694. Number of Distinct Islands

• Difficulty: Medium

• Topics: Hash Table, Depth-first Search

• Similar Questions:

  • Number of Islands

  • Number of Distinct Islands II

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.

Count the number of distinct islands. An island is considered to be the same as another if and only if one island can be translated (and not rotated or reflected) to equal the other.

Example 1:

11000
11000
00011
00011

Example 2:

11011
10000
00001
11011

11
1

 1
11

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

Solutions:

class Solution {
public:
    int numDistinctIslands(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));
        unordered_set<string> islands;

        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (grid[i][j] && !visited[i][j]) {
                    string digest;
                    dfs(grid, visited, i, j, digest);
                    islands.insert(digest);
                }
            }
        }

        return islands.size();
    }

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

         if (row < 0 || row >= m || col < 0 || col >= n || !grid[row][col] || visited[row][col]) {
             digest.push_back('e'); // empty
             return;
         }

         visited[row][col] = true;
         digest.push_back('d'); dfs(grid, visited, row + 1, col, digest); // down
         digest.push_back('u'); dfs(grid, visited, row - 1, col, digest); // up
         digest.push_back('r'); dfs(grid, visited, row, col + 1, digest); // right
         digest.push_back('l'); dfs(grid, visited, row, col - 1, digest); // left
     }

};