[LeetCode] 787. Cheapest Flights Within K Stops_Medium tag: Dynamic Programming, BFS, Heap
There are n
cities connected by m
flights. Each fight starts from city u
and arrives at v
with a price w
.
Now given all the cities and fights, together with starting city src
and the destination dst
, your task is to find the cheapest price from src
to dst
with up to k
stops. If there is no such route, output -1
.
Example 1:
Input:
n = 3, edges = [[0,1,100],[1,2,100],[0,2,500]]
src = 0, dst = 2, k = 1
Output: 200
Explanation:
The graph looks like this:
The cheapest price from city0
to city2
with at most 1 stop costs 200, as marked red in the picture.
Example 2:
Input:
n = 3, edges = [[0,1,100],[1,2,100],[0,2,500]]
src = 0, dst = 2, k = 0
Output: 500
Explanation:
The graph looks like this:
The cheapest price from city0
to city2
with at most 0 stop costs 500, as marked blue in the picture.
Note:
- The number of nodes
n
will be in range[1, 100]
, with nodes labeled from0
ton
- 1
. - The size of
flights
will be in range[0, n * (n - 1) / 2]
. - The format of each flight will be
(src,
dst
, price)
. - The price of each flight will be in the range
[1, 10000]
. k
is in the range of[0, n - 1]
.- There will not be any duplicated flights or self cycles.
这个题目有点类似于[Leetcode] 863. All Nodes Distance K in Binary Tree_ Medium tag: BFS, Amazon, 所以我用BFS, 只是不将dst add进入visited里面, 然后利用 stops <K来做一个
避免太多判断, 但是并不能pass所有的test cases, 我想可能是因为有些node需要重复利用, 因此就将visited去掉, 但是利用stops <K 和 psum <= ans 来避免过多的重复遍历某些不需要的值.
1. Constraints
1) 题目的Note解释很清楚, 基本没有特殊的test case, 但是没提到src == dst, 所以加上这个edge case
2. Ideas
BFS 时间复杂度还真的不好说...
3. Code
class Solution:
def cheapestFlight(self, n, flights, src, dst, K):
if src == dst: return 0
queue, graph, prices, ans = collections.deque([(src, -1, 0)]), collections.defaultdict(set), collections.Counter(), None
for s, e, p in flights:
graph[s].add(e)
prices[(s,e)] = p
while queue:
node, stops, psum = queue.popleft()
if stops <= K and (not ans or psum < ans):
if node == dst:
ans = psum
for each in graph[node]:
queue.append((each, stops + 1, psum + prices[(node, each)]))
return ans if ans else -1
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