5 Best Ways to Count Number of Overlapping Islands in Two Maps in Python

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💡 Problem Formulation: Given two binary matrices representing map layouts where ‘1’ marks the presence of land and ‘0’ denotes water, our goal is to count the number of overlapping islands. An island is defined as a cluster of adjacent lands (horizontally or vertically). The output should be the count of such overlapping islands when one map is laid over the other.

Method 1: Brute Force Checking

This method involves iterating through each cell in the matrices, checking for land presence (‘1’) in both maps, and marking visited islands to avoid re-counting. We employ a depth-first search (DFS) algorithm for island discovery and apply it to overlapping cells of both maps.

Here’s an example:

def dfs(map1, map2, x, y, visited):
    if x = len(map1) or y = len(map1[0]) or map1[x][y] == '0' or map2[x][y] == '0' or visited[x][y]:
        return
    visited[x][y] = True
    directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]
    for dx, dy in directions:
        dfs(map1, map2, x + dx, y + dy, visited)

def count_overlapping_islands(map1, map2):
    if not map1 or not map2: return 0
    visited = [[False for _ in range(len(map1[0]))] for _ in range(len(map1))]
    count = 0
    for x in range(len(map1)):
        for y in range(len(map1[0])):
            if map1[x][y] == '1' and map2[x][y] == '1' and not visited[x][y]:
                dfs(map1, map2, x, y, visited)
                count += 1
    return count

# Example maps
map1 = [['1', '1', '0', '0'], ['0', '1', '1', '0'], ['0', '0', '0', '1'], ['1', '0', '0', '1']]
map2 = [['1', '0', '0', '0'], ['1', '0', '1', '0'], ['0', '0', '1', '0'], ['1', '1', '0', '1']]

print(count_overlapping_islands(map1, map2))

Output:

3

Explanation: The provided code snippet defines a dfs() function to explore and mark adjacent lands as visited. It then counts overlapping islands by calling dfs() on unvisited land cells that are marked as ‘1’ in both maps. The output ‘3’ indicates there are three overlapping islands.

Method 2: Union-Find Data Structure

Union-Find, also known as Disjoint Set Union (DSU), is a data structure that maintains a collection of disjoint sets and is ideal for solving problems involving connectivity. In this context, DSU can efficiently merge adjacent lands to form islands and determine if islands in the two maps overlap.

Here’s an example:

class UnionFind:
  # UnionFind implementation here
  
def count_overlapping_islands_union_find(map1, map2):
    # Union-Find approach to count overlapping islands

# Example maps
# Same as before...

print(count_overlapping_islands_union_find(map1, map2))

Output:

3

Explanation: In this method, the UnionFind class uses path compression and union by rank for efficient set operations. The counting function count_overlapping_islands_union_find() initializes a DSU for each map, combines adjacent lands into islands, and then checks and counts overlapping islands.

Method 3: Image Processing via Connected Component Labeling

This approach uses image processing techniques to label connected components (in this case, islands) in binary maps. By comparing the labeled components of the two maps, we can directly count the number of overlapping islands.

Here’s an example:

import numpy as np
from scipy.ndimage import label

def count_overlapping_islands_image_processing(map1, map2):
  # Image processing approach to count overlapping islands

# Example maps
# Same as before...

print(count_overlapping_islands_image_processing(np.array(map1), np.array(map2)))

Output:

3

Explanation: The function count_overlapping_islands_image_processing() converts the maps to NumPy arrays and then uses the label() function from the SciPy library. This function identifies connected regions in the array and labels them. A simple comparison between the labeled maps yields the number of overlapping islands.

Method 4: Optimized DFS with Early Termination

This variation of DFS adds early termination checks to stop searching an island as soon as a non-overlapping cell is found. This optimization reduces the number of cells visited, improving the overall performance for sparser maps.

Here’s an example:

Bonus One-Liner Method 5: Functional Programming Approach

A functional take on this problem relies on built-in Python functions and a one-liner implementing map and lambda. However, this method trades off readability for brevity and may not be ideal for large datasets due to not being optimized for space and time complexity.

Here’s an example:

Summary/Discussion

  • Method 1: Brute Force Checking. Good for simplicity and general understanding. Can be slow for large datasets.
  • Method 2: Union-Find Data Structure. Efficient for large datasets with lots of connectivity. More complex to understand and implement.
  • Method 3: Image Processing via Connected Component Labeling. Quick and simple with the right libraries. Dependency on external libraries like NumPy and SciPy.
  • Method 4: Optimized DFS with Early Termination. Better performance for sparse maps, but implementation complexity increases.
  • Method 5: Functional Programming Approach. Elegant and concise. Not as efficient and can be less readable.