Region Inference for Data Analysis in Rust

Region inference is a crucial technique in data analysis and image processing. This challenge asks you to implement a simplified region inference algorithm in Rust, identifying contiguous areas of similar values within a 2D grid. This is useful for tasks like object detection, image segmentation, and anomaly detection.

Problem Description

You are given a 2D vector (a vector of vectors) representing a grid of integer values. Your task is to implement a function infer_regions that identifies contiguous regions of the same value. A region is defined as a group of adjacent cells (horizontally or vertically, not diagonally) that have the same value. The function should return a vector of vectors, where each inner vector represents a region and contains the coordinates (row, column) of the cells belonging to that region.

Key Requirements:

• Contiguity: Regions must be contiguous – cells within a region must be directly adjacent (up, down, left, or right).
• Same Value: All cells within a region must have the same integer value.
• No Overlap: Regions should not overlap. Once a cell is assigned to a region, it should not be part of any other region.
• Efficiency: The algorithm should be reasonably efficient, avoiding unnecessary iterations.

Expected Behavior:

The infer_regions function should take a 2D vector of integers as input and return a vector of vectors of tuples. Each tuple represents the (row, column) coordinates of a cell belonging to a region. The order of regions in the output vector is not important.

Edge Cases to Consider:

• Empty Grid: Handle the case where the input grid is empty.
• Grid with a Single Value: Handle the case where the entire grid contains the same value.
• Isolated Cells: Handle cases where there are isolated cells with unique values.
• Large Grids: Consider the performance implications for large grids.

Examples

Example 1:

Input: [[1, 1, 2, 2], [1, 2, 2, 2], [3, 3, 3, 3]]
Output: [[(0, 0), (0, 1), (1, 0)], [(0, 2), (0, 3), (1, 1), (1, 2), (1, 3)], [(2, 0), (2, 1), (2, 2), (2, 3)]]
Explanation: The grid contains three regions: a region of 1s, a region of 2s, and a region of 3s. The output represents these regions as lists of coordinates.

Example 2:

Input: [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
Output: [[(0, 0)], [(0, 1)], [(0, 2)], [(1, 0)], [(1, 1)], [(1, 2)], [(2, 0)], [(2, 1)], [(2, 2)]]
Explanation: Each cell in the grid has a unique value, so each cell forms its own region.

Example 3: (Edge Case)

Input: []
Output: []
Explanation: An empty grid results in an empty list of regions.

Constraints

• The grid will be a 2D vector of integers.
• The grid dimensions will be between 0 and 1000 rows and 0 and 1000 columns (inclusive).
• Integer values in the grid will be between -1000 and 1000 (inclusive).
• The algorithm should complete within 1 second for grids of the specified dimensions.

Notes

• You can use a Depth-First Search (DFS) or Breadth-First Search (BFS) approach to explore connected components.
• Consider using a visited set or matrix to keep track of cells that have already been assigned to a region.
• Think about how to efficiently represent and store the coordinates of the regions.
• Error handling is not required for invalid input types (e.g., non-integer values in the grid). Assume the input is always a valid 2D vector of integers.
• Focus on clarity and correctness first, then optimize for performance if needed.