|
| 1 | +from collections import deque |
| 2 | +from math import ceil |
| 3 | +from typing import List, Tuple |
| 4 | + |
| 5 | + |
| 6 | +class Solution: |
| 7 | + def __build_adj_list(self, n: int, edges: List[int]) -> List[List[int]]: |
| 8 | + adj_list = [[] for _ in range(n)] |
| 9 | + for u, v in edges: |
| 10 | + adj_list[u].append(v) |
| 11 | + adj_list[v].append(u) |
| 12 | + return adj_list |
| 13 | + |
| 14 | + def __find_diameter(self, n: int, adj_list: List[List[int]]) -> int: |
| 15 | + farthest_node, _ = self.__find_farthest_node(n, adj_list) |
| 16 | + _, diameter = self.__find_farthest_node(n, adj_list, farthest_node) |
| 17 | + return diameter |
| 18 | + |
| 19 | + def __find_farthest_node( |
| 20 | + self, n: int, adj_list: List[List[int]], source_node: int = 0 |
| 21 | + ) -> Tuple[int, int]: |
| 22 | + queue = deque([source_node]) |
| 23 | + visited = [i == source_node for i in range(n)] |
| 24 | + |
| 25 | + max_distance = 0 |
| 26 | + farthest_node = source_node |
| 27 | + |
| 28 | + while queue: |
| 29 | + for _ in range(len(queue)): |
| 30 | + current_node = queue.popleft() |
| 31 | + farthest_node = current_node |
| 32 | + for neighbor in adj_list[current_node]: |
| 33 | + if not visited[neighbor]: |
| 34 | + visited[neighbor] = True |
| 35 | + queue.append(neighbor) |
| 36 | + if queue: |
| 37 | + max_distance += 1 |
| 38 | + |
| 39 | + return farthest_node, max_distance |
| 40 | + |
| 41 | + def minimumDiameterAfterMerge(self, edges1: List[List[int]], edges2: List[List[int]]) -> int: |
| 42 | + n, m = len(edges1) + 1, len(edges2) + 1 |
| 43 | + |
| 44 | + adj_list1 = self.__build_adj_list(n, edges1) |
| 45 | + adj_list2 = self.__build_adj_list(m, edges2) |
| 46 | + |
| 47 | + diameter1 = self.__find_diameter(n, adj_list1) |
| 48 | + diameter2 = self.__find_diameter(m, adj_list2) |
| 49 | + |
| 50 | + combined_diameter = ceil(diameter1 / 2) + ceil(diameter2 / 2) + 1 |
| 51 | + return max(diameter1, diameter2, combined_diameter) |
| 52 | + |
| 53 | + |
| 54 | +def main(): |
| 55 | + edges1 = [[0, 1], [0, 2], [0, 3]] |
| 56 | + edges2 = [[0, 1]] |
| 57 | + assert Solution().minimumDiameterAfterMerge(edges1, edges2) == 3 |
| 58 | + |
| 59 | + edges1 = [[0, 1], [0, 2], [0, 3], [2, 4], [2, 5], [3, 6], [2, 7]] |
| 60 | + edges2 = [[0, 1], [0, 2], [0, 3], [2, 4], [2, 5], [3, 6], [2, 7]] |
| 61 | + assert Solution().minimumDiameterAfterMerge(edges1, edges2) == 5 |
| 62 | + |
| 63 | + |
| 64 | +if __name__ == '__main__': |
| 65 | + main() |
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