Making A Large Island Python Solution

lcpy gen -n 827   # by problem number
lcpy gen -s making_a_large_island   # by problem name

Input: grid = [[1,0],[0,1]]
Output: 3
Explanation: Change one 0 to 1 and connect two 1s, then we get an island with area = 3.

Input: grid = [[1,1],[1,0]]
Output: 4
Explanation: Change the 0 to 1 and make the island bigger, only one island with area = 4.

Input: grid = [[1,1],[1,1]]
Output: 4
Explanation: Can't change any 0 to 1, only one island with area = 4.

class Solution:
    # Time: O(n^2)
    # Space: O(n^2)
    def largest_island(self, grid: list[list[int]]) -> int:
        n = len(grid)
        sizes = [0, 0]  # island ids start at 2 so 0/1 stay sentinel-free
        label = [[0] * n for _ in range(n)]

        for r in range(n):
            for c in range(n):
                if grid[r][c] == 0 or label[r][c]:
                    continue
                island_id = len(sizes)
                stack = [(r, c)]
                size = 0
                while stack:
                    x, y = stack.pop()
                    if not (0 <= x < n and 0 <= y < n) or grid[x][y] != 1 or label[x][y]:
                        continue
                    label[x][y] = island_id
                    size += 1
                    stack.extend(((x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1)))
                sizes.append(size)

        best = max(sizes)
        for r in range(n):
            for c in range(n):
                if grid[r][c] != 0:
                    continue
                nbr_ids = set()
                for x, y in ((r + 1, c), (r - 1, c), (r, c + 1), (r, c - 1)):
                    if 0 <= x < n and 0 <= y < n and grid[x][y] == 1:
                        nbr_ids.add(label[x][y])
                best = max(best, 1 + sum(sizes[i] for i in nbr_ids))
        return best