The Dog Task
Time Limit: 2 Seconds
Memory Limit: 65536 KB
Hunter Bob often walks with his dog Ralph. Bob walks with a constant speed
and his route is a polygonal line (possibly self-intersecting) whose vertices
are specified by N pairs of integers (Xi, Yi) - their Cartesian coordinates.
Ralph walks on his own way but always meets his master at the specified N points.
The dog starts his journey simultaneously with Bob at the point (X1, Y1) and
finishes it also simultaneously with Bob at the point (XN, YN).
Ralph can travel at a speed that is up to two times greater than his master's
speed. While Bob travels in a straight line from one point to another the cheerful
dog seeks trees, bushes, hummocks and all other kinds of interesting places
of the local landscape which are specified by M pairs of integers (Xj', Yj').
However, after leaving his master at the point (Xi, Yi) (where 1 <= i <
N) the dog visits at most one interesting place before meeting his master again
at the point (Xi+1, Yi+1).
Your task is to find the dog's route, which meets the above requirements and
allows him to visit the maximal possible number of interesting places. The answer
should be presented as a polygonal line that represents Ralph's route. The vertices
of this route should be all points (Xi, Yi) and the maximal number of interesting
places (Xj', Yj'). The latter should be visited (i.e. listed in the route description)
at most once.
An example of Bob's route (solid line), a set of interesting places (dots) and
one of the best Ralph's routes (dotted line) are presented in the following
The first line of the input contains two integers N and M, separated by a space
(2 <= N <= 100, 0 <= M <= 100). The second line contains N pairs
of integers X1, Y1, ..., XN, YN, separated by spaces, that represent Bob's route.
The third line contains M pairs of integers X1', Y1', ..., XM', YM', separated
by spaces, that represent interesting places.
All points in the input are different and their coordinates are integers not
greater than 1000 by the absolute value.
The first line of the output should contain the single integer K - the number
of vertices of the best dog's route. The second line should contain K pairs
of coordinates X1", Y1", ..., XK", YK", separated by spaces,
that represent this route. If there are several such routes, then you may write
any of them.
This problem contains multiple test cases!
The first line of a multiple input is an integer N, then a blank line followed
by N input blocks. Each input block is in the format indicated in the problem
description. There is a blank line between input blocks.
The output format consists of N output blocks. There is a blank line between
1 4 5 7 5 2 -2 4
-4 -2 3 9 1 2 -1 3 8 -3
1 4 3 9 5 7 5 2 1 2 -2 4
Source: Northeastern Europe 1998