7007: ABC269 —— D - Do use hexagon grid
[Creator : ]
Description
We have an infinite hexagonal grid shown below. Initially, all squares are white.
A hexagonal cell is represented as $(i,j)$ with two integers $i$ and $j$.
Cell $(i,j)$ is adjacent to the following six cells:
Find the number of connected components formed by the black cells.
Two black cells belong to the same connected component when one can travel between those two black cells by repeatedly moving to an adjacent black cell.
A hexagonal cell is represented as $(i,j)$ with two integers $i$ and $j$.
Cell $(i,j)$ is adjacent to the following six cells:
- $(i−1,j−1)$
- $(i−1,j)$
- $(i,j−1)$
- $(i,j+1)$
- $(i+1,j)$
- $(i+1,j+1)$
Find the number of connected components formed by the black cells.
Two black cells belong to the same connected component when one can travel between those two black cells by repeatedly moving to an adjacent black cell.
Input
The input is given from Standard Input in the following format:
$N$
$X_1\ Y_1$
$X_2\ Y_2$
$\vdots$
$X_N\ Y_N$
$N$
$X_1\ Y_1$
$X_2\ Y_2$
$\vdots$
$X_N\ Y_N$
Output
Print the answer as an integer.
Constraints
All values in the input are integers.
$1 \le N \le 1000$
$|X_i|,|Y_i| \le 1000$
The pairs $(X_i,Y_i)$ are distinct.
$1 \le N \le 1000$
$|X_i|,|Y_i| \le 1000$
The pairs $(X_i,Y_i)$ are distinct.
Sample 1 Input
6
-1 -1
0 1
0 2
1 0
1 2
2 0
Sample 1 Output
3
After Takahashi paints cells black, the grid looks as shown below.
The black squares form the following three connected components:
The black squares form the following three connected components:
- $(-1,-1)$
- $(1,0),(2,0)$
- $(0,1),(0,2),(1,2)$
Sample 2 Input
4
5 0
4 1
-3 -4
-2 -5
Sample 2 Output
4
Sample 3 Input
5
2 1
2 -1
1 0
3 1
1 -1
Sample 3 Output
1