Is Regions Cut By Slashes easy or hard?

Regions Cut By Slashes is rated Medium difficulty on LeetCode with a high acceptance rate around 77%. The challenge lies in modeling the grid correctly rather than implementing complex algorithms. Once the cell subdivision idea or DSU mapping is clear, the implementation becomes straightforward.

How to solve Regions Cut By Slashes in O(n^2)?

Split each grid cell into four triangles and treat them as nodes in a graph. Connect triangles inside the cell depending on whether the character is '/', '\\', or space. Then connect boundary triangles with adjacent cells and run DFS/BFS to count connected components. This traversal visits each triangle once, giving O(n^2) time complexity.

Regions Cut By Slashes Python or Java solution

Python and Java implementations usually follow the triangle subdivision model. Each cell is expanded into four nodes, stored in arrays or adjacency relationships, and explored with DFS/BFS. Alternatively, a DSU structure unions triangles and counts unique parents after processing the grid.

What is the best approach for Regions Cut By Slashes?

Union-Find with cell subdivision into four triangles is the most common optimal approach. Each triangle becomes a node, and union operations connect triangles inside the cell and with neighboring cells. After processing the grid, the number of disjoint sets equals the number of regions. Time complexity is O(n^2 α(n)) with near-constant DSU operations.

Is Regions Cut By Slashes asked at Google/Amazon/Meta?

Grid connectivity and Union-Find problems like Regions Cut By Slashes appear frequently in interviews at companies such as Google, Amazon, and Meta. The problem tests graph modeling, connected components, and DSU implementation skills, which are common patterns in system-level algorithm interviews.

What data structure is used in Regions Cut By Slashes?

Two main data structures are used: graph traversal structures (for DFS or BFS) and Disjoint Set Union (Union-Find). The grid is typically modeled as four subcells per grid cell, and either traversal or DSU tracks connectivity between these regions.

What is the time complexity of Regions Cut By Slashes?

Both common solutions run in O(n^2) time because each grid cell is processed a constant number of times. The DFS/BFS subdivision approach explores up to 4*n*n nodes, while the Union-Find approach performs a constant number of union operations per cell. DSU operations add an inverse Ackermann factor α(n), which is effectively constant.

Description Solution Video 16:06

959. Regions Cut By Slashes

Medium77.8% acceptance6 companies

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 ' '.

Asked at 6 companies

Uber Tiktok

Google Amazon Microsoft Meta

Topics

16:06

Still stuck?Read 4 approaches, or watch a walkthrough.

Open solution

LanguageLoading editor…

1class Solution:
2    def regionsBySlashes(self, grid: List[str]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[" /","/ "]

Input

[" /","  "]

Input

["/\\","\\/"]

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