It is the
sports event of the year for the residents of Sportsville. Their team had finally made it to the finals
of the Bowls League Cup.
Problem
Description
It is the
sports event of the year for the residents of Sportsville. Their team had finally made it to the finals
of the Bowls League Cup.
They have
booked tickets for the city contingent for the same row, and the size of the
contingent (N) is smaller than the number of seats booked(S).Unfortunately,
there was rain the previous night and some of the seats are still wet. Some of
the contingent love Bowls so much and are excited enough not to mind sitting on
a wet chair. There are k of these. However, others want to sit on a dry seat so
that they can enjoy the match more.
The
contingent wants to minimize the distance between the first and last person in
the row so that they can still conduct Mexican Waves, and other forms of
support for their team.
Because they
want to sit together, any block of 15 or more contiguous unoccupied seats
between the first person sitting and the last person sitting is unacceptable.
There are M
blocks of seats, starting with a dry block, with alternating wet and dry
blocks. The number of seats in each
block is known.
Given S (the
number of seats in the row), N (the size of the contingent),k (the number of
the contingent who are willing to sit in a wet seat), and the distribution of
wet and dry blocks, write a program to find the minimum distance between the
first and the last member of the contingent in the row.
Input
The first
line contains four comma separated numbers representing S, N, k and M
respectively.
The second
line is a set of M comma separated numbers representing the number of seats in
each block of seats. The first block is
dry, and the remaining blocks alternate between wet and dry.
Output
One integer
representing the minimum distance between the first and last member of the
row. If it is impossible to seat all the
members according to their preferences,and with the unoccupied seat
restriction, the result should be 0.
Constraints
S,N,k <
1000, M < 30
Example 1
Input
100,50,5,6
3,10,30,5,30,22
Output
49
Explanation
S = 100, and
there are 100 seats in the row. N=50,
and there are 50 members in the contingent. k=5, and 5 people (out of the 50)
do not mind sitting on wet seats. M=6,
and there are 6 blocks of seats. The
number of seats in each block is 3,10,30,5,30 and 22, with the first block of 3
seats being dry, the next 10 being wet and so on.
One possible
positioning to achieve the minimum distance is to place the a set of 30 people
in seats 14 to 43 (the dry block), the 5 people who do not mind sitting on wet
seats in the wet block 44 to 48, and the remaining 15 people (of the 50) in the
seats 49 to 63. There is no unoccupied
seat between the first person and the last person, and so this is
acceptable.The distance between the last allocated seat (63) and the first
allocated seat (14), is 49. This is the
output.
Example 2
Input
100,50,5,8
3,7,10,10,20,10,20,20
Output
64
Explanation
S = 100, and
there are 100 seats in the row. N=50,
and there are 50 members in the contingent. k=5, and 5 people (out of the 50)
do not mind sitting on wet seats. M=8,
and there are 8 blocks of seats.
One possible
positioning is to have a set of 10 people sit in the dry block 11 – 20, the 5
people who will accept wet seats in seats 21 – 25 (in the wet block 21 –
30), another 20 people in the dry block 31 – 50, leave the wet block 51-60
empty, and seat the remaining 15 people in seats 61 – 75 (in the dry block
61-80. There is a block of 5 unoccupied
seats (26-30) between the first person and the last person. As this is not more than 15, this is
acceptable. The distance from the last allocated seat (75) and the first
allocated seat (11) is 64. This is the
result.
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