694. Number of Distinct Islands

You are given an m x n binary matrix grid. 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.

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.

Return the number of distinct islands.

class Solution {
    vector<pair<int,int>> bfs(vector<vector<int>>& grid, int y, int x) {
        int dy[4] = {-1,0,1,0};
        int dx[4] = {0,1,0,-1};
        int n = grid.size(), m = grid[0].size();
        queue<pair<int, int>> q;
        q.push({y,x});
        vector<pair<int,int>> res{{y,x}};
        grid[y][x] = 0;
        
        while(!q.empty()) {
            auto [cy, cx] = q.front(); q.pop();
            for(int i = 0; i < 4; i++) {
                int ny = cy + dy[i], nx = cx + dx[i];
                if(0 <= ny and ny < n and 0 <= nx and nx < m and grid[ny][nx]) {
                    q.push({ny,nx});
                    grid[ny][nx] = 0;
                    res.push_back({ny,nx});
                }
            }
        }
        
        
        sort(res.begin(), res.end());
        
        return res;
    }
    pair<int,int> getDiff(pair<int, int>& p1, pair<int,int>& p2) {
        return {p1.first - p2.first, p1.second - p2.second};
    }
    bool verify(vector<vector<pair<int,int>>>& islands, vector<pair<int,int>>& target) {
        for(auto island : islands) {
            auto diff = getDiff(island[0], target[0]);
            bool eq = true;
            for(int i = 0; i < target.size() and eq; i++) {
                if(diff != getDiff(island[i], target[i]))
                    eq = false;
            }
            if(eq) return false;
        }
        return true;
    }
public:
    int numDistinctIslands(vector<vector<int>>& grid) {
        int n = grid.size(), m = grid[0].size();
        int island = 0;
        unordered_map<int, vector<vector<pair<int,int>>>> mp;
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                if(grid[i][j]) {
                    auto pos = bfs(grid,i,j);
                    if(verify(mp[pos.size()], pos)) {
                        mp[pos.size()].push_back(pos);
                        island++;
                    }
                }
        return island;
    }
};