[LeetCode] Max Area of Island 島的最大面積

 

Given a non-empty 2D array grid of 0's and 1's, an island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.

Find the maximum area of an island in the given 2D array. (If there is no island, the maximum area is 0.)

Example 1:

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

Given the above grid, return  6. Note the answer is not 11, because the island must be connected 4-directionally.

 

Example 2:

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

Given the above grid, return  0.

 

Note: The length of each dimension in the given grid does not exceed 50.

 

這道題跟之前的那兩道Number of Islands和Number of Distinct Islands是同一個類型的，只不過這次需要統計出每個島的大小，再來更新結果res。先用遞歸來做，遍歷grid，當遇到為1的點，我們調用遞歸函數，在遞歸函數中，我們首先判斷i和j是否越界，還有grid[i][j]是否為1，我們沒有用visited數組，而是直接修改了grid數組，遍歷過的標記為-1。如果合法，那么cnt自增1，並且更新結果res，然后對其周圍四個相鄰位置分別調用遞歸函數即可，參見代碼如下：

 

解法一：

class Solution {
public:
    vector<vector<int>> dirs{{0,-1},{-1,0},{0,1},{1,0}};
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        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] != 1) continue;
                int cnt = 0;
                helper(grid, i, j, cnt, res);
            }
        }
        return res;
    }
    void helper(vector<vector<int>>& grid, int i, int j, int& cnt, int& res) {
        int m = grid.size(), n = grid[0].size();
        if (i < 0 || i >= m || j < 0 || j >= n || grid[i][j] <= 0) return;
        res = max(res, ++cnt);
        grid[i][j] *= -1;
        for (auto dir : dirs) {
            helper(grid, i + dir[0], j + dir[1], cnt, res);
        }
    }
};

 

下面是迭代的寫法，BFS遍歷，使用queue來輔助運算，思路沒啥太大區別，都是套路，都是模版，往里套就行了，參見代碼如下：

 

解法二：

class Solution {
public:
    vector<vector<int>> dirs{{0,-1},{-1,0},{0,1},{1,0}};
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        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] != 1) continue;
                int cnt = 0;
                queue<pair<int, int>> q{{{i, j}}};
                grid[i][j] *= -1;
                while (!q.empty()) {
                    auto t = q.front(); q.pop();
                    res = max(res, ++cnt);
                    for (auto dir : dirs) {
                        int x = t.first + dir[0], y = t.second + dir[1];
                        if (x < 0 || x >= m || y < 0 || y >= n || grid[x][y] <= 0) continue;
                        grid[x][y] *= -1;
                        q.push({x, y});
                    }
                }
            }
        }
        return res;
    }
};

 

類似題目：

Number of Distinct Islands

Island Perimeter

Number of Islands

 

LeetCode All in One 題目講解匯總(持續更新中...)