Find the number of distinct islands in a 2D matrix
Given a boolean 2D matrix. The task is to find the number of distinct islands where a group of connected 1s (horizontally or vertically) forms an island. Two islands are considered to be distinct if and only if one island is equal to another (not rotated or reflected).
Examples:
Input: grid[][] =
{{1, 1, 0, 0, 0},
1, 1, 0, 0, 0},
0, 0, 0, 1, 1},
0, 0, 0, 1, 1}}Output: 1
Island 1, 1 at the top left corner is same as island 1, 1 at the bottom right cornerInput: grid[][] =
{{1, 1, 0, 1, 1},
1, 0, 0, 0, 0},
0, 0, 0, 0, 1},
1, 1, 0, 1, 1}}Output: 3
Distinct islands in the example above are: 1, 1 at the top left corner; 1, 1 at the top right corner and 1 at the bottom right corner. We ignore the island 1, 1 at the bottom left corner since 1, 1 it is identical to the top right corner.
Approach: This problem is an extension of the problem Number of Islands.
The core of the question is to know if 2 islands are equal. The primary criteria is that the number of 1’s should be same in both. But this cannot be the only criteria as we have seen in example 2 above. So how do we know? We could use the position/coordinates of the 1’s.
If we take the first coordinates of any island as a base point and then compute the coordinates of other points from the base point, we can eliminate duplicates to get the distinct count of islands. So, using this approach, the coordinates for the 2 islands in example 1 above can be represented as: [(0, 0), (0, 1), (1, 0), (1, 1)].
Below is the implementation of above approach:
C++
// C++ implementation of above approach #include <bits/stdc++.h> using namespace std; // 2D array for the storing the horizontal and vertical // directions. (Up, left, down, right} vector<vector<int> > dirs = { { 0, -1 }, { -1, 0 }, { 0, 1 }, { 1, 0 } }; // Function to perform dfs of the input grid void dfs(vector<vector<int> >& grid, int x0, int y0, int i, int j, vector<pair<int, int> >& v) { int rows = grid.size(), cols = grid[0].size(); if (i < 0 || i >= rows || i < 0 || j >= cols || grid[i][j] <= 0) return; // marking the visited element as -1 grid[i][j] *= -1; // computing coordinates with x0, y0 as base v.push_back({ i - x0, j - y0 }); // repeat dfs for neighbors for (auto dir : dirs) { dfs(grid, x0, y0, i + dir[0], j + dir[1], v); } } // Main function that returns distinct count of islands in // a given boolean 2D matrix int countDistinctIslands(vector<vector<int> >& grid) { int rows = grid.size(); if (rows == 0) return 0; int cols = grid[0].size(); if (cols == 0) return 0; set<vector<pair<int, int> > > coordinates; for (int i = 0; i < rows; ++i) { for (int j = 0; j < cols; ++j) { // If a cell is not 1 // no need to dfs if (grid[i][j] != 1) continue; // vector to hold coordinates // of this island vector<pair<int, int> > v; dfs(grid, i, j, i, j, v); // insert the coordinates for // this island to set coordinates.insert(v); } } return coordinates.size(); } // Driver code int main() { vector<vector<int> > grid = { { 1, 1, 0, 1, 1 }, { 1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1 }, { 1, 1, 0, 1, 1 } }; cout << "Number of distinct islands is " << countDistinctIslands(grid); return 0; } |
chevron_right
filter_none
Python3
# Python implementation of above approach # 2D array for the storing the horizontal and vertical # directions. (Up, left, down, right dirs = [ [ 0, -1 ], [ -1, 0 ], [ 0, 1 ], [ 1, 0 ] ] # Function to perform dfs of the input grid def dfs(grid, x0, y0, i, j, v): rows = len(grid) cols = len(grid[0]) if i < 0 or i >= rows or i < 0 or j >= cols or grid[i][j] <= 0: return # marking the visited element as -1 grid[i][j] *= -1 # computing coordinates with x0, y0 as base v.append( [i - x0, j - y0] ) # repeat dfs for neighbors for dir in dirs: dfs(grid, x0, y0, i + dir[0], j + dir[1], v) # Main function that returns distinct count of islands in # a given boolean 2D matrix def countDistinctIslands(grid): rows = len(grid) if rows == 0: return 0 cols = len(grid[0]) if cols == 0: return 0 coordinates = [] for i in range(rows): for j in range(cols): # If a cell is not 1 # no need to dfs if grid[i][j] != 1: continue # to hold coordinates # of this island v = [] dfs(grid, i, j, i, j, v) # insert the coordinates for # this island to set coordinates.append(v) return len(coordinates) # Driver code grid = [[ 1, 1, 0, 1, 1 ], [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 1, 1, 0, 1, 1 ] ] print("Number of distinct islands is",countDistinctIslands(grid)) # This code is contributed by ankush_953 |
chevron_right
filter_none
Output:
Number of distinct islands is 3
Time complexity: O(rows * cols)
Space complexity: O(rows * cols)
Recommended Posts:
- Find the number of islands | Set 1 (Using DFS)
- Find the number of Islands | Set 2 (Using Disjoint Set)
- Find distinct elements common to all rows of a matrix
- Find row number of a binary matrix having maximum number of 1s
- Count number of islands where every island is row-wise and column-wise separated
- Find number of cavities in a matrix
- Find row with maximum and minimum number of zeroes in given Matrix
- Find number of transformation to make two Matrix Equal
- Find alphabet in a Matrix which has maximum number of stars around it
- Find the minimum number of moves needed to move from one cell of matrix to another
- Islands in a graph using BFS
- Minimum number of steps to convert a given matrix into Diagonally Dominant Matrix
- Minimum number of steps to convert a given matrix into Upper Hessenberg matrix
- Find trace of matrix formed by adding Row-major and Column-major order of same matrix
- Queries for number of distinct integers in Suffix
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
Improved By : ankush_953
