959. Regions Cut By Slashes.cpp

Author: keineahnung2345

959. Regions Cut By Slashes.cpp

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+//Runtime: 12 ms, faster than 71.71% of C++ online submissions for Regions Cut By Slashes.
+//Memory Usage: 9.9 MB, less than 50.00% of C++ online submissions for Regions Cut By Slashes.
+/Approach 1: Union-Find
+class DSU{
+public:
+    vector<int> parent;
+    
+    DSU(int N){
+        parent = vector<int>(N);
+        iota(parent.begin(), parent.end(), 0);
+    }
+    
+    int find(int x){
+        if(parent[x] != x){
+            parent[x] = find(parent[x]);
+        }
+        return parent[x];
+    }
+    
+    void unite(int x, int y){
+        parent[find(x)] = find(y);
+    }
+};
+
+class Solution {
+public:
+    int regionsBySlashes(vector<string>& grid) {
+        int N = grid.size();
+        //0,1,2,3 for north, west, east, south
+        DSU dsu = DSU(4*N*N);
+        for(int r = 0; r < N; r++){
+            for(int c = 0; c < N; c++){
+                //one grid has max of 4 regions
+                int root = 4 * (r*N+c);
+                char val = grid[r][c];
+                //Note here it is "!="
+                if(val != '\\'){
+                    //north and west are connected
+                    dsu.unite(root + 0, root + 1);
+                    //east and south are connected
+                    dsu.unite(root + 2, root + 3);
+                }
+                if(val != '/'){
+                    //north and east are connected
+                    dsu.unite(root + 0, root + 2);
+                    //west and south are connected
+                    dsu.unite(root + 1, root + 3);
+                }
+                
+                //connecting with other grids
+                //connect south of current grid and north of the grid below
+                if(r + 1 < N)
+                    dsu.unite(root + 3, (root + 4*N) + 0);
+                //north and upper's south
+                if(r - 1 >= 0)
+                    dsu.unite(root + 0, (root - 4*N) + 3);
+                //east and rhs's west
+                if(c + 1 < N)
+                    dsu.unite(root + 2, (root + 4) + 1);
+                //west and lhs's east
+                if(c - 1 >= 0)
+                    dsu.unite(root + 1, (root - 4) + 2);
+            }
+        }
+        
+        int ans = 0;
+        for(int x = 0; x < 4*N*N; x++){
+            if(dsu.find(x) == x)
+                ans++;
+        }
+        
+        return ans;
+    }
+};