University of Toronto ACM-ICPC Tryouts 2012
Having been sucked into your father's secret computer through a projector in the back of his arcade (or something), you find yourself in the wonderful world of Tron! Here, you play games all day, and if you ever lose, you die.
One such game involves you and an opponent driving around a flat grid on
light cycles, which leave behind a permanent trail of...light...wherever
they go. This grid can be modeled with the Cartesian plane, and is
enclosed by a rectangle of impenetrable walls which ensure that the
-coordinate of each light cycle is always between
and
, while its
-coordinate is between
and
(inclusive). Light cycles always stay on the grid lines, and move at a
speed of
square per second.
A match lasts
seconds. You start at
coordinates
and follow a set of
instructions, with your
instruction consisting of
moving
squares in the direction given by the character
(with
U
, D
, L
, and R
representing up, down, left, and right,
respectively). Similarly, your opponent starts at coordinates
and follows a set of
instructions, with their
instruction described by
and
. Of course, neither player's instructions will ever take them
beyond the boundaries of the walls, and it will take each player exactly
seconds to execute their instructions. Additionally, for each
player, no instruction will have an equal or opposite direction to that
of their previous instruction. Finally, if a grid point is ever visited
more than once throughout the course of the match, it is guaranteed that
one of the path segments intersecting there is passing directly through
vertically, while the other is passing directly through horizontally (as
such, this cannot happen at either player's starting or ending points).
Whenever both light cycles reach the same grid point at the same time,
or a light cycle hits an existing trail of light (in other words, a grid
point which either light cycle had previously passed through), a
collision occurs. Because you're just playing a practice match for now,
neither player dies when this occurs, and, in fact, the collision is not
counted in favour of either you or your opponent. Instead, for
scenarios as described above, you're simply interested in
the number of collisions that will occur throughout each match.
Input Specification
Line 1: 1 integer,
For each scenario:
Line 1: 1 integer,
Next line: 3 integers, ,
, and
Next lines: 1 character,
, and 1 integer,
, for
Next line: 3 integers, ,
, and
Next lines: 1 character,
, and 1 integer,
, for
Output Specification
For each scenario:
1 integer: The total number of collisions that will occur.
Sample Input
1
12
2 5 5
R 4
U 1
L 1
D 4
L 2
3 3 4
U 3
L 2
D 2
R 5
Sample Output
4
Explanation of Sample
The following diagram illustrates the paths of the light cycles (yours drawn in solid lines, and your opponent's drawn in dotted ones), as well as all of the collision points (indicated with large dots):
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