You are given an array routes representing bus routes where routes[i] is a bus route that the ith bus repeats forever.
For example, if routes[0] = [1, 5, 7], this means that the 0th bus travels in the sequence 1 -> 5 -> 7 -> 1 -> 5 -> 7 -> 1 -> ... forever.
You will start at the bus stop source (You are not on any bus initially), and you want to go to the bus stop target. You can travel between bus stops by buses only.
Return the least number of buses you must take to travel from source to target. Return -1 if it is not possible.
Example 1:
Input: routes = [[1,2,7],[3,6,7]], source = 1, target = 6
Output: 2
Explanation: The best strategy is take the first bus to the bus stop 7, then take the second bus to the bus stop 6.
Example 2:
Input: routes = [[7,12],[4,5,15],[6],[15,19],[9,12,13]], source = 15, target = 12
Output: -1
Constraints:
1 <= routes.length <= 500.
1 <= routes[i].length <= 10^5
All the values of routes[i] are unique.
sum(routes[i].length) <= 10^5
0 <= routes[i][j] < 10^6
0 <= source, target < 10^6
Solved after help.
Since the requirement is the minimum bus instead of minimum stops, we use bus as the node, then BFS to find the shortest path.
class Solution:
def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
stop_to_route = {}
for route_i, each_route in enumerate(routes):
for each_stop in each_route:
if each_stop not in stop_to_route:
stop_to_route[each_stop] = set()
stop_to_route[each_stop].add(route_i)
queue = collections.deque([(source, 0)])
visited = set()
while queue:
node, step = queue.popleft()
if node == target:
return step
visited.add(node)
for stop_route in stop_to_route[node]:
for neighbor in routes[stop_route]:
if neighbor not in visited:
queue.append((neighbor, step + 1))
routes[stop_route] = []
return -1
An easier but MLE version:
class Solution:
def numBusesToDestination(self, routes: List[List[int]], source: int, target: int) -> int:
stop_to_route = {}
for route_i, each_route in enumerate(routes):
for each_stop in each_route:
if each_stop not in stop_to_route:
stop_to_route[each_stop] = set()
stop_to_route[each_stop].add(route_i)
queue = collections.deque([(source, 0, -1)])
visited = set()
while queue:
node, step, route = queue.popleft()
if node in visited:
continue
visited.add(node)
if node == target:
return step
for stop_route in stop_to_route[node]:
if stop_route == route:
continue
for neighbor in routes[stop_route]:
queue.append((neighbor, step + 1, stop_route))
return -1