hamidgasmi · Jul 24, 2022
diff --git a/‎09-problems/lc_787_cheapest_flights_within_k_stops.py
Lines changed: 43 additions & 34 deletions b/‎09-problems/lc_787_cheapest_flights_within_k_stops.py
Lines changed: 43 additions & 34 deletions
@@ -25,8 +25,7 @@
             - To visit cities multiple-times: when curr visit path price < prev visit path price
             - To stop a path if its price > dst cheapest path price
         - DFS + memoization:
-            - 
-        - We could do better:
+        - Dijkstra:
 
     3. Implementation
     4. Tests:
@@ -35,6 +34,7 @@
        Space Compexity:
 
 """
+import heapq
 from typing import List
 
 class Solution_Base:
@@ -164,35 +164,44 @@ def __dfs(self, src: int, dst: int, adjacency_list: List[List[int]], remaining_s
         memo[(src, remaining_stops_count)] = cheapest_price
         return cheapest_price
 
-'''
-4
-[[0,1,100],[1,2,100],[2,0,100],[1,3,600],[2,3,200]]
-0
-3
-1
-
-5
-[[0,1,5],[1,2,5],[0,3,2],[3,1,2],[1,4,1],[4,2,1]]
-0
-2
-2
-
-17
-[[0,12,28],[5,6,39],[8,6,59],[13,15,7],[13,12,38],[10,12,35],[15,3,23],[7,11,26],[9,4,65],[10,2,38],[4,7,7],[14,15,31],[2,12,44],[8,10,34],[13,6,29],[5,14,89],[11,16,13],[7,3,46],[10,15,19],[12,4,58],[13,16,11],[16,4,76],[2,0,12],[15,0,22],[16,12,13],[7,1,29],[7,14,100],[16,1,14],[9,6,74],[11,1,73],[2,11,60],[10,11,85],[2,5,49],[3,4,17],[4,9,77],[16,3,47],[15,6,78],[14,1,90],[10,5,95],[1,11,30],[11,0,37],[10,4,86],[0,8,57],[6,14,68],[16,8,3],[13,0,65],[2,13,6],[5,13,5],[8,11,31],[6,10,20],[6,2,33],[9,1,3],[14,9,58],[12,3,19],[11,2,74],[12,14,48],[16,11,100],[3,12,38],[12,13,77],[10,9,99],[15,13,98],[15,12,71],[1,4,28],[7,0,83],[3,5,100],[8,9,14],[15,11,57],[3,6,65],[1,3,45],[14,7,74],[2,10,39],[4,8,73],[13,5,77],[10,0,43],[12,9,92],[8,2,26],[1,7,7],[9,12,10],[13,11,64],[8,13,80],[6,12,74],[9,7,35],[0,15,48],[3,7,87],[16,9,42],[5,16,64],[4,5,65],[15,14,70],[12,0,13],[16,14,52],[3,10,80],[14,11,85],[15,2,77],[4,11,19],[2,7,49],[10,7,78],[14,6,84],[13,7,50],[11,6,75],[5,10,46],[13,8,43],[9,10,49],[7,12,64],[0,10,76],[5,9,77],[8,3,28],[11,9,28],[12,16,87],[12,6,24],[9,15,94],[5,7,77],[4,10,18],[7,2,11],[9,5,41]]
-13
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-1
-99
-99
-'''
-    
+class Solution_Dijktra(Solution_Base):
+    '''
+        Time Complexity: O(E * Log|E|)
+            T = T(Build Adjacency List) + T(Dijkstra)
+              = O(|E|)                  + O(E * Log|E|)
+            
+        Space Complexity: O(|V| + |E|)
+            S = S(Adjacency_list) + S(Dijkstra)
+              = O(|V| + |E|)      + O(|V| + |E|)
+    
+    '''
+    def find_cheapest_price(self, cities_count: int, flights: List[List[int]], src: int, dst: int, max_stops_count: int) -> int:
+        adjacency_list = self.__build_adjacency_list(cities_count, flights)
+
+        if (self.__indegree(dst) == 0):
+            return -1
+
+        stops = [ max_stops_count+1 for _ in range(cities_count) ]
+        prices = [ self.__max_pirce for _ in range(cities_count) ]
+        stops[src], prices[src] = 0, 0
+
+        cheapest_flights = [ (0, 0, src) ]
+        while cheapest_flights:
+            (path_price, path_stops, path_stop_city) = heapq.heappop(cheapest_flights) 
+            if path_stop_city == dst:
+                return path_price
+            
+            elif path_stop_city == max_stops_count + 1:
+                continue
+
+            for [ next_city, price ] in adjacency_list[path_stop_city]: # each edge can be pushed only 1 time into the heap
+                candidate_path_price = path_price + price
+                candidate_path_stops = path_stops + 1
+                if candidate_path_price < prices[next_city]:
+                    prices[next_city] = candidate_path_price
+                    heapq.heappush(cheapest_flights, (candidate_path_price, candidate_path_stops, next_city))
+                
+                elif candidate_path_price < stops[next_city]:
+                    heapq.heappush(cheapest_flights, (candidate_path_price, candidate_path_stops, next_city))
+        
+        return -1 if prices[dst] == self.__max_pirce else prices[dst]