Want to try solving this problem? You can submit your code online if you log in or register.

It's that time of year again! The Annual Ruckus World Championships is fast
approaching and you are absolutely determined to see Australia victorious.
As the name implies, the goal of the competition is to be as loud and obnoxious
as possible. Players compete in teams of at least *M* people (there is no upper
limit on team sizes). To make sure teams don't mix, team members must hold hands
with each other.

Of course, you've found that there is nothing more obnoxious than spoilt
kindergarteners, so you've rounded up *N* of the loudest ones you could find.
You were hoping to send as many teams as possible, but some of the children have
already started holding hands with their friends. Being as stubborn as they are, you are finding it
rather difficult to convince them to let go of each other, or even to hold hands
with anyone else.

Now for any other person, the story would end here; you'd have to send whatever teams
their 'friendships' have forged. However, being the social engineering master
you are, you've brought *K* lollipops to use to bribe the children. You can pass a
lollipop to the hand of a child, which will make them let go of the hand
they are holding.

Using your *K* lollipops, what is the largest number of teams with at
least *M* children you can form?

The first line of the input file will contain four space separated integers on a single line, in
the format: *N L K M*.

*N*is the number of children you have gathered.*L*is the number of pairs of hands that are already joined together.*K*is the number of lollipops you have.*M*is the minimum size of a team. All teams must have at least*M*people.

The following *L* lines will each contain two integers, in the format:
*l _{i} r_{i}*. This indicates that the

Output should consist of a single integer: the maximum number of teams with at least
*M* children you can form.

8 6 0 1 1 2 4 6 5 4 2 3 7 5 6 7

3

In the first example, you cannot break up any pair of hands (since you
have no lollipops), and teams can have any number of people in them. Initially,
the children have formed three teams: one of size 3, one of size 4 and
one of size 1. Thus the output should be `3`

.

15 13 5 2 1 2 2 6 6 10 10 7 8 9 9 8 3 4 4 5 15 11 11 12 12 13 13 14 14 15

6

In the second example, each team needs at least 2 people. Currently there
are four teams of size 2, 3, 5 and 5. (The team of size 2 consists of
children 8 and holding both hands with each other.)
By breaking the friendships 6-10, 14-15 and 11-12, we can create up to
six teams, of size 2, 2, 2, 3, 3 and 3. Thus the best answer is `6`

.

Note that even though we have 5 lollipops, we don't have to use them all in order to make the maximum number of teams (even though we can).

- For Subtask 1 (20 marks),
*K = 0, M = 1*and*N ≤ 1,000*. - For Subtask 2 (20 marks),
*K = 0*and*N ≤ 100,000*. - For Subtask 3 (20 marks),
*N ≤ 100,000*and everybody is holding hands with exactly two other people. - For Subtask 4 (20 marks),
*N ≤ 100,000*. Additionally, if the*i*th person is holding hands with two people, then they are holding hands with one person with a number less than them and one with a number greater. If they are holding hands with one or no person, this condition does not apply. - For Subtask 5 (20 marks),
*N ≤ 100,000*and no further constraints apply.

Privacy
statement

© Australian Mathematics Trust 2001-2021

Page generated: 21 April 2021, 6:52pm AEST