Codeforces Problem 707B Bakery(思维题)

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比赛链接→Codeforces Round #368 (Div. 2)

 Codeforces Problem 707B Bakery

Accept: 0    Submit: 0
Time Limit: 2 seconds    Memory Limit : 256 megabytes

 Problem Description

Masha wants to open her own bakery and bake muffins in one of the n cities numbered from 1 to n. There are m bidirectional roads, each of whose connects some pair of cities.

To bake muffins in her bakery, Masha needs to establish flour supply from some storage. There are only k storages, located in different cities numbered a1, a2, ..., ak.

Unforunately the law of the country Masha lives in prohibits opening bakery in any of the cities which has storage located in it. She can open it only in one of another n - k cities, and, of course, flour delivery should be paid — for every kilometer of path between storage and bakery Masha should pay 1 ruble.

Formally, Masha will pay x roubles, if she will open the bakery in some city b (ai ≠ b for every 1 ≤ i ≤ k) and choose a storage in some city s (s = aj for some 1 ≤ j ≤ k) and b and s are connected by some path of roads of summary length x (if there are more than one path, Masha is able to choose which of them should be used).

Masha is very thrifty and rational. She is interested in a city, where she can open her bakery (and choose one of k storages and one of the paths between city with bakery and city with storage) and pay minimum possible amount of rubles for flour delivery. Please help Masha find this amount.

 Input

The first line of the input contains three integers n, m and k (1 ≤ n, m ≤ 10^5, 0 ≤ k ≤ n) — the number of cities in country Masha lives in, the number of roads between them and the number of flour storages respectively.

Then m lines follow. Each of them contains three integers u, v and l (1 ≤ u, v ≤ n, 1 ≤ l ≤ 10^9, u ≠ v) meaning that there is a road between cities u and v of length of l kilometers .

If k > 0, then the last line of the input contains k distinct integers a1, a2, ..., ak (1 ≤ ai ≤ n) — the number of cities having flour storage located in. If k = 0 then this line is not presented in the input.

 Output

Print the minimum possible amount of rubles Masha should pay for flour delivery in the only line.

If the bakery can not be opened (while satisfying conditions) in any of the n cities, print  - 1 in the only line.

 Sample Input

5 4 2
1 2 5
1 2 3
2 3 4
1 4 10
1 5
3 1 1
1 2 3
3

 Sample Output

3
-1

 Hint

Image illustrates the first sample case. Cities with storage located in and the road representing the answer are darkened.

 Problem Idea

解题思路:

【题意】
n个城市,m条双向路

n个城市中有k个城市中有仓库

现在要在一个没有仓库的城市开一家面包店,使得该面包店能够至少到达一个仓库,且到达该仓库的距离尽可能小

问最小距离为多少,若没有城市适合开设面包店,则输出"-1"

【类型】
思维题

【分析】
该开始觉得有点难以下手,因为既不知道应该以哪个城市作为起点,又不知道应该以哪个城市作为终点,且又不能用floyd暴力求解两两城市之间的距离

但是,仔细思考一下,你会发现,我们只需要考虑和仓库直接相连的城市就可以了,因为那些可达但和仓库没有直接相连的城市必定是经过了某个与仓库直接相连的城市,这样距离势必会比直接相连来得长,如图

城市1和城市5有仓库,那我们只需要考虑城市2和城市4,之所以不考虑城市3是因为仓库1到城市3必须要经过城市2,显然城市2比城市3离仓库1更近

于是,我们只要把有仓库的城市标记,如果某条双向路一端连着有仓库的城市,另一端连着没有仓库的城市,那就把这条路的长度取来作比较,留下距离最短的路即可

【时间复杂度&&优化】
O(n)

题目链接→Codeforces Problem 707B Bakery

 Source Code

/*Sherlock and Watson and Adler*/
#pragma comment(linker, "/STACK:1024000000,1024000000")
#include
#include
#include
#include
#include
#include
#include
#include

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