Regions Cut By Slashes
An n x n
grid is composed of 1 x 1
squares where each 1 x 1
square consists of a '/'
, '\'
, or blank space ' '
. These characters divide the square into contiguous regions.
Given the grid grid
represented as a string array, return the number of regions.
Note that backslash characters are escaped, so a '\'
is represented as '\\'
.
Example 1:
Input: grid = [" /","/ "]
Output: 2
Example 2:
Input: grid = [" /"," "]
Output: 1
Example 3:
Input: grid = ["/\\\\","\\\\/"]
Output: 5
Explanation: Recall that because \ characters are escaped, "\\/" refers to \/, and "/\\" refers to /\.
Constraints:
n == grid.length == grid[i].length
1 <= n <= 30
grid[i][j]
is either'/'
,'\'
, or' '
.
Solution
With the cutted sections, we will join the sections depending on the slashes. For example, '/' means that north
joins west
and south
joins east
.
Note that we must also join the north
region of a square to the south
region of the square to the top of it. Similar for the left square's east
region and current square's west
region.
This is best approached by DSU, in the very end after joining all sections, we just have to find the number of components in the map regions
.
Implementation
1def regionsBySlashes(grid: List[str]) -> int:
2 regions = {}
3 def find(x):
4 y = regions.get(x, x)
5 if y != x:
6 regions[x] = y = find(y)
7 return y
8 def union(x, y):
9 regions[find(x)] = find(y)
10
11 size = len(grid)
12 for i in range(size):
13 for j in range(size):
14 if i > 0: # connect square with top
15 union((i - 1, j, 'S'), (i, j, 'N'))
16 if j > 0: # connect square with left
17 union((i, j - 1, 'E'), (i, j, 'W'))
18 if grid[i][j] != "/": # ' ' or '\'
19 union((i, j, 'N'), (i, j, 'E')) # connect NE
20 union((i, j, 'S'), (i, j, 'W')) # connect SW
21 if grid[i][j] != "\\": # ' ' or '/'
22 union((i, j, 'N'), (i, j, 'W')) # connect NW
23 union((i, j, 'S'), (i, j, 'E')) # connect SE
24 return len(set(map(find, regions)))
Alternatively, we can find the number of connected components as in Number of Coneected Components, but bare in mind that we should only decrease the component count when we know that two elements aren't from the same set.
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