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Problem solution · Python

ABC315 E — Prerequisites

ABC315 E — Prerequisites: 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
130 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 ABC315 E — Prerequisites, 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

  • 130 lines of Python from the credited upstream file abc315_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 codeABC315 E — Prerequisites · PythonPython
Use this to learn the idea, then write your own version.
# -*- coding: utf-8 -*-  from collections import dequefrom typing import List, Tuple  class TopologicalSorting:    """    See:    https://atcoder.jp/contests/abc291/submissions/39241055    """     def __init__(self, vertex_count: int) -> None:        self.vertex_count = vertex_count        self.graph = [[] for _ in range(vertex_count)]        self.indegrees = [0] * vertex_count     def add_edge(self, frm: int, to: int) -> None:        """        Args:            frm(from) -> to: Vertex number (0-indexed).        """        assert 0 <= frm < self.vertex_count        assert 0 <= to < self.vertex_count         self.graph[frm].append(to)        self.indegrees[to] += 1     def sort(self) -> Tuple[bool, List[int]]:        """        Returns:            is_DAG: Is it DAG (Directed Acyclic Graph) ?            orders: Order of vertices (0-indexed).        """        que = deque([i for i in range(self.vertex_count) if self.indegrees[i] == 0])        results = list()        # initial_value = 0  # TODO: Set value if needs.        # costs = [initial_value] * self.vertex_count         if len(que) == 0:            return False, []         while que:            # No more than two vertices with indegree 0 are allowed.            # if len(que) >= 2:            #     return False, []             vertex = que.popleft()            results.append(vertex)             for to in self.graph[vertex]:                self.indegrees[to] -= 1                 # Update costs.                # costs[to] = max(costs[to], costs[vertex] + 1)                 if self.indegrees[to] == 0:                    que.append(to)         if len(results) == self.vertex_count:            return True, results            # return True, costs        else:            return False, []     def sort_only_reachable_vertices_from(        self, start_id: int = 0    ) -> Tuple[bool, List[int]]:        """        Returns:            is_DAG: Is it DAG (Directed Acyclic Graph) ?            orders: Order of vertices (1-indexed).        """        is_DAG, orders = self.sort()         if not is_DAG:            return is_DAG, orders         que = deque([start_id])        visited = [False] * self.vertex_count         while que:            cur = que.popleft()             if visited[cur]:                continue             visited[cur] = True             for to in self.graph[cur]:                if visited[to]:                    continue                 que.append(to)         reachable_orders = list()         for order in orders:            if visited[order]:                reachable_orders.append(order + 1)         return is_DAG, reachable_orders  def main():    import sys     input = sys.stdin.readline     n = int(input())    ts = TopologicalSorting(n)     for i in range(n):        ci, *pi = map(int, input().split())         if ci == 0:            continue         for pij in pi:            pij -= 1            ts.add_edge(frm=i, to=pij)     is_DAG, orders = ts.sort_only_reachable_vertices_from(start_id=0)    print(*orders[1:][::-1])  if __name__ == "__main__":    main()

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