959. Regions Cut By Slashes
Medium
Topics: Array, Hash Table, Depth-First Search, Breadth-First Search, Union Find, Matrix
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:
We can represent each 1×1 square as 4 triangles, which allows us to apply a Union-Find (Disjoint Set Union, DSU) algorithm to count the distinct regions.
Step-by-Step Approach:
Grid Representation:
We treat each 1×1 square as 4 triangles:
Top-left triangle
Top-right triangle
Bottom-left triangle
Bottom-right triangle
Each of these triangles is represented by an index in the Union-Find structure.
Mapping Characters:
If the square is ‘ ‘, all 4 triangles within it are connected.
If the square is ‘/’, the top-left triangle is connected to the bottom-right, and the top-right triangle is connected to the bottom-left.
If the square is ”, the top-left triangle is connected to the top-right, and the bottom-left triangle is connected to the bottom-right.
Connecting Adjacent Cells:
We connect the triangles of adjacent cells across the grid’s boundaries. This ensures that regions spanning multiple cells are properly connected.
Counting the Regions:
We count the number of unique sets in the Union-Find structure, which corresponds to the number of regions.
Let’s implement this solution in PHP: 959. Regions Cut By Slashes
// Test cases
$grid1 = [” /”, “/ “];
$grid2 = [” /”, ” “];
$grid3 = [“/\“, “\/”];
echo regionsBySlashes($grid1); // Output: 2
echo regionsBySlashes($grid2); // Output: 1
echo regionsBySlashes($grid3); // Output: 5
?>
Explanation:
The UnionFind class is used to manage the connected components (regions) in the grid.
For each cell in the grid, we apply the union operation based on the character (‘/’, ”, or ‘ ‘).
Finally, the number of unique regions is determined by counting the distinct root parents in the Union-Find structure.
This solution efficiently handles the problem within the given constraints.
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