Bzoj1003 (Short Circuit + dp)

1003: [zjoi2006] Logistics and Transportation transtime limit: 10 sec memory limit: 162 MB
Submit: 3479 solved: 1416
[Submit] [Status] Description

The logistics company wants to ship a batch of goods from Pier A to Terminal B. Because the cargo volume is large, it takes n days to complete the operation. In the process of cargo transportation, it is generally necessary to stop several docks. Logistics companies usually design a fixed transportation route to strictly manage and track the entire transportation process. Due to various factors, sometimes the cargo cannot be loaded or unloaded at a certain pier. At this time, you must modify the transportation route so that the goods can arrive at the destination on time. However, modifying the route is a very troublesome task and will incur additional costs. Therefore, the logistics company wants to set up a transportation plan for N days to minimize the total cost.

Input

The first row contains four integers, n (1 <= n <= 100), m (1 <= m <= 20), K, and E. N indicates the number of days required for cargo transportation, M indicates the total number of terminals, and K indicates the cost required for each modification of the transportation route. Next, each line of line E is a route description, which contains three integers, indicating the number of two terminals connected to the route and the length of the route (> 0 ). Pier A is 1 and pier B is M. The transportation fee per unit is 1. The route is bidirectional. The next row is an integer d, and the next row of D is three integers p (1 <p <m), A, B (1 <= A <= B <= N ). It indicates that goods (including head and tail) cannot be loaded and loaded from day A to day B of the pier numbered p ). The same pier may be unavailable for multiple time periods. However, there is at least one transportation route from Pier A to pier B at any time.

Output

An integer is included to indicate the minimum total cost. Total cost = the sum of N-day transportation route lengths + K * The number of transportation routes changed.

Sample input5 5 10 8
1 2 1
1 3 3
1 4 2
2 3 2
2 4 4
3 4 1
3 5 2
4 5 2
4
2 2 3
3 1 1
3 3 3
4 4 5
Sample output32hint

Take 1-4-5 for the first three days, and 1-3-5 for the next two days. The total cost is (2 + 2) x 3 + (3 + 2) * 2 + 10 = 32

Question: RT
Train of Thought: pre-process the minimum cost of not changing the route for all interval days
Use DP [I] [J] to represent the minimum cost of the route from day I to day J without changing the route (use DJs or spfa to run the shortest path each time)
Then dp2 [I] is used to indicate the minimum cost until the day I.
Transfer to dp2 [I] = min (dp2 [J] + dp [J + 1] [I] + k)

Bzoj1003 (Short Circuit + dp)