Regions cut by slashes leetcode 959 python

certainly! the "regions cut by slashes" problem (leetcode 959) is an interesting problem that involves using a union-find (or disjoint set) data structure to determine the number of distinct regions formed by slashes in a grid.

### problem description

you are given a grid of size `n x n` consisting of slashes (`'/'` and `'\\'`). the slashes divide the grid into regions. the goal is to determine how many distinct regions there are in the grid.

each cell can contain:
- a `/` character dividing the cell into two triangles.
- a `\` character dividing the cell into two triangles.
- an empty space that does not divide the cell.

the regions are defined as connected components of triangles. two triangles are in the same region if they share a common edge.

### example

consider the following grid:

the grid can be visualized as:

in this example, there are two distinct regions.

### approach

1. **union-find data structure**: we use a union-find data structure to keep track of connected components. each triangle (upper or lower) can be treated as a separate node.

2. **mapping triangles**: each cell in the grid can be divided into two triangles:
- for a cell `(i, j)`:
- upper triangle is represented by `2 * (i * n + j)`
- lower triangle is represented by `2 * (i * n + j) + 1`

3. **union operations**: based on the character in each cell, we will perform union operations to connect the triangles:
- if the cell contains `/`, connect the upper triangle to the lower triangle of the cell to the left and the lower triangle to the upper triangle of the cell above.
- if the cell contains `\`, connect the lower triangle to the upper triangle of the cell to the right and the upper triangle to the lower triangle of the cell below.

4. **count distinct regions**: finally, we count the number of distinct roots in the union-find structure to determine the number of regions.

### implementation

here’s a python implementation of the above approach:

### e ...

#python cut string before character
#python cut off decimal
#python cutting machine
#python cut open
#python cute

python cut string before character
python cut off decimal
python cutting machine
python cut open
python cute
python cut
python cut string
python cut string to length
python cut open to reveal woman
python cut string after character
python leetcode solutions
python leetcode interview questions
python leetcode cheat sheet
python leetcode 75
python leetcode questions
python leetcode course
python leetcode reddit
python leetcode medium