You are given a map in form of a two-dimensional integer grid where 1 represents land and 0 represents water. Grid cells are connected horizontally/vertically (not diagonally). The grid is completely surrounded by water, and there is exactly one island (i.e., one or more connected land cells). The island doesn‘t have "lakes" (water inside that isn‘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‘t exceed 100. Determine the perimeter of the island.

Example:

[[0,1,0,0],
 [1,1,1,0],
 [0,1,0,0],
 [1,1,0,0]]

Answer: 16
Explanation: The perimeter is the 16 yellow stripes in the image below:

給一個二維的格子圖，格子是1表示陸地，0表示水，格子水平或者垂直連接，若幹的格子連在一起形成一個小島，只有一個相連的島，且島中沒有湖，求島的周長。

解法1: 遇到為1的格子，檢驗四個方向是否和陸地相連

解法2: 遇到為1的格子，檢查上面和左面是否和陸地相連

Java:

public class Solution {
    public int islandPerimeter(int[][] grid) {
        int islands = 0, neighbours = 0;

        for (int i = 0; i < grid.length; i++) {
            for (int j = 0; j < grid[i].length; j++) {
                if (grid[i][j] == 1) {
                    islands++; // count islands
                    if (i < grid.length - 1 && grid[i + 1][j] == 1) neighbours++; // count down neighbours
                    if (j < grid[i].length - 1 && grid[i][j + 1] == 1) neighbours++; // count right neighbours
                }
            }
        }

        return islands * 4 - neighbours * 2;
    }
}

Python:

def islandPerimeter(self, grid):
    """
    :type grid: List[List[int]]
    :rtype: int
    """
    ans = 0
    for i in range(len(grid)):
        for j in range(len(grid[0])):
            if grid[i][j] == 1:
                ans += 4
                if i > 0 and grid[i-1][j] == 1:
                    ans -= 2
                if j > 0 and grid[i][j-1] == 1:
                    ans -= 2
    return ans　　

Python:

class Solution(object):
    def islandPerimeter(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        if not grid:
            return 0

        def sum_adjacent(i, j):
            adjacent = (i + 1, j), (i - 1, j), (i, j + 1), (i, j - 1),
            res = 0
            for x, y in adjacent:
                if x < 0 or y < 0 or x == len(grid) or y == len(grid[0]) or grid[x][y] == 0:
                    res += 1
            return res

        count = 0
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1:
                    count += sum_adjacent(i, j)
        return count　　

Python:

class Solution:
    def islandPerimeter(self, grid):
        if not grid:
            return 0

        N = len(grid)
        M = len(grid[0])
        ans = 0
        for i in range(N):
            for j in range(M):
                for k in [(-1, 0), (0, 1), (1, 0), (0, -1)]:
                    if i+k[0] < 0 or i + k[0] >= N or j+k[1] < 0 or j+k[1] >= M or grid[i+k[0]][j+k[1]] == 0:
                        ans += 1
        return ans　　

C++:

class Solution {
public:
    int islandPerimeter(vector<vector<int>>& grid) {
        if (grid.empty() || grid[0].empty()) return 0;
        int m = grid.size(), n = grid[0].size(), res = 0;
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (grid[i][j] == 0) continue;
                if (j == 0 || grid[i][j - 1] == 0) ++res;
                if (i == 0 || grid[i - 1][j] == 0) ++res;
                if (j == n - 1 || grid[i][j + 1] == 0) ++res;
                if (i == m - 1 || grid[i + 1][j] == 0) ++res;
            }
        }
        return res;
    }
};

C++:

class Solution {
public:
    int islandPerimeter(vector<vector<int>>& grid) {
        if (grid.empty() || grid[0].empty()) return 0;
        int res = 0, m = grid.size(), n = grid[0].size();
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (grid[i][j] == 0) continue;
                res += 4;
                if (i > 0 && grid[i - 1][j] == 1) res -= 2;
                if (j > 0 && grid[i][j - 1] == 1) res -= 2;
            }
        }
        return res;
    }
};

[LeetCode] 463. Island Perimeter 島的周長