695. Max Area of Island

• Difficulty: Medium

• Topics: Array, Depth-first Search

• Similar Questions:

  • Number of Islands

  • Island Perimeter

Problem:

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]]

Example 2:

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

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

Solutions:

class Solution {
public:
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int m = grid.size();
        if (m == 0) return 0;
        int n = grid[0].size();
        if (n == 0) return 0;


        vector<vector<bool>> visited(m, vector<bool> (n, false));
        int ret = 0;

        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (grid[i][j] && !visited[i][j]) {
                    ret = max(ret, dfs(grid, visited, i, j));
                }
            }
        }

        return ret;
    }
private:
    int dfs(const vector<vector<int>>& grid, vector<vector<bool>>& visited, int row, int col) {
        int m = grid.size();
        int n = grid[0].size();

        if (row < 0 || row >= m || col < 0 || col >= n || !grid[row][col] || visited[row][col]) return 0;
        visited[row][col] = true;

        int ret = 1;
        ret += dfs(grid, visited, row + 1, col);
        ret += dfs(grid, visited, row - 1, col);
        ret += dfs(grid, visited, row, col + 1);
        ret += dfs(grid, visited, row, col - 1);

        return ret;
    }

};