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You do not need to read the Interleaved Output: Part 2 problem to be able to solve this problem. Both Part 1 and Part 2 have the same first two paragraphs (not including this informational text). We have underlined the critical difference between the two parts.
On a distant moon of Jupiter, some developer conference events are about to happen! They are called IO
(uppercase I, uppercase O), Io
(uppercase I, lowercase o), iO
(lowercase I, uppercase O), and io
(lowercase I, lowercase O).
The best way to advertise an event is by using special computers that print the event's name one character at a time, with the output appearing on a digital display. Each such computer only knows the name of one event, and is programmed to print its event's name zero or more times. For example, a computer programmed to print IO
twice prints an I
, followed by an O
, followed by an I
, followed by an O
, for a final string of IOIO
.
You know that the conference organizers are using these computers, but you do not know how many computers are advertising each event. For each event, there may be any number of computers (including zero) programmed to print the event's name. Moreover, the computers are not necessarily all programmed to print the same number of times. For example, it is possible that there are three computers programmed to print Io
once each, and one computer programmed to print Io
twice.
The computers have all finished printing, but unfortunately, they all printed to the same display! Because the computers printed concurrently, event names in the final output string may be interleaved. You are considering the possible ways in which that string could have been produced.
For example, the string IiOioIoO
could have been produced by two computers, as follows:
Io
twiceiO
twiceindex: 1 2 3 4 5 6 7 8 A: I . . . o I o . B: . i O i . . . O string: I i O i o I o O
In this interpretation, the Io
event was advertised twice, the iO
event was advertised twice, and the other two events were not advertised at all.
But the string could have also been produced by three computers:
IO
twiceio
onceio
onceindex: 1 2 3 4 5 6 7 8 A: I . O . . I . O B: . i . . o . . . C: . . . i . . o . string: I i O i o I o O
In this interpretation, the IO
event was advertised twice, the io
event was advertised twice, and the other two events were not advertised at all. Notice that this interpretation required two computers printing io
; there could not have been just one computer printing io
twice, because it would have had to print i
twice in a row, which is not allowed.
Given a final output string, what is the maximum possible number of times that the event IO
could have been advertised?
It is guaranteed that the string has at least one valid interpretation. For example, oI
and IOI
are not valid inputs.
The first line of the input gives the number of test cases, T. T lines follow; each represents a single test case. Each case consists of a string S containing only the characters from the set I
, O
, i
, and o
.
For each test case, output one line containing Case #x: y
, where x
is the test case number (starting from 1) and y
is the maximum number of times IO
could have been advertised, as described above.
i
characters plus the number of I
characters in S' is not less than the number of o
characters plus the number of O
characters in S'.i
s plus the number of I
s in S is equal to the number of o
s plus the number of O
s in S.5 IiOioIoO IiOOIo IoiOiO io IIIIOOOO
Case #1: 2 Case #2: 1 Case #3: 0 Case #4: 0 Case #5: 4
Sample Case #1 is the one described in the problem statement. We saw that there is an interpretation in which IO
was advertised twice. There are only two I
s and two O
s in the string, so the answer cannot be larger than this.
In Sample Case #2, notice that it is not possible that IO
was advertised twice. The only possible interpretations are as follows:
IO
onceiO
onceIo
onceindex: 1 2 3 4 5 6 A: I . . O . . B: . i O . . . C: . . . . I o string: I i O O I o
or the same but with
index: 1 2 3 4 5 6 A: I . O . . . B: . i . O . . C: . . . . I o string: I i O O I o
In either of these interpretations, IO
was advertised only once.
In Sample Case #3, there is no possible interpretation in which IO
was advertised. There must have been one computer programmed to print Io
once, and either one computer printing iO
twice, or two computers printing iO
once each.
In Sample Case #4, notice that it is possible that I
and/or O
might not even show up in the string.
In Sample Case #5, an interpretation in which IO
was advertised four times requires four computers, each of which was programmed to print IO
once.
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