaving the "oo" at the end of the string unmatched). That still doesn't match the f in the regex, so it backtracks one more step (leaving the "foo" at the end of the string unmatched). Now, the matcher finally matches the f in the regex, and the o and the next o are matched too. Success!
A reluctant or "non-greedy" quantifier first matches as little as possible. So the .* matches nothing at first, leaving the entire string unmatched. Then the matcher tries to match the f following, but the unmatched portion of the string starts with "x" so that doesn't work. So the matcher backtracks, making the non-greedy quantifier match one more character (now it matches the "x", leaving "fooxxxxxxfoo" unmatched). Then it tries to match the f, which succeeds, and the o and the next o in the regex match too. Success!
In your example, it then starts the process over with the remaining unmatched portion of the string, "xxxxxxfoo", following the same process.
A possessive quantifier is just like the greedy quantifier, but it doesn't backtrack. So it starts out with .* matching the entire string, leaving nothing unmatched. Then there is nothing left for it to match with the f in the regex. Since the possessive quantifier doesn't backtrack, the match fails there.
It is just my practice output to visualise the scene-
I haven't heard the exact terms 'regurgitate' or 'backing off' before; the phrase that would replace these is "backtracking", but 'regurgitate' seems like as good a phrase as any for "the content that had been tentatively accepted before backtracking threw it away again".
The important thing to realize about most regex engines is that they are backtracking: they will tentatively accept a potential, partial match, while trying to match the entire contents of the regex. If the regex cannot be completely matched at the first attempt, then the regex engine will backtrack on one of its matches. It will try matching *, +, ?, alternation, or {n,m} repetition differently, and try again. (And yes, this process can take a long time.)
The first example uses the greedy
quantifier .* to find "anything", zero
or more times, followed by the letters
"f" "o" "o". Because the quantifier is
greedy, the .* portion of the
expression first eats the entire input
string. At this point, the overall
expression cannot succeed, because the
last three letters ("f" "o" "o") have
already been consumed (by whom?).
The last three letters, f, o, and o were already consumed by the initial .* portion of the rule. However, the next element in the regex, f, has nothing left in the input string. The engine will be forced to backtrack on its initial .* match, and try matching all-but-the-last character. (It might be smart and backtrack to all-but-the-last-three, because it has three literal terms, but I'm unaware of implementation details at this level.)
So the matcher
slowly backs off (from right-to-left?) one letter at a time
until the rightmost occurrence of
"foo" has been regurgitated (what does this mean?), at which
This means the foo had tentatively been including when matching .*. Because that attempt failed, the regex engine tries accepting one fewer character in .*. If there had been a successful match before the .* in this example, then the engine would probably try shortening the .* match (from right-to-left, as you pointed out, because it is a greedy qualifier), and if it was unable to match the entire inputs, then it might be forced to re-evaluate what it had matched before the .* in my hypothetical example.
point the match succeeds and the
search ends.
The second example, however, is
reluctant, so it starts by first
consuming (by whom?) "nothing". Because "foo"
The initial nothing is consumed by .?*, which will consume the shortest possible amount of anything that allows the rest of the regex to match.
doesn't appear at the beginning of the
string, it's forced to swallow (who swallows?) the
Again the .?* consumes the first character, after backtracking on the initial failure to match the entire regex with the shortest possible match. (In this case, the regex engine is extending the match for .*? from left-to-right, because .*? is reluctant.)
first letter (an "x"), which triggers
the first match at 0 and 4. Our test
harness continues the process until
the input string is exhausted. It
finds another match at 4 and 13.
The third example fails to find a
match because the quantifier is
possessive. In this case, the entire
input string is consumed by .*+, (how?)
A .*+ will consume as much as possible, and will not backtrack to find new matches when the regex as a whole fails to find a match. Because the possessive form does not perform backtracking, you probably won't see many uses with .*+, but rather with character classes or similar restrictions: account: [[:digit:]]*+ phone: [[:digit:]]*+.
This can drastically speed up regex matching, because you're telling the regex engine that it should never backtrack over potential matches if an input doesn't match. (If you had to write all the matching code by hand, this would be similar to never using putc(3) to 'push back' an input character. It would be very similar to the naive code one might write on a first try. Except regex engines are way better than a single character of push-back, they can rewind all the back to zero and try again. :)
But more than potential speed ups, this also can let you write regexs that match exactly what you need to match. I'm having trouble coming up with an easy example :) but writing a regex using possessive vs greedy quantifiers can give you different matches, and one or the other may be more appropriate.
leaving nothing left over to satisfy
the "foo" at the end of the
expression. Use a possessive
quantifier for situations where you
want to seize all of something without
ever backing off (what does back off mean?); it will outperform
"Backing off" in this context means "backtracking" -- throwing away a tentative partial match to try another partial match, which may or may not succeed.
the equivalent greedy quantifier in
cases where the match is not
immediately found.
http://swtch.com/~rsc/regexp/regexp1.html
I'm not sure that's the best explanation on the internet, but it's reasonably well written and appropriately detailed, and I keep coming back to it. You might want to check it out.
If you want a higher-level (less detailed explanation), for simple regular expressions such as the one you're looking at, a regular expression engine works by backtracking. Essentially, it chooses ("eats") a section of the string and tries to match the regular expression against that section. If it matches, great. If not, the engine alters its choice of the section of the string and tries to match the regexp against that section, and so on, until it's tried every possible choice.
This process is used recursively: in its attempt to match a string with a given regular expression, the engine will split the regular expression into pieces and apply the algorithm to each piece individually.
The difference between greedy, reluctant, and possessive quantifiers enters when the engine is making its choices of what part of the string to try to match against, and how to modify that choice if it doesn't work the first time. The rules are as follows:
A greedy quantifier tells the engine to start with the entire string (or at least, all of it that hasn't already been matched by previous parts of the regular expression) and check whether it matches the regexp. If so, great; the engine can continue with the rest of the regexp. If not, it tries again, but trimming one character (the last one) off the section of the string to be checked. If that doesn't work, it trims off another character, etc. So a greedy quantifier checks possible matches in order from longest to shortest.
A reluctant quantifier tells the engine to start with the shortest possible piece of the string. If it matches, the engine can continue; if not, it adds one character to the section of the string being checked and tries that, and so on until it finds a match or the entire string has been used up. So a reluctant quantifier checks possible matches in order from shortest to longest.
A possessive quantifier is like a greedy quantifier on the first attempt: it tells the engine to start by checking the entire string. The difference is that if it doesn't work, the possessive quantifier reports that the match failed right then and there. The engine doesn't change the section of the string being looked at, and it doesn't make any more attempts.
This is why the possessive quantifier match fails in your example: the .*+ gets checked against the entire string, which it matches, but then the engine goes on to look for additional characters foo after that - but of course it doesn't find them, because you're already at the end of the string. If it were a greedy quantifier, it would backtrack and try making the .* only match up to the next-to-last character, then up to the third to last character, then up to the fourth to last character, which succeeds because only then is there a foo left after the .* has "eaten" the earlier part of the string.
Here is my take using Cell and Index positions (See the diagram here to distinguish a Cell from an Index).
Greedy - Match as much as possible to the greedy quantifier and the entire regex. If there is no match, backtrack on the greedy quantifier.
Input String: xfooxxxxxxfoo
Regex: .*foo
The above Regex has two parts:
(i)'.*' and
(ii)'foo'
Each of the steps below will analyze the two parts. Additional comments for a match to 'Pass' or 'Fail' is explained within braces.
Step 1:
(i) .* = xfooxxxxxxfoo - PASS ('.*' is a greedy quantifier and will use the entire Input String)
(ii) foo = No character left to match after index 13 - FAIL
Match failed.
Step 2:
(i) .* = xfooxxxxxxfo - PASS (Backtracking on the greedy quantifier '.*')
(ii) foo = o - FAIL
Match failed.
Step 3:
(i) .* = xfooxxxxxxf - PASS (Backtracking on the greedy quantifier '.*')
(ii) foo = oo - FAIL
Match failed.
Step 4:
(i) .* = xfooxxxxxx - PASS (Backtracking on the greedy quantifier '.*')
(ii) foo = foo - PASS
Report MATCH
Result: 1 match(es)
I found the text "xfooxxxxxxfoo" starting at index 0 and ending at index 13.
Reluctant - Match as little as possible to the reluctant quantifier and match the entire regex. if there is no match, add characters to the reluctant quantifier.
Input String: xfooxxxxxxfoo
Regex: .*?foo
The above regex has two parts:
(i) '.*?' and
(ii) 'foo'
Step 1:
.*? = '' (blank) - PASS (Match as little as possible to the reluctant quantifier '.*?'. Index 0 having '' is a match.)
foo = xfo - FAIL (Cell 0,1,2 - i.e index between 0 and 3)
Match failed.
Step 2:
.*? = x - PASS (Add characters to the reluctant quantifier '.*?'. Cell 0 having 'x' is a match.)
foo = foo - PASS
Report MATCH
Step 3:
.*? = '' (blank) - PASS (Match as little as possible to the reluctant quantifier '.*?'. Index 4 having '' is a match.)
foo = xxx - FAIL (Cell 4,5,6 - i.e index between 4 and 7)
Match failed.
Step 4:
.*? = x - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4.)
foo = xxx - FAIL (Cell 5,6,7 - i.e index between 5 and 8)
Match failed.
Step 5:
.*? = xx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 5.)
foo = xxx - FAIL (Cell 6,7,8 - i.e index between 6 and 9)
Match failed.
Step 6:
.*? = xxx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 6.)
foo = xxx - FAIL (Cell 7,8,9 - i.e index between 7 and 10)
Match failed.
Step 7:
.*? = xxxx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 7.)
foo = xxf - FAIL (Cell 8,9,10 - i.e index between 8 and 11)
Match failed.
Step 8:
.*? = xxxxx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 8.)
foo = xfo - FAIL (Cell 9,10,11 - i.e index between 9 and 12)
Match failed.
Step 9:
.*? = xxxxxx - PASS (Add characters to the reluctant quantifier '.*?'. Cell 4 thru 9.)
foo = foo - PASS (Cell 10,11,12 - i.e index between 10 and 13)
Report MATCH
Step 10:
.*? = '' (blank) - PASS (Match as little as possible to the reluctant quantifier '.*?'. Index 13 is blank.)
foo = No character left to match - FAIL (There is nothing after index 13 to match)
Match failed.
Result: 2 match(es)
I found the text "xfoo" starting at index 0 and ending at index 4.
I found the text "xxxxxxfoo" starting at index 4 and ending at index 13.
Possessive - Match as much as possible to the possessive quantifer and match the entire regex. Do NOT backtrack.
Input String: xfooxxxxxxfoo
Regex: .*+foo
The above regex has two parts: '.*+' and 'foo'.
Step 1:
.*+ = xfooxxxxxxfoo - PASS (Match as much as possible to the possessive quantifier '.*')
foo = No character left to match - FAIL (Nothing to match after index 13)
Match failed.
Note: Backtracking is not allowed.
Result: 0 match(es)
Greedy: "match the longest possible sequence of characters"
Reluctant: "match the shortest possible sequence of characters"
Possessive: This is a bit strange as it does NOT (in contrast to greedy and reluctant) try to find a match for the whole regex.
By the way: No regex pattern matcher implementation will ever use backtracking. All real-life pattern matcher are extremely fast - nearly independent of the complexity of the regular expression!
Greedy Quantification involves pattern matching using all of the remaining unvalidated characters of a string during an iteration. Unvalidated characters start in the active sequence. Every time a match does not occur, the character at the end is quarantined and the check is performed again.
When only leading conditions of the regex pattern are satisfied by the active sequence, an attempt is made to validate the remaining conditions against the quarantine. If this validation is successful, matched characters in the quarantine are validated and residual unmatched characters remain unvalidated and will be used when the process begins anew in the next iteration.
The flow of characters is from the active sequence into the quarantine. The resulting behavior is that as much of the original sequence is included in a match as possible.
Reluctant Quantification is mostly the same as greedy qualification except the flow of characters is the opposite--that is, they start in the quarantine and flow into the active sequence. The resulting behavior is that as little of the original sequence is included in a match as possible.
Possessive Quantification does not have a quarantine and includes everything in a fixed active sequence.

How exactly does the possessive quantifier work?

At the end of the page there is at attempted explanation of how do greedy, reluctant and possessive quantifiers work: http://docs.oracle.com/javase/tutorial/essential/regex/quant.html
However I tried myself an example and I don't seem to understand it fully.
I will paste my results directly:
Enter your regex: .*+foo
Enter input string to search: xfooxxxxxxfoo
No match found.
Enter your regex: (.*)+foo
Enter input string to search: xfooxxxxxxfoo
I found the text "xfooxxxxxxfoo" starting at index 0 and ending at index 13.
Why does the first reg.exp. find no match and the second does?
What is the exact difference between those 2 reg.exp.?
The + after another quantifier means "don't allow the regex engine to backtrack into whatever the previous token has matched". (See a tutorial on possessive quantifiers here).
So when you apply .*foo to "xfooxxxxxxfoo", the .* first matches the entire string. Then, since foo can't be matched, the regex engine backtracks until that's possible, achieving a match when .* has matched "xfooxxxxxx" and foo has matched "foo".
Now the additional + prevents that backtracking from happening, so the match fails.
When you write (.*)+foo. the + takes on an entirely different meaning; now it means "one or more of the preceding token". You've created nested quantifiers, which is not a good idea, by the way. If you apply that regex to a string like "xfoxxxxxxxxxfox", you'll run into catastrophic backtracking.
The possessive quantifier takes the entire string and checks if it matches, if not it fails. In your case xfooxxxxxxfoo matches the .*+ but then you ask for another foo, which isn't present, so the matcher fails.
The greedy quantifier first does the same, but instead of failing it "backs off" and tries again:
xfooxxxxxxfoo fail
xfooxxxxxxfo fail
xfooxxxxxxf fail
xfooxxxxxx match
In your second regex you ask for something else by confusing the grouping mechanism. You ask for "one or more matches of (.*)" as the + now relates to the () and there is one match.

Greedy Quantifiers

I was reading K.Sierra and found the following sentance:
The greedy quantifier does in fact read the entire source data, and then it works
backward (from the right) until it finds the rightmost match. At that point, it
includes everything from earlier in the source data up to and including the data that
is part of the rightmost match.
Now, Suppose we have a source as follows:
"proj3.txt,proj1sched.pdf,proj1,proj2,proj1.java"
and pattern: proj1([^,])*
why doesn't it match the whole text? Being greedy it should have match the rightmost "proj1.java" and the returned match should have been the entire source before the right most match? Instead it returns:
proj1sched.pdf
proj1
proj1.java
why doesn't it match the whole text?
Because you stated it must start with proj1
Being greedy it should have match the rightmost "proj1.java"
correct.
and the returned match should have been the entire source before the right most match?
no idea why you would think that, or why that would be useful. You can just do .*proj1.* if that is what you want.
why doesn't it match the whole text?
Oh, it tried. But it found the sequence p, r, o, j, 1 in one spot, then went on to find zero or more characters not being a comma, therefore matching ., p, d, f. And it stopped there, since the next character, being a comma, did not match [^,].
Note that the next matching attempt will start at the next character, ie r, and so on until it finds a p; when it finds one, it will try r, etc etc.
The regex being satisfied in its entirety, the engine decided that it was a success and didn't try any further, even though there are matches beyond that point.
The text matched is therefore proj1.pdf. And not the entire input. Regular expressions are lazy, they only match what they need to match and never go any further.
BUT. And this is where it gets interesting. Some engines don't work this way.
Consider the regex cat(|flap) and the input text catflap. POSIX has had a go at regex engines, and dictated that a regex engine should match the leftmost, longest match.
So, if a regex engine obeys POSIX, it should match catflap. But most regex engines in existence, here, will only match cat: the empty alternation matches first, the regex is satisfied, end of story!
Now, to the core of the question: quantifiers are of three types, greedy, lazy and possessive:
greedy: the default, *;
lazy, aka the overused: *?;
possessive: *+.
A greedy quantifier will try and match as much text as it can, and give back only when it has to; a lazy quantifier will try and match as little text as it can; a possessive quantifier will try and match as much text as it can, and it will not give text back.
Illustration: here is the input text:
The answer to everything is 42, says the mouse
Here are three regexes to match this text, with a capturing group:
.*(\d+) (greedy);
.*?(\d+) (lazy);
.*+(\d+) (possessive).
Question: what will the group capture in each of these expressions? Answer:
the first: 2;
the second: 42;
the third: will not even match the text! .*+ will have swallowed everything but will not give back, \d+ is therefore left with nothing which can match, regex failure.
We have proj1([^,])* in which -
([^,])* means it will concatenate sub-string of any combination of
characters (occurred zero or more times), which does not consists of char ',' with string "proj1" like:
"sched.pdf" or " " or ".java" all three does not include a ',' character. Hence the result.

Matching Multiple Patterns in One Line

Can someone please tell me why my pattern: <p(\s+(.*)?)?>(.[^</p>]*)?</p> does not work correctly. Example matches:
<p>This is a test and anything can be here even other <tags>tags</tags></p>
<p style="test">This is a test</p>
<p></p>
And if the above were all on one line it should find 3 separate patterns. The link below demonstrates its true behaviour which is very odd...
http://regexr.com?33jrn
The matches it finds should always immediately start when it finds <p and immediately stop when it finds </p>
There are a couple of problems with your regex. Let's see what they look like.
Here's your regex: -
<p(\s+(.*)?)?>(.[^</p>]*)?</p>
Problem 1: - Notice the pattern (.*)?. It is not doing what you think. It is not a enforcing a reluctant behaviour on * quantifier. Rather it's a enforcing an optional quantifier (?) over a greedy * quantifier. It simply means match 0 or 1 repetition of (.*). For making it reluctant, you need to move ? inside the bracket. So, you need to use (.*?) instead of (.*)?.
Problem 2: - [^</p>] does not negate </p> rather it negates - <, /, p, > as separate characters. Note that in a character class, each character is taken literally. There is not grouping in there. So, (.[^</p>]*) means match a character if is not followed by 0 or more repetition of either of [</p>]. That is not what you want. If you want to match a sequence that is not </p>, then you can use a negative look-ahead like this: - ((?!</p>).)*. Now this will check first whether the following sequence is not </p>, then it matches the next character.
So, your regex pattern should be: -
<p(\s+(.*?))?>((?!</p>).)*</p>
Or, you can even simplify your regex to: -
<p[^>]*>((?!</p>).)*</p>
Try this:
<p.*?>.*?</p>
Please read about greedy and reluctant on this page: "Differences Among Greedy, Reluctant, and Possessive Quantifiers".
The problem is in (.[^</p>]*)?, which means:
a single char
followed by any char n times but not a <, neither a /, nor a p and nor a >
I guess you wanted to mean not the </p> string n times, but this is not the way to do it.
Try with .*? instead: <p(\s+(.*)?)?>.*?</p>.
While .* means match the longest string, .*? means match the shortest string.
For example, for the string #foo#bar#, .* will match #foo#bar# while .*? will match #foo#.

What is the difference between `Greedy` and `Reluctant` regular expression quantifiers?

From the Pattern javadocs:
Greedy quantifiers:
X? X, once or not at all
X* X, zero or more times
X+ X, one or more times
X{n} X, exactly n times
X{n,} X, at least n times
X{n,m} X, at least n but not more than m times
Reluctant quantifiers:
X?? X, once or not at all
X*? X, zero or more times
X+? X, one or more times
X{n}? X, exactly n times
X{n,}? X, at least n times
X{n,m}? X, at least n but not more than m times
The description of what they do is the same...so, what is the difference?
I would really appreciate some examples.
I am coding in Java, but I hear this concept is the same for most modern regex implementations.
A greedy operator always try to "grab" as much of the input as possible, while a reluctant quantifier will match as little of the input as possible and still create a match.
Example:
"The red fox jumped over the red fence"
/(.*)red/ => \1 = "The red fox jumped over the "
/(.*?)red/ => \1 = "The "
"aaa"
/a?a*/ => \1 = "a", \2 = "aa"
/a??a*/ => \1 = "", \2 = "aaa"
"Mr. Doe, John"
/^(?:Mrs?.)?.*\b(.*)$/ => \1 = "John"
/^(?:Mrs?.)?.*?\b(.*)$/ => \1 = "Doe, John"
From this link, where the tutorial author acknowledges the spirit of your question:
At first glance it may appear that
the quantifiers X?, X?? and X?+ do
exactly the same thing, since they all
promise to match "X, once or not at
all". There are subtle implementation
differences which will be explained
near the end of this section.
They go on to put together examples and offer the explanation:
Greedy quantifiers are considered
"greedy" because they force the
matcher to read in, or eat, the entire
input string prior to attempting the
first match. If the first match
attempt (the entire input string)
fails, the matcher backs off the input
string by one character and tries
again, repeating the process until a
match is found or there are no more
characters left to back off from.
Depending on the quantifier used in
the expression, the last thing it will
try matching against is 1 or 0
characters.
The reluctant quantifiers, however,
take the opposite approach: They start
at the beginning of the input string,
then reluctantly eat one character at
a time looking for a match. The last
thing they try is the entire input
string.
And for extra credit, the possessive explanation:
Finally, the possessive quantifiers
always eat the entire input string,
trying once (and only once) for a
match. Unlike the greedy quantifiers,
possessive quantifiers never back off,
even if doing so would allow the
overall match to succeed.
A greedy quantifier will match as much as possible and still get a match
A reluctant quantifier will match the smallest amount possible.
for example given the string
abcdef
the greedy qualifier
ab[a-z]*[a-z] would match abcdef
the reluctant qualifier
ab[a-z]*?[a-z] would match abc
say you have a regex "a\w*b", and use it on "abab"
Greedy matching will match "abab" (it looks for an a, as much occurrences of \w as possible, and a b) and reluctant matching will match just "ab" (as little \w as possible)
There is documentation on how Perl handles these quantifiers perldoc perlre.
By default, a quantified subpattern is "greedy", that is, it will match as many times as possible (given a particular starting location) while still allowing the rest of the pattern to match. If you want it to match the minimum number of times possible, follow the quantifier with a "?". Note that the meanings don't change, just the "greediness":
*? Match 0 or more times, not greedily
+? Match 1 or more times, not greedily
?? Match 0 or 1 time, not greedily
{n}? Match exactly n times, not greedily
{n,}? Match at least n times, not greedily
{n,m}? Match at least n but not more than m times, not greedily
By default, when a quantified subpattern does not allow the rest of the overall pattern to match, Perl will backtrack. However, this behaviour is sometimes undesirable. Thus Perl provides the "possessive" quantifier form as well.
*+ Match 0 or more times and give nothing back
++ Match 1 or more times and give nothing back
?+ Match 0 or 1 time and give nothing back
{n}+ Match exactly n times and give nothing back (redundant)
{n,}+ Match at least n times and give nothing back
{n,m}+ Match at least n but not more than m times and give nothing back
For instance,
'aaaa' =~ /a++a/
will never match, as the a++ will gobble up all the a 's in the string and won't leave any for the remaining part of the pattern. This feature can be extremely useful to give perl hints about where it shouldn't backtrack. For instance, the typical "match a double-quoted string" problem can be most efficiently performed when written as:
/"(?:[^"\\]++|\\.)*+"/
as we know that if the final quote does not match, backtracking will not help. See the independent subexpression (?>...) for more details; possessive quantifiers are just syntactic sugar for that construct. For instance the above example could also be written as follows:
/"(?>(?:(?>[^"\\]+)|\\.)*)"/

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