200. Number of Islands

class Solution:
    def numIslands(self, grid: List[List[str]]) -> int:
        if grid == []:
            return 0
        
        count = 0
        state = grid
        width = len(grid[0])
        height = len(grid)
        
        def search(x, y):
            state[y][x] = 0
            # search horizontal
            if ((x + 1) < width) and (state[y][x + 1] == "1"):
                search(x + 1, y)
            if ((x - 1) >= 0) and (state[y][x - 1] == "1"):
                search(x - 1, y)
            # search vertical
            if ((y + 1) < height) and (state[y + 1][x] == "1"):
                search(x, y + 1)
            if ((y - 1) >= 0) and (state[y - 1][x] == "1"):
                search(x, y - 1)
            
        for h in range(height):
            for w in range(width):
                if state[h][w] == "1":
                    # search land and mutate state
                    count += 1
                    search(w, h)
        
        return count