[Leetcode] Problem 959 - Regions Cut By Slashes

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In a N x N grid composed of 1 x 1 squares, each 1 x 1 square consists of a /, \, or blank space. These characters divide the square into contiguous regions.

(Note that backslash characters are escaped, so a \ is represented as “\\“.)

Return the number of regions.

Example

No.1

Input:

1
2
3
4
[
  " /",
  "/ "
]

Output: 2

Explanation: The 2x2 grid is as follows:

0tEV1A.png

No.2

Input:

1
2
3
4
[
  " /",
  "  "
]

Output: 1

Explanation: The 2x2 grid is as follows:

0tE8pj.png

No.3

Input:

1
2
3
4
[
  "\\/",
  "/\\"
]

Output: 4

Explanation: (Recall that because \ characters are escaped, “\\/“ refers to \/, and “/\\“ refers to /\.)
The 2x2 grid is as follows:

0tEycR.png

No.4

Input:

1
2
3
4
[
  "/\\",
  "\\/"
]

Output: 5

Explanation: (Recall that because \ characters are escaped, “/\\“ refers to /\, and “\\/“ refers to \/.)
The 2x2 grid is as follows:

0tE7jI.png

No.5

Input:

1
2
3
4
[
  "//",
  "/ "
]

Output: 3

Explanation: The 2x2 grid is as follows:

0tVpgs.png

Note

  1. 1 <= grid.length == grid[0].length <= 30
  2. grid[i][j] is either ‘/‘, ‘\‘, or ‘ ‘.

Code

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public class UnionFind {
    private int[] id;
    private int[] size;
    private int count;

    public UnionFind(int n) {
        this.id = new int[n];
        this.size = new int[n];
        count = n;

        for (int i = 0; i < n; i++) {
            id[i] = i;
            size[i] = 1;
        }
    }

    public int count() {
        return count;
    }

    public boolean union(int p, int q) {
        int pRoot = find(p);
        int qRoot = find(q);

        if (pRoot == qRoot)
            return false;

        if (size[pRoot] < size[qRoot]) {
            id[pRoot] = qRoot;
            size[qRoot] += size[pRoot];
        } else {
            id[qRoot] = pRoot;
            size[pRoot] += size[qRoot];
        }

        count--;

        return true;
    }

    public int find(int p) {
        while (p != id[p])
            p = id[p];

        return p;
    }
}

public int regionsBySlashes(String[] grid) {
    int n = grid.length;
    UnionFind uf = new UnionFind(4 * n * n);

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            int idx = 4 * (i * n + j);

            if (grid[i].charAt(j) == '/') {
                uf.union(idx, idx + 3);
                uf.union(idx + 1, idx + 2);
            } else if (grid[i].charAt(j) == '\\') {
                uf.union(idx, idx + 1);
                uf.union(idx + 2, idx + 3);
            } else {
                uf.union(idx, idx + 1);
                uf.union(idx + 1, idx + 2);
                uf.union(idx + 2, idx + 3);
            }

            if (i < n - 1)
                uf.union(idx + 2, idx + 4 * n);

            if (j < n - 1)
                uf.union(idx + 1, idx + 4 + 3);
        }
    }

    return uf.count();
}