Island Perimeter

Count perimeter locally instead of tracing the boundary. Every land cell initially contributes four sides. For each shared edge between two land cells, subtract two because that edge was counted once by each cell but is not exposed. To count each shared edge once, while scanning only check the right and down neighbors, or equivalently subtract one for every land neighbor in all four directions. The result naturally includes coastlines around internal water holes if the problem defines perimeter as all land-water boundaries; clarify if it wants only the outside boundary. If the grid may contain multiple islands, the same formula returns their combined perimeter. Test a single land cell, one row, a solid rectangle, an L shape, border land, and a lake inside an island. This is O(rows*cols) time and O(1) extra space, with no visited matrix required. A DFS boundary walk is possible but is more complex and needs careful treatment of holes.