Number of Distinct Islands

DFS

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.

Thought Process

• Since we are dealing with a distinct characteristic, we can utilize a hash set

Solution

class Solution:
    def numDistinctIslands(self, grid: List[List[int]]) -> int:
        
        islandSet = set()
        
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1:  
                    self.path = "" #needs to be global variable 
                    self.dfsearch(i,j,grid,"s")
                    print(self.path)
                    islandSet.add(self.path)
                    
        print(islandSet)
        return len(islandSet)
                
    def dfsearch(self, i, j, grid, direction):
        if i < 0 or i >= len(grid) or j < 0 or j >= len(grid[0]) or grid[i][j] != 1:
            return 
        
        grid[i][j] = 0
        self.path+=direction
        
        self.dfsearch(i-1,j,grid,"u")
        self.dfsearch(i+1,j,grid,"d")
        self.dfsearch(i,j-1,grid,"l")
        self.dfsearch(i,j+1,grid,"r")
        
        self.path+="e"
        

Time Complexity

• Time: O(m*n)

• Space: O(m*n)