Update 0261-graph-valid-tree.py

python/0261-graph-valid-tree.py

@@ -29,3 +29,45 @@ def dfs(i, prev):
             return True
 
         return dfs(0, -1) and n == len(visit)
+
+
+
+    # alternative solution via DSU O(ElogV) time complexity and 
+    # save some space as we don't recreate graph\tree into adjacency list prior dfs and loop over the edge list directly
+    class Solution:
+    """
+    @param n: An integer
+    @param edges: a list of undirected edges
+    @return: true if it's a valid tree, or false
+    """
+    def __find(self, n: int) -> int:
+        while n != self.parents.get(n, n):
+            n = self.parents.get(n, n)
+        return n
+
+    def __connect(self, n: int, m: int) -> None:
+        pn = self.__find(n)
+        pm = self.__find(m)
+        if pn == pm:
+            return
+        if self.heights.get(pn, 1) > self.heights.get(pm, 1):
+            self.parents[pn] = pm
+        else:
+            self.parents[pm] = pn
+            self.heights[pm] = self.heights.get(pn, 1) + 1
+        self.components -= 1
+
+    def valid_tree(self, n: int, edges: List[List[int]]) -> bool:
+        # init here as not sure that ctor will be re-invoked in different tests
+        self.parents = {}
+        self.heights = {}
+        self.components = n
+
+        for e1, e2 in edges:
+            if self.__find(e1) == self.__find(e2):  # 'redundant' edge
+                return False
+            self.__connect(e1, e2)
+
+        return self.components == 1  # forest contains one tree
+
+