Finding Disjoint Regions in a Grid (removed duplicate)

Sean Hannity

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09-11-2024

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In computational problems, identifying disjoint regions within a grid is a common task. This can be useful in various applications such as image processing, geographical mapping, and game development. In this article, we will explore how to find disjoint regions in a grid effectively.

Understanding the Grid

A grid can be represented as a two-dimensional array where each cell can be either occupied (1) or empty (0). Disjoint regions are defined as groups of adjacent occupied cells. Two cells are considered adjacent if they are next to each other horizontally or vertically.

Example of a Grid

Consider the following grid representation:

1 1 0 0
0 1 0 1
0 0 0 1
1 0 1 1

In this grid:

• The first region consists of three cells connected vertically and horizontally (the 1s in the first two rows).
• The second region consists of three cells located at different positions.

Algorithm to Find Disjoint Regions

To find the disjoint regions in a grid, we can utilize a depth-first search (DFS) or breadth-first search (BFS) algorithm. Here’s a step-by-step explanation of the DFS approach:

Steps:

1. Initialize a Visited Matrix: Create a boolean matrix to keep track of visited cells.

2. Iterate Through the Grid: Loop through each cell in the grid. When you encounter an occupied cell (1) that hasn't been visited yet, it signifies the start of a new region.

3. Perform DFS/BFS: From that cell, explore all connected cells using a DFS or BFS. Mark all these cells as visited.

4. Count the Region: Each time you initiate a DFS/BFS from an unvisited occupied cell, increment your region count.

5. Continue Until All Cells are Processed: Repeat the above steps until every cell in the grid has been checked.

Pseudo Code

Here is a simple pseudo code to illustrate the DFS approach:

function findDisjointRegions(grid):
    visited = create a 2D array with same dimensions as grid, initialized to false
    regionCount = 0

    for each cell (i, j) in grid:
        if grid[i][j] == 1 and not visited[i][j]:
            regionCount += 1
            dfs(grid, visited, i, j)

    return regionCount

function dfs(grid, visited, i, j):
    if i < 0 or i >= number of rows in grid or j < 0 or j >= number of columns in grid:
        return
    if grid[i][j] == 0 or visited[i][j]:
        return

    visited[i][j] = true

    dfs(grid, visited, i+1, j)  // down
    dfs(grid, visited, i-1, j)  // up
    dfs(grid, visited, i, j+1)  // right
    dfs(grid, visited, i, j-1)  // left

Complexity Analysis

• Time Complexity: O(N * M), where N is the number of rows and M is the number of columns in the grid. Each cell is visited once.
• Space Complexity: O(N * M) for the visited matrix in addition to the recursive stack space for DFS.

Conclusion

Finding disjoint regions in a grid can be efficiently accomplished using DFS or BFS algorithms. This method provides a systematic way to explore connected components in grid-based data structures. The concepts discussed can be applied in various domains, making it a valuable skill for developers and data scientists alike.