Number of Islands in Python

The Number of Islands problem involves counting connected components of land (represented by 1s) in a 2D grid surrounded by water (represented by 0s). An island is formed by connecting adjacent lands horizontally or vertically.

Consider this grid example ?

This grid contains three islands: one large island (blue), one single-cell island (orange), and one small island (pink).

Algorithm Overview

The solution uses Depth-First Search (DFS) to solve this problem ?

• Iterate through each cell in the grid
• When we find a land cell (1), increment the island counter
• Use DFS to mark all connected land cells as water (0) to avoid counting them again
• Continue until all cells are processed

Implementation

class Solution:
    def numIslands(self, grid):
        if len(grid) == 0:
            return 0
        
        n = len(grid)
        m = len(grid[0])
        islands = 0
        
        for i in range(n):
            for j in range(m):
                if grid[i][j] == "1":
                    islands += 1
                    self.make_water(i, j, n, m, grid)
        
        return islands
    
    def make_water(self, i, j, n, m, grid):
        # Check boundaries
        if i < 0 or j < 0 or i >= n or j >= m:
            return
        
        # If already water, return
        if grid[i][j] == "0":
            return
        
        # Mark current cell as water
        grid[i][j] = "0"
        
        # Explore all 4 directions
        self.make_water(i + 1, j, n, m, grid)  # Down
        self.make_water(i - 1, j, n, m, grid)  # Up
        self.make_water(i, j + 1, n, m, grid)  # Right
        self.make_water(i, j - 1, n, m, grid)  # Left

# Test the solution
solution = Solution()
grid = [
    ["1","1","0","0","0"],
    ["1","1","0","0","0"],
    ["0","0","1","0","0"],
    ["0","0","0","1","1"]
]

result = solution.numIslands(grid)
print(f"Number of islands: {result}")

Number of islands: 3

How It Works

The algorithm works in two phases ?

1. Discovery Phase: When we find a land cell ("1"), we increment the island counter
2. Marking Phase: We use DFS to mark all connected land cells as water ("0")

The make_water() method recursively explores all four directions (up, down, left, right) from the current cell, converting connected land cells to water.

Time and Space Complexity

Conclusion

The Number of Islands problem is efficiently solved using DFS to identify and mark connected components. The algorithm counts each island once and uses the "sink the island" technique to avoid recounting connected land cells.