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Solution 18: Max Extent Analysis (Max Area of Island)

Approach Explanation

Iterate through the grid. When a '1' is found, use DFS to calculate the size of that island and update the global max_area. To avoid revisiting, set visited cells to '0'.

Step-by-Step Logic

  1. max_area = 0.
  2. For each cell (r, c):
    • If grid[r][c] == 1:
      • max_area = max(max_area, dfs(r, c)).
  3. dfs(r, c):
    • If out of bounds or grid[r][c] == 0, return 0.
    • grid[r][c] = 0.
    • Return 1 + dfs(r+1, c) + dfs(r-1, c) + dfs(r, c+1) + dfs(r, c-1).

Complexity

  • Time Complexity: O(M * N).
  • Space Complexity: O(M * N).

Code

def max_area_of_island(grid):
    rows, cols = len(grid), len(grid[0])
    
    def dfs(r, c):
        if (r < 0 or r >= rows or 
            c < 0 or c >= cols or 
            grid[r][c] == 0):
            return 0
            
        grid[r][c] = 0 # Mark visited
        return 1 + dfs(r + 1, c) + dfs(r - 1, c) + dfs(r, c + 1) + dfs(r, c - 1)
        
    mx = 0
    for r in range(rows):
        for c in range(cols):
            if grid[r][c] == 1:
                mx = max(mx, dfs(r, c))
    return mx