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Problem solution · Python

ABC361 E — Tree and Hamilton Path 2

ABC361 E — Tree and Hamilton Path 2: a Python solution using breadth-first search. Learn the idea, check the complexity, and read the full code, with credit to KATO-Hiro AtCoder Solutions.

Technique
Breadth-first search
Source
KATO-Hiro AtCoder Solutions
Length
78 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Breadth-first search

For ABC361 E — Tree and Hamilton Path 2, the implementation explores reachable states in layers, which is the standard shape for unweighted shortest paths and minimum-step transitions.

  1. Model each valid configuration as a state and each legal move as an edge.
  2. Seed the queue with the starting state and mark it immediately.
  3. Expand each state once, recording distance or reachability for unseen neighbours.

Code notes

  • 78 lines of Python from the credited upstream file abc361_e.py.
  • The implementation visibly relies on sequence storage, ordered lookup, work queue.
  • No explicit loop blocks detected.

Complexity

Verify that each state and transition is processed only a bounded number of times; that determines the traversal cost.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from KATO-Hiro AtCoder Solutions by KATO-Hiro and is used under the CC0-1.0 licence.

Open problem ↗Original source ↗
Full codeABC361 E — Tree and Hamilton Path 2 · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  class TreeDiameter:    def __init__(self, vertex_count: int, graph) -> None:        self.vertex_count = vertex_count        self.graph = graph     def calc(self, source: int) -> tuple[int, int, int]:        assert 0 <= source < self.vertex_count         p, _ = self._find_farthest_vertex(source=source)        q, dist_max = self._find_farthest_vertex(source=p)         return dist_max, p, q     def _find_farthest_vertex(self, source: int) -> tuple[int, int]:        from collections import deque         visited = [False for _ in range(self.vertex_count)]        que = deque([(0, source)])         farthest_vertex = source        dist_max = 0         while que:            dist, vertex = que.popleft()             if visited[vertex]:                continue             visited[vertex] = True             for weight, next_vertex in self.graph[vertex]:                if not (0 <= next_vertex < self.vertex_count):                    continue                if visited[next_vertex]:                    continue                 new_dist = dist + weight                que.append((new_dist, next_vertex))                 if new_dist > dist_max:                    farthest_vertex = next_vertex                    dist_max = new_dist         return farthest_vertex, dist_max  def main():    import sys     input = sys.stdin.readline     n = int(input())    graph = [[] for _ in range(n)]    ans = 0     # 2 * Σ Ci - 木の直径    for _ in range(n - 1):        ai, bi, ci = map(int, input().split())        ai -= 1        bi -= 1         graph[ai].append((ci, bi))        graph[bi].append((ci, ai))         ans += ci * 2     tree_diameter = TreeDiameter(vertex_count=n, graph=graph)    dist, _, _ = tree_diameter.calc(source=0)    ans -= dist    print(ans)  if __name__ == "__main__":    main()

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