diff --git a/graph-valid-tree/EGON.py b/graph-valid-tree/EGON.py new file mode 100644 index 000000000..bb006799f --- /dev/null +++ b/graph-valid-tree/EGON.py @@ -0,0 +1,83 @@ +from typing import List +from unittest import TestCase, main + + +class ListNode: + def __init__(self, val=0, next=None): + self.val = val + self.next = next + + +class Solution: + def valid_tree(self, n: int, edges: List[List[int]]) -> bool: + return self.solve_union_find(n, edges) + + """ + LintCode 로그인이 안되어서 https://neetcode.io/problems/valid-tree에서 실행시키고 통과만 확인했습니다. + + Runtime: ? ms (Beats ?%) + Time Complexity: O(max(m, n)) + - UnionFind의 parent 생성에 O(n) + - edges 조회에 O(m) + - Union-find 알고리즘의 union을 매 조회마다 사용하므로, * O(α(n)) (α는 아커만 함수의 역함수) + - UnionFind의 모든 노드가 같은 부모, 즉 모두 연결되어 있는지 확인하기 위해, n번 find에 O(n * α(n)) + > O(n) + O(m * α(n)) + O(n * α(n)) ~= O(max(m, n) * α(n)) ~= O(max(m, n)) (∵ α(n) ~= C) + + Memory: ? MB (Beats ?%) + Space Complexity: O(n) + - UnionFind의 parent와 rank가 크기가 n인 리스트이므로, O(n) + O(n) + > O(n) + O(n) ~= O(n) + """ + def solve_union_find(self, n: int, edges: List[List[int]]) -> bool: + + class UnionFind: + def __init__(self, size: int): + self.parent = [i for i in range(size)] + self.rank = [1] * size + + def union(self, first: int, second: int) -> bool: + first_parent, second_parent = self.find(first), self.find(second) + if first_parent == second_parent: + return False + + if self.rank[first_parent] > self.rank[second_parent]: + self.parent[second_parent] = first_parent + elif self.rank[first_parent] < self.rank[second_parent]: + self.parent[first_parent] = second_parent + else: + self.parent[second_parent] = first_parent + self.rank[first_parent] += 1 + + return True + + def find(self, node: int): + if self.parent[node] != node: + self.parent[node] = self.find(self.parent[node]) + + return self.parent[node] + + unionFind = UnionFind(size=n) + for first, second in edges: + is_cycle = unionFind.union(first, second) is False + if is_cycle: + return False + + root = unionFind.find(0) + for i in range(1, n): + if unionFind.find(i) != root: + return False + + return True + + +class _LeetCodeTestCases(TestCase): + def test_1(self): + n = 5 + edges = [[0, 1], [1, 2], [2, 3], [1, 3], [1, 4]] + output = False + + self.assertEqual(Solution().valid_tree(n, edges), output) + + +if __name__ == '__main__': + main()