|
| 1 | +import sys |
| 2 | +from collections import defaultdict, deque |
| 3 | + |
| 4 | +read = lambda: sys.stdin.readline().rstrip() |
| 5 | + |
| 6 | + |
| 7 | +class Problem: |
| 8 | + def __init__(self): |
| 9 | + self.n, self.m = int(read()), int(read()) |
| 10 | + self.graph, self.reverse_graph, self.in_degree = ( |
| 11 | + defaultdict(list[tuple[int, int]]), |
| 12 | + defaultdict(list[tuple[int, int]]), |
| 13 | + [0 for _ in range(self.n)], |
| 14 | + ) |
| 15 | + |
| 16 | + for src, dest, time in [map(int, read().split()) for _ in range(self.m)]: |
| 17 | + self.graph[src - 1].append((dest - 1, time)) |
| 18 | + self.reverse_graph[dest - 1].append((src - 1, time)) |
| 19 | + self.in_degree[dest - 1] += 1 |
| 20 | + |
| 21 | + self.src, self.dest = map(lambda x: int(x) - 1, read().split()) |
| 22 | + |
| 23 | + def solve(self) -> None: |
| 24 | + costs = self.topological_sort() |
| 25 | + |
| 26 | + print(costs[self.dest]) |
| 27 | + print(self.count_critical_paths(costs)) |
| 28 | + |
| 29 | + def topological_sort(self) -> list[int]: |
| 30 | + queue, costs = deque([self.src]), [0 for _ in range(self.n)] |
| 31 | + |
| 32 | + while queue: |
| 33 | + node = queue.popleft() |
| 34 | + |
| 35 | + for next_node, next_time in self.graph[node]: |
| 36 | + if costs[next_node] < costs[node] + next_time: |
| 37 | + costs[next_node] = costs[node] + next_time |
| 38 | + |
| 39 | + self.in_degree[next_node] -= 1 |
| 40 | + if self.in_degree[next_node] == 0: |
| 41 | + queue.append(next_node) |
| 42 | + |
| 43 | + return costs |
| 44 | + |
| 45 | + def count_critical_paths(self, costs: list[int]) -> int: |
| 46 | + queue, visited, count = deque([self.dest]), {self.dest}, 0 |
| 47 | + |
| 48 | + while queue: |
| 49 | + node = queue.popleft() |
| 50 | + |
| 51 | + for prev, cost in self.reverse_graph[node]: |
| 52 | + if costs[prev] + cost != costs[node]: |
| 53 | + continue |
| 54 | + |
| 55 | + count += 1 |
| 56 | + if prev not in visited: |
| 57 | + visited.add(prev) |
| 58 | + queue.append(prev) |
| 59 | + |
| 60 | + return count |
| 61 | + |
| 62 | + |
| 63 | +if __name__ == "__main__": |
| 64 | + Problem().solve() |
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