# Broken necklace(USACO training gateway)

hi everyone,
I try to solve “Broken Necklace” problem in USACO training. problem is:
Broken Necklace
You have a necklace of N red, white, or blue beads (3<=N<=350) some of which are red, others blue, and others white, arranged at random. Here are two examples for n=29:

``````            1 2                               1 2
r b b r                           b r r b
r         b                       b         b
r           r                     b           r
r             r                   w             r
b               r                 w               w
b                 b               r                 r
b                 b               b                 b
b                 b               r                 b
r               r                 b               r
b             r                   r             r
b           r                     r           r
r       r                         r       b
r b r                             r r w
Figure A                         Figure B
``````

The beads considered first and second in the text that follows have been marked in the picture.

The configuration in Figure A may be represented as a string of b’s and r’s, where b represents a blue bead and r represents a red one, as follows: brbrrrbbbrrrrrbrrbbrbbbbrrrrb .

Suppose you are to break the necklace at some point, lay it out straight, and then collect beads of the same color from one end until you reach a bead of a different color, and do the same for the other end (which might not be of the same color as the beads collected before this).

Determine the point where the necklace should be broken so that the most number of beads can be collected.

Example

For example, for the necklace in Figure A, 8 beads can be collected, with the breaking point either between bead 9 and bead 10 or else between bead 24 and bead 25.

In some necklaces, white beads had been included as shown in Figure B above. When collecting beads, a white bead that is encountered may be treated as either red or blue and then painted with the desired color. The string that represents this configuration will include the three symbols r, b and w.

Write a program to determine the largest number of beads that can be collected from a supplied necklace.

INPUT FORMAT

Line 1: N, the number of beads
Line 2: a string of N characters, each of which is r, b, or w

29
wwwbbrwrbrbrrbrbrwrwwrbwrwrrb
OUTPUT FORMAT

A single line containing the maximum of number of beads that can be collected from the supplied necklace.

11
OUTPUT EXPLANATION

Consider two copies of the beads (kind of like being able to runaround the ends). The string of 11 is marked.
original ‘split’
v

wwwbbrwrbrbrrbrbrwrwwrbwrwrrb|wwwbbrwrbrbrrbrbrwrwwrbwrwrrb

``````                   ******|*****
rrrrrb|bbbbb  <-- assignments
5 x r  6 x b  <-- 11 total
``````

I solved this problem but my program didn’t pass one test which is
N=77, and strings is:“rwrwrwrwrwrwrwrwrwrwrwrwbwrwbwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwr”
answer must be 74 but I don’t understand how is it possible? can anyone explain me how is the answer equal 74?

P.S: if it is forbidden to write another website problem ,please delete my question.

The answer is 74 because according to the question the white beads can be considered as either blue or red according to the given situation…

For example, if N=6 and the string be “rwbwrb”, the answer would be 4. This is because if you cut the necklace at position 2 (or “rw | bwrb”), you will get 2 beads (“rw” => “rr”) to the left and 2 beads (“bw” => “bb”) to the right.

It happens the same way in the test case your program is giving erroneous output.

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ok I know but if you watch the test case if I cut the necklace at position 29 “rwrwrwrwrwrwrwrwrwrwrwrwbwrwb|wrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwr” in this case I have 48 red which is the right part. and lef part I have 24 red so max collected beads is 72 not 74

@shikimaru: See the necklace is circular right…

so we can write the given string as “bwrwbwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrrwrwrwrwrwrwrwrwrwrwrwrw” instead of “rwrwrwrwrwrwrwrwrwrwrwrwbwrwbwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwr”…

Now cut the necklace at position 5…

“bwrwb|wrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrrwrwrwrwrwrwrwrwrwrwrwrw”… you will get 72 red to your right and 2 blue to your left which will give 74 as the answer…

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thank you very much

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