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

This is highly related to connected component labeling. The number of connected component is just a byproduct of the labeling. Algorithm described in the linked wikipedia article works in linear time.