Canadian Computing Competition: 2009 Stage 2, Day 1, Problem 2
On the way to dinner, the CCC competitors are lining up for their delicious curly fries. The ~N~ ~(1 \le N \le 100)~ competitors have lined up single-file to enter the cafeteria.
Doctor V, who runs the CCC, realized at the last minute that programmers simply hate standing in line next to programmers who use a different language. Thankfully, only two languages are allowed at the CCC: Gnold and Helpfile. Furthermore, the competitors have decided that they will only enter the cafeteria if they are in a group of at least ~K~ ~(1 \le K \le 6)~ competitors.
Doctor V decided to iterate the following scheme:
- He will find a group of ~K~ or more competitors who use the same language standing next to each other in line and send them to dinner.
- The remaining competitors will close the gap, potentially putting similar-language competitors together.
So Doctor V recorded the sequence of competitors for you. Can all the competitors dine? If so, what is the minimum number of groups of competitors to be sent to dinner?
Note: Test cases worth ~60\%~ of the points have ~K \le 2~. Out of these, on test cases worth one third of the points (~20\%~ of the total points), ~N \le 10~.
The first line contains two integers ~N~ and ~K~.
The second line contains ~N~ characters that are the sequence of competitors in line (
H represents Helpfile,
G represents Gnold)
Output, on one line, the single number that is the minimum number of groups that are
formed for dinner. If not all programmers can dine, output
7 2 GHHGHHG
Description of Sample Input
There are seven competitors: a Gnold programmer followed by two Helpfile programmers, followed by another Gnold programmer, followed by another two Helpfile programmers followed by a final Gnold programmer. Programmers want to go to dinner in pairs.
Output for Sample Input
Description of Output for Sample Input
First send the first pair of
Hs to dinner, leaving
GGHHG. Then send the second pair of
Hs to dinner, leaving
GGG; finally, send in the group of
Gs. It might be coincidental that
the two pairs of Helpfile programmers entered the cafeteria successively.