Max Area of Island

Signal

The same flood-fill-per-unvisited-land-cell shape as counting islands, but this time the fill needs to hand back how many cells it touched, not just the fact that it ran — a flood fill that returns a size instead of a boolean.

Approach

Scan every cell. On an unvisited land cell, flood fill outward and count how many cells the fill visits, then compare that count against a running maximum. The fill itself is identical to the island-counting version — only what you do with its result changes.

Skeleton

best = 0
for each cell:
    if cell is land and not visited:
        best = max(best, flood_fill_and_count(cell))
return best

Solution

def max_area_of_island(grid: list[list[int]]) -> int:
    rows, cols = len(grid), len(grid[0])
    visited = set()

    def flood_fill(r: int, c: int) -> int:
        stack = [(r, c)]
        visited.add((r, c))
        area = 0
        while stack:
            cr, cc = stack.pop()
            area += 1
            for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                nr, nc = cr + dr, cc + dc
                if (
                    0 <= nr < rows
                    and 0 <= nc < cols
                    and (nr, nc) not in visited
                    and grid[nr][nc] == 1
                ):
                    visited.add((nr, nc))
                    stack.append((nr, nc))
        return area

    best = 0
    for r in range(rows):
        for c in range(cols):
            if grid[r][c] == 1 and (r, c) not in visited:
                visited.add((r, c))
                best = max(best, flood_fill(r, c))
    return best

Complexity

O(rows · cols) time — every cell is visited once across all fills combined. O(rows · cols) space for the visited set.

Pitfalls

• Returning the count of fills (like the islands-count problem) instead of the size of the largest fill — an easy mix-up if you've just solved Number of Islands and copy the shape too literally.
• Forgetting the "no land at all" edge case — the loop naturally returns 0 since best starts at 0 and the inner condition never triggers, but it's worth stating explicitly if asked.
• Off-by-one on grid bounds when checking neighbors — always guard with 0 <= nr < rows and 0 <= nc < cols before indexing.