링크

https://leetcode.com/problems/cheapest-flights-within-k-stops/

문제 설명

There are n cities connected by some number of flights. You are given an array flights where flights[i] = [fromi, toi, pricei] indicates that there is a flight from city fromi to city toi with cost pricei.

You are also given three integers src, dst, and k, return the cheapest price from src to dst with at most k stops. If there is no such route, return -1.

입력

출력

Input: n = 4, flights = [[0,1,100],[1,2,100],[2,0,100],[1,3,600],[2,3,200]], src = 0, dst = 3, k = 1
Output: 700
Explanation:
The graph is shown above.
The optimal path with at most 1 stop from city 0 to 3 is marked in red and has cost 100 + 600 = 700.
Note that the path through cities [0,1,2,3] is cheaper but is invalid because it uses 2 stops.

제한 조건

1 <= n <= 100
0 <= flights.length <= (n * (n - 1) / 2)
flights[i].length == 3
0 <= fromi, toi < n
fromi != toi
1 <= pricei <= 104
There will not be any multiple flights between two cities.
0 <= src, dst, k < n
src != dst

전체 코드

import heapq

class Solution:
    
    def dijkstra(self,graph:dict,start:int,end:int,k:int)->int:
        heap=[]
        visited_set=set()
        # (cost,node,visit_count)
        visited_set.add((0,start,0))
        
        #(node,cost,visit_count)
        heapq.heappush(heap,(0,start,0))
        
        while heap:
            cost,node,visit_count=heapq.heappop(heap)
            if node==end:
                return cost
        
            for adj_node,adj_cost in graph[node]:
                new_state=(cost+adj_cost,adj_node,visit_count+1)
                if visit_count+1<=k and new_state not in visited_set:
                    visited_set.add(new_state)
                    heapq.heappush(heap,new_state)
                
        return -1
            
        
    def findCheapestPrice(self, n: int, flights: List[List[int]], src: int, dst: int, k: int) -> int:
        graph=dict()
        for i in range(n):
            graph[i]=[]
            
        for u,v,cost in flights:
            graph[u].append((v,cost))
        
        return self.dijkstra(graph,src,dst,k+1)
        

해설

방문했던 노드라도 방문 횟수에 따라 상태가 다르다. 따라서 힙에 담을 때 (비용,노드,방문 횟수) 튜플로 담아야 한다.