Iterate through each of the cell and if it is an island, do dfs to mark all adjacent islands, then increase the counter by 1.

```
def numIslands(self, grid):
if not grid:
return 0
count = 0
for i in range(len(grid)):
for j in range(len(grid[0])):
if grid[i][j] == '1':
self.dfs(grid, i, j)
count += 1
return count
def dfs(self, grid, i, j):
if i<0 or j<0 or i>=len(grid) or j>=len(grid[0]) or grid[i][j] != '1':
return
grid[i][j] = '#'
self.dfs(grid, i+1, j)
self.dfs(grid, i-1, j)
self.dfs(grid, i, j+1)
self.dfs(grid, i, j-1)
```