class Graph: def __init__(self, n, directed=False, decrement=True, edges=[]): self.n = n self.directed = directed self.decrement = decrement self.edges = [[] for _ in range(self.n)] for x, y, cost in edges: self.add_edge(x, y, cost) def add_edge(self, x, y, cost): if self.decrement: x -= 1 y -= 1 self.edges[x].append((y, cost)) if self.directed == False: self.edges[y].append((x, cost)) def dijkstra(self, start=None, INF=10**18): """ 返り値は 0-indexed !!! :param start: スタート地点 :return: スタート地点から各点への距離のリスト 備考: heqpq の比較のための key は第一引数である点に注意( = heappush(heapq, (key,value)) ) """ self.parent=parent=[-1]*N res = [INF] * self.n if start is None: start=self.decrement start=start-self.decrement res[start] = 0 next_set = [(0, start)] while next_set: dist, p = heappop(next_set) if res[p] < dist: continue """ここで頂点pまでの最短距離が確定。よって、ここを通るのはN回のみ""" for q, cost in self.edges[p]: temp_d = dist + cost if temp_d < res[q]: res[q] = temp_d parent[q] = p heappush(next_set, (temp_d, q)) return res def path_restoring(self,start,goal): start,goal=start-self.decrement,goal-self.decrement q=goal res=[] while q!=start: res.append(q+self.decrement) q=self.parent[q] if q<0: return -1 res.append(start+self.decrement) return res[::-1] def draw(self): """ :return: グラフを可視化 """ import matplotlib.pyplot as plt import networkx as nx if self.directed: G = nx.DiGraph() else: G = nx.Graph() for x in range(self.n): for y, cost in self.edges[x]: G.add_edge(x + self.decrement, y + self.decrement, weight=cost) edge_labels = {(i, j): w['weight'] for i, j, w in G.edges(data=True)} pos = nx.spring_layout(G) nx.draw_networkx(G, pos, with_labels=True, connectionstyle='arc3, rad = 0.1') nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels) plt.axis("off") plt.show() ######################################################### def example(): global input example = iter( """ 3 3 1 2 1 1 3 1 2 3 3 """ .strip().split("\n")) input = lambda: next(example) def example2(): global input example = iter( """ 6 9 1 2 7 2 3 10 1 3 9 1 6 14 3 6 2 5 6 9 4 5 6 2 4 15 3 4 11 """ .strip().split("\n")) input = lambda: next(example) ######################################################### import sys from heapq import * input = sys.stdin.readline # example2() INF = 10**18 # 大きい数字 N, M = map(int, input().split()) graph = Graph(N, directed=False, decrement=True) data=[] for _ in range(M): x, y, cost, cost2 = map(int, input().split()) graph.add_edge(x, y, cost) data.append((x,y,cost,cost2)) dist = graph.dijkstra(start=1,INF=INF) path=graph.path_restoring(1,N) used=set() for i in range(len(path)-1): used.add((path[i],path[i+1])) used.add((path[i+1],path[i])) graph2 = Graph(N, directed=False, decrement=True) for x, y, cost, cost2 in data: if (x,y) in used: graph2.add_edge(x, y, cost2) else: graph2.add_edge(x, y, cost) dist2 = graph2.dijkstra(start=1,INF=INF) print(dist[-1]+dist2[-1])