|
| 1 | +import heapq |
| 2 | +import math |
| 3 | +import sys |
| 4 | +from collections import defaultdict, deque |
| 5 | + |
| 6 | +read = lambda: sys.stdin.readline().rstrip() |
| 7 | + |
| 8 | + |
| 9 | +class Problem: |
| 10 | + def __init__(self): |
| 11 | + self.n, self.m = map(int, read().split()) |
| 12 | + self.s, self.d = map(int, read().split()) |
| 13 | + |
| 14 | + self.graph = defaultdict(list[tuple[int, int]]) |
| 15 | + for _ in range(self.m): |
| 16 | + u, v, p = map(int, read().split()) |
| 17 | + self.graph[u].append((v, p)) |
| 18 | + |
| 19 | + def solve(self) -> None: |
| 20 | + result = self.dijkstra(self.s, self.remove_edges(self.dijkstra(self.s)))[self.d] |
| 21 | + print(result if result != math.inf else -1) |
| 22 | + |
| 23 | + def dijkstra(self, start_node: int, removed: list[set[int]] = None): |
| 24 | + heap, dist, prev = ( |
| 25 | + [(0, start_node)], |
| 26 | + [0 if x == start_node else math.inf for x in range(self.n)], |
| 27 | + [[] for _ in range(self.n)], |
| 28 | + ) |
| 29 | + |
| 30 | + while heap: |
| 31 | + cost, node = heapq.heappop(heap) |
| 32 | + if cost > dist[node]: |
| 33 | + continue |
| 34 | + |
| 35 | + for next_node, weight in self.graph[node]: |
| 36 | + if removed and next_node in removed[node]: |
| 37 | + continue |
| 38 | + |
| 39 | + if cost + weight < dist[next_node]: |
| 40 | + dist[next_node] = cost + weight |
| 41 | + prev[next_node] = [node] |
| 42 | + heapq.heappush(heap, (cost + weight, next_node)) |
| 43 | + elif removed is None and cost + weight == dist[next_node]: |
| 44 | + prev[next_node].append(node) |
| 45 | + |
| 46 | + return prev if removed is None else dist |
| 47 | + |
| 48 | + def remove_edges(self, prev: list[list[int]]) -> list[set[int]]: |
| 49 | + queue, removed, visited = deque([self.d]), [set() for _ in range(self.n)], {self.d} |
| 50 | + |
| 51 | + while queue: |
| 52 | + node = queue.popleft() |
| 53 | + |
| 54 | + for prev_node in prev[node]: |
| 55 | + removed[prev_node].add(node) |
| 56 | + if prev_node not in visited: |
| 57 | + visited.add(prev_node) |
| 58 | + queue.append(prev_node) |
| 59 | + |
| 60 | + return removed |
| 61 | + |
| 62 | + |
| 63 | +if __name__ == "__main__": |
| 64 | + while True: |
| 65 | + try: |
| 66 | + Problem().solve() |
| 67 | + except (EOFError, ValueError): |
| 68 | + break |
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