can counting contiguous regions in a bitmap be improved over O(r * c)?

Question

You are given an image of a surface photographed by a satellite.The image is a bitmap where water is marked by \'.\' and land is marked by \'*\'. Adjacent group of

Answer 1

1. Create a undirected graph, where each island node connects to its neighboor island nodes.

2. While there are unvisited nodes:

   • pick an unvisited node, do a depth-first traversal and mark every node visited, increase number_of_islands.

3. Done.

Both (1) and (2) takes O(n) time.