# 959. Regions Cut By Slashes

## Description

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 ' '.

## Solutions

• class Solution {
private int[] p;
private int size;

public int regionsBySlashes(String[] grid) {
int n = grid.length;
size = n * n * 4;
p = new int[size];
for (int i = 0; i < p.length; ++i) {
p[i] = i;
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
int k = i * n + j;
if (i < n - 1) {
union(4 * k + 2, (k + n) * 4);
}
if (j < n - 1) {
union(4 * k + 1, (k + 1) * 4 + 3);
}
char v = grid[i].charAt(j);
if (v == '/') {
union(4 * k, 4 * k + 3);
union(4 * k + 1, 4 * k + 2);
} else if (v == '\\') {
union(4 * k, 4 * k + 1);
union(4 * k + 2, 4 * k + 3);
} else {
union(4 * k, 4 * k + 1);
union(4 * k + 1, 4 * k + 2);
union(4 * k + 2, 4 * k + 3);
}
}
}
return size;
}

private int find(int x) {
if (p[x] != x) {
p[x] = find(p[x]);
}
return p[x];
}

private void union(int a, int b) {
int pa = find(a);
int pb = find(b);
if (pa == pb) {
return;
}
p[pa] = pb;
--size;
}
}

• class Solution {
public:
vector<int> p;
int size;

int regionsBySlashes(vector<string>& grid) {
int n = grid.size();
size = n * n * 4;
p.resize(size);
for (int i = 0; i < size; ++i) p[i] = i;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
int k = i * n + j;
if (i < n - 1) merge(4 * k + 2, (k + n) * 4);
if (j < n - 1) merge(4 * k + 1, (k + 1) * 4 + 3);
char v = grid[i][j];
if (v == '/') {
merge(4 * k, 4 * k + 3);
merge(4 * k + 1, 4 * k + 2);
} else if (v == '\\') {
merge(4 * k, 4 * k + 1);
merge(4 * k + 2, 4 * k + 3);
} else {
merge(4 * k, 4 * k + 1);
merge(4 * k + 1, 4 * k + 2);
merge(4 * k + 2, 4 * k + 3);
}
}
}
return size;
}

void merge(int a, int b) {
int pa = find(a);
int pb = find(b);
if (pa == pb) return;
p[pa] = pb;
--size;
}

int find(int x) {
if (p[x] != x) p[x] = find(p[x]);
return p[x];
}
};

• class Solution:
def regionsBySlashes(self, grid: List[str]) -> int:
def find(x):
if p[x] != x:
p[x] = find(p[x])
return p[x]

def union(a, b):
pa, pb = find(a), find(b)
if pa != pb:
p[pa] = pb
nonlocal size
size -= 1

n = len(grid)
size = n * n * 4
p = list(range(size))
for i, row in enumerate(grid):
for j, v in enumerate(row):
k = i * n + j
if i < n - 1:
union(4 * k + 2, (k + n) * 4)
if j < n - 1:
union(4 * k + 1, (k + 1) * 4 + 3)
if v == '/':
union(4 * k, 4 * k + 3)
union(4 * k + 1, 4 * k + 2)
elif v == '\\':
union(4 * k, 4 * k + 1)
union(4 * k + 2, 4 * k + 3)
else:
union(4 * k, 4 * k + 1)
union(4 * k + 1, 4 * k + 2)
union(4 * k + 2, 4 * k + 3)
return size


• func regionsBySlashes(grid []string) int {
n := len(grid)
size := n * n * 4
p := make([]int, size)
for i := range p {
p[i] = i
}
var find func(x int) int
find = func(x int) int {
if p[x] != x {
p[x] = find(p[x])
}
return p[x]
}
union := func(a, b int) {
pa, pb := find(a), find(b)
if pa == pb {
return
}
p[pa] = pb
size--
}
for i, row := range grid {
for j, v := range row {
k := i*n + j
if i < n-1 {
union(4*k+2, (k+n)*4)
}
if j < n-1 {
union(4*k+1, (k+1)*4+3)
}
if v == '/' {
union(4*k, 4*k+3)
union(4*k+1, 4*k+2)
} else if v == '\\' {
union(4*k, 4*k+1)
union(4*k+2, 4*k+3)
} else {
union(4*k, 4*k+1)
union(4*k+1, 4*k+2)
union(4*k+2, 4*k+3)
}
}
}
return size
}