def oi(): return int(input()) def os(): return input() def mi(): return list(map(int, input().split())) # import sys # input = sys.stdin.readline # import sys # sys.setrecursionlimit(10**8) # import pypyjit # pypyjit.set_param('max_unroll_recursion=-1') input_count = 0 input_count = 0 N,M,K = mi() NODE = N LOOP_NUM = M maps = {i:[] for i in range(NODE)} cost_dict = {} for i in range(LOOP_NUM): a,b,c = mi() maps[a-1].append((b-1, c)) maps[b-1].append((a-1,c)) cost_dict[(a-1,b-1)] = c cost_dict[(b-1,a-1)] = c # K 未満の時 from collections import deque reached = [0] * N ## 1つ前のノードを持たせると微妙に遅くなるのでやめよう deq = deque([[0,0]]) mins = float("inf") while deq: node, count = deq.pop() #BFS if node == N-1: if count < K : mins = 0 break reached[node] = -1 for next_node, cost in maps[node]: # 訪問済み判定 if reached[next_node] == -1: continue if count+1 <= K: mins = min(mins, cost) reached[next_node] = -1 deq.append([next_node, count+1]) # https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py import math from bisect import bisect_left, bisect_right, insort from typing import Generic, Iterable, Iterator, TypeVar, Union, List T = TypeVar('T') class SortedMultiset(Generic[T]): BUCKET_RATIO = 50 REBUILD_RATIO = 170 def _build(self, a=None) -> None: "Evenly divide `a` into buckets." if a is None: a = list(self) size = self.size = len(a) bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO))) self.a = [a[size * i // bucket_size : size * (i + 1) // bucket_size] for i in range(bucket_size)] def __init__(self, a: Iterable[T] = []) -> None: "Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)" a = list(a) if not all(a[i] <= a[i + 1] for i in range(len(a) - 1)): a = sorted(a) self._build(a) def __iter__(self) -> Iterator[T]: for i in self.a: for j in i: yield j def __reversed__(self) -> Iterator[T]: for i in reversed(self.a): for j in reversed(i): yield j def __len__(self) -> int: return self.size def __repr__(self) -> str: return "SortedMultiset" + str(self.a) def __str__(self) -> str: s = str(list(self)) return "{" + s[1 : len(s) - 1] + "}" def _find_bucket(self, x: T) -> List[T]: "Find the bucket which should contain x. self must not be empty." for a in self.a: if x <= a[-1]: return a return a def __contains__(self, x: T) -> bool: if self.size == 0: return False a = self._find_bucket(x) i = bisect_left(a, x) return i != len(a) and a[i] == x def count(self, x: T) -> int: "Count the number of x." return self.index_right(x) - self.index(x) def add(self, x: T) -> None: "Add an element. / O(√N)" if self.size == 0: self.a = [[x]] self.size = 1 return a = self._find_bucket(x) insort(a, x) self.size += 1 if len(a) > len(self.a) * self.REBUILD_RATIO: self._build() def discard(self, x: T) -> bool: "Remove an element and return True if removed. / O(√N)" if self.size == 0: return False a = self._find_bucket(x) i = bisect_left(a, x) if i == len(a) or a[i] != x: return False a.pop(i) self.size -= 1 if len(a) == 0: self._build() return True def lt(self, x: T) -> Union[T, None]: "Find the largest element < x, or None if it doesn't exist." for a in reversed(self.a): if a[0] < x: return a[bisect_left(a, x) - 1] def le(self, x: T) -> Union[T, None]: "Find the largest element <= x, or None if it doesn't exist." for a in reversed(self.a): if a[0] <= x: return a[bisect_right(a, x) - 1] def gt(self, x: T) -> Union[T, None]: "Find the smallest element > x, or None if it doesn't exist." for a in self.a: if a[-1] > x: return a[bisect_right(a, x)] def ge(self, x: T) -> Union[T, None]: "Find the smallest element >= x, or None if it doesn't exist." for a in self.a: if a[-1] >= x: return a[bisect_left(a, x)] def __getitem__(self, x: int) -> T: "Return the x-th element, or IndexError if it doesn't exist." if x < 0: x += self.size if x < 0: raise IndexError for a in self.a: if x < len(a): return a[x] x -= len(a) raise IndexError def index(self, x: T) -> int: "Count the number of elements < x." ans = 0 for a in self.a: if a[-1] >= x: return ans + bisect_left(a, x) ans += len(a) return ans def index_right(self, x: T) -> int: "Count the number of elements <= x." ans = 0 for a in self.a: if a[-1] > x: return ans + bisect_right(a, x) ans += len(a) return ans if mins != 0: # K以上の時 sets = SortedMultiset([]) # 帰りがけ deq = deque([[-1, 0, True]]) # 一番最後のTrue, Falseで while deq: old_node, node, preorder = deq.pop() # 行き if preorder: # 帰りに寄るようにFalseをpush deq.append([old_node, node, False]) if node == N-1: mins = min(sets[-K], mins) continue for next_node, cost in maps[node]: if next_node != old_node: # 新たな探索をpush deq.append([node, next_node, True]) sets.add(cost) # 帰り else: if old_node!=-1: # ここで帰りがけに行いたい処理を書く C = cost_dict[(node,old_node)] sets.discard(C) print(mins)