<p>You are given <code>row x col</code> <code>grid</code> representing a map where <code>grid[i][j] = 1</code> represents&nbsp;land and <code>grid[i][j] = 0</code> represents water.</p>

<p>Grid cells are connected <strong>horizontally/vertically</strong> (not diagonally). The <code>grid</code> is completely surrounded by water, and there is exactly one island (i.e., one or more connected land cells).</p>

<p>The island doesn&#39;t have &quot;lakes&quot;, meaning the water inside isn&#39;t connected to the water around the island. One cell is a square with side length 1. The grid is rectangular, width and height don&#39;t exceed 100. Determine the perimeter of the island.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://assets.leetcode.com/uploads/2018/10/12/island.png" style="width: 221px; height: 213px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,0,0],[1,1,1,0],[0,1,0,0],[1,1,0,0]]
<strong>Output:</strong> 16
<strong>Explanation:</strong> The perimeter is the 16 yellow stripes in the image above.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1]]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,0]]
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>row == grid.length</code></li>
	<li><code>col == grid[i].length</code></li>
	<li><code>1 &lt;= row, col &lt;= 100</code></li>
	<li><code>grid[i][j]</code> is <code>0</code> or <code>1</code>.</li>
	<li>There is exactly one island in <code>grid</code>.</li>
</ul>

class Solution:
    def islandPerimeter(self, grid: List[List[int]]) -> int:
        directions = [(0, 1), (0, -1), (1, 0), (-1, 0)]
        visited = [[0 for i in range(len(grid[0]))] for j in range(len(grid))]
        peri = 0
        
        def inbound(row, col):
            return (0 <= row < len(grid) and 0 <= col < len(grid[0]))
        
        def perimeterCalculator(row, col):
            perimeter = 0
            for row_change, col_change in directions:
                new_row = row + row_change
                new_col = col + col_change
                if inbound(new_row, new_col) and grid[new_row][new_col] == 0:
                    perimeter += 1
                elif not inbound(new_row, new_col):
                    perimeter += 1
            return perimeter
        
        def dfs(grid, visited, row, col):
            nonlocal peri
            # base case
            if grid[row][col] == 1:     
                peri += perimeterCalculator(row, col)
            
            visited[row][col] = True
            for row_change, col_change in directions:
                new_row = row + row_change
                new_col = col + col_change
                if inbound(new_row, new_col) and not visited[new_row][new_col]:
                    dfs(grid, visited, new_row, new_col)
        
        dfs(grid, visited, 0, 0)
        return peri
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