Kenan drew a plan of the buildings and skywalks along one side of the main avenue of
Baku. There are buildings numbered from
to
and
skywalks numbered from
to
. The plan is drawn on a two-dimensional plane, where the buildings and
skywalks are vertical and horizontal segments respectively.
The bottom of building
is located at point
and the building has
height
. Hence, it is a segment connecting the points
and
.
Skywalk
has endpoints at buildings numbered
and
and has a
positive
-coordinate
. Hence, it is a segment connecting the points
and
.
A skywalk and a building intersect if they share a common point. Hence, a skywalk intersects two buildings at its two endpoints, and may also intersect other buildings in between.
Kenan would like to find the length of the shortest path from the bottom of building
to the bottom of building
, assuming that one can only walk along the buildings and
skywalks, or determine that no such path exists. Note that it is not allowed to walk on
the ground, i.e. along the horizontal line with
-coordinate
.
One can walk from a skywalk into a building or vice versa at any intersection. If the endpoints of two skywalks are at the same point, one can walk from one skywalk to the other.
Your task is to help Kenan answer his question.
Implementation details
You should implement the following procedure. It will be called by the grader once for each test case.
long long min_distance(std::vector<int> x, std::vector<int> h, std::vector<int> l, std::vector<int> r, std::vector<int> y, int s, int g)
and
: integer arrays of length
, and
: integer arrays of length
and
: two integers
- This procedure should return the length of the shortest path between the bottom
of building and the bottom of building
, if such path exists. Otherwise, it should return
.
Examples
Example 1
Consider the following call:
min_distance({0, 3, 5, 7, 10, 12, 14},
{8, 7, 9, 7, 6, 6, 9},
{0, 0, 0, 2, 2, 3, 4},
{1, 2, 6, 3, 6, 4, 6},
{1, 6, 8, 1, 7, 2, 5},
1, 5)
The correct answer is .
The figure below corresponds to Example 1:
Example 2
min_distance({0, 4, 5, 6, 9},
{6, 6, 6, 6, 6},
{3, 1, 0},
{4, 3, 2},
{1, 3, 6},
0, 4)
The correct answer is .
Constraints
for all
for all
for all
- No two skywalks have a common point, except maybe on their endpoints.
Subtasks
- (
points)
- (
points) Each skywalk intersects at most
buildings.
- (
points)
, and all buildings have the same height.
- (
points)
- (
points) No additional constraints.
Sample grader
The sample grader reads the input in the following format:
- line
:
- line
:
- line
:
- line
:
The sample grader prints a single line containing the return value of min_distance
.
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