P3008 [USACO11JAN]道路和飞机Roads and Planes

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  • 题目提供者 FarmerJohn2
  • 评测方式 云端评测
  • 标签 USACO 2011 高性能
  • 难度 提高+/省选-
  • 时空限制 1000ms / 128MB

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    题目描述

    Farmer John is conducting research for a new milk contract in a new territory. He intends to distribute milk to T (1 <= T <= 25,000) towns conveniently numbered 1..T which are connected by up to R (1 <= R <= 50,000) roads conveniently numbered 1..R and/or P (1 <= P <= 50,000) airplane flights conveniently numbered 1..P.

    Either road i or plane i connects town A_i (1 <= A_i <= T) to town B_i (1 <= B_i <= T) with traversal cost C_i. For roads, 0 <= C_i <= 10,000; however, due to the strange finances of the airlines, the cost for planes can be quite negative (-10,000 <= C_i <= 10,000).

    Roads are bidirectional and can be traversed from A_i to B_i or B_i to A_i for the same cost; the cost of a road must be non-negative.

    Planes, however, can only be used in the direction from A_i to B_i specified in the input. In fact, if there is a plane from A_i to B_i it is guaranteed that there is no way to return from B_i to A_i with any sequence of roads and planes due to recent antiterror regulation.

    Farmer John is known around the world as the source of the world's finest dairy cows. He has in fact received orders for his cows from every single town. He therefore wants to find the cheapest price for delivery to each town from his distribution center in town S (1 <= S <= T) or to know that it is not possible if this is the case.

    MEMORY LIMIT: 64MB

    Farmer John正在一个新的销售区域对他的牛奶销售方案进行调查。他想把牛奶送到T个城镇 (1 <= T <= 25,000),编号为1T。这些城镇之间通过R条道路 (1 <= R <= 50,000,编号为1到R) 和P条航线 (1 <= P <= 50,000,编号为1到P) 连接。每条道路i或者航线i连接城镇A_i (1 <= A_i <= T)到B_i (1 <= B_i <= T),花费为C_i。

    对于道路,0 <= C_i <= 10,000;然而航线的花费很神奇,花费C_i可能是负数(-10,000 <= C_i <= 10,000)。道路是双向的,可以从A_i到B_i,也可以从B_i到A_i,花费都是C_i。然而航线与之不同,只可以从A_i到B_i。

    事实上,由于最近恐怖主义太嚣张,为了社会和谐,出台 了一些政策保证:如果有一条航线可以从A_i到B_i,那么保证不可能通过一些道路和航线从B_i回到A_i。由于FJ的奶牛世界公认十分给力,他需要运送奶牛到每一个城镇。他想找到从发送中心城镇S(1 <= S <= T) 把奶牛送到每个城镇的最便宜的方案,或者知道这是不可能的。

    输入输出格式

    输入格式:

    * Line 1: Four space separated integers: T, R, P, and S

    * Lines 2..R+1: Three space separated integers describing a road: A_i, B_i and C_i

    * Lines R+2..R+P+1: Three space separated integers describing a plane: A_i, B_i and C_i

    输出格式:

    * Lines 1..T: The minimum cost to get from town S to town i, or 'NO PATH' if this is not possible

    输入输出样例

    输入样例#1: 复制
    6 3 3 4 
    1 2 5 
    3 4 5 
    5 6 10 
    3 5 -100 
    4 6 -100 
    1 3 -10 
    
    输出样例#1: 复制
    NO PATH 
    NO PATH 
    5 
    0 
    -95 
    -100 
    

    说明

    6 towns. There are roads between town 1 and town 2, town 3 and town 4, and town 5 and town 6 with costs 5, 5 and 10; there are planes from town 3 to town 5, from town 4 to town 6, and from town 1 to town 3 with costs -100, - 100 and -10. FJ is based in town 4.

    FJ's cows begin at town 4, and can get to town 3 on the road. They can get to towns 5 and 6 using planes from towns 3 and 4. However, there is no way to get to towns 1 and 2, since they cannot go

    backwards on the plane from 1 to 3.

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