1003. Emergency（25分）求图的最短距离，最大点权，最短路径条数（dijkstra算法）

本文链接：https://blog.youkuaiyun.com/rnzhiw/article/details/102825099

As an emergency rescue team leader of a city, you are given a special map of your country. The map shows several scattered cities connected by some roads. Amount of rescue teams in each city and the length of each road between any pair of cities are marked on the map. When there is an emergency call to you from some other city, your job is to lead your men to the place as quickly as possible, and at the mean time, call up as many hands on the way as possible.

Input Specification:

Each input file contains one test case. For each test case, the first line contains 4 positive integers: N (≤500) - the number of cities (and the cities are numbered from 0 to N−1), M - the number of roads, C1 and C2- the cities that you are currently in and that you must save, respectively. The next line contains N integers, where the i-th integer is the number of rescue teams in the i-th city. Then M lines follow, each describes a road with three integers c1, c2 and L, which are the pair of cities connected by a road and the length of that road, respectively. It is guaranteed that there exists at least one path from C1 to C2.

Output Specification:

For each test case, print in one line two numbers: the number of different shortest paths between C1 and C2, and the maximum amount of rescue teams you can possibly gather. All the numbers in a line must be separated by exactly one space, and there is no extra space allowed at the end of a line.

Sample Input:

Sample Output:

2 4

题意：先给出点的数目，边的数目，起点，终点，再给出每个点的点权，再给出边之间的边权，求最短距离的条数和最短距离上的点权和。

思路：用dijkstra算法求最短路径，最短路径的条数，以及这些最短路径中点权最大的值，d[i]表示从当前点出发到i点的最短距离，w[i]表示从当前点出发到i点的最大点权，num[i]表示从当前点出发到达i点的最短距离的条数。
当判定v未经过，当前点u到v点能到达，并且以u为中介可以使d[v]更优，则更新最短路径，点权值，最短路径的数目，如果以u为中介使得d[v]的值没有变，则比较点权以u为中介有没有使得w[v]发生变化，如果发生变化，则更新点权，不管有没有发生变化，最短路径条数都是之前的条数加上现在的条数。

#include<iostream>
#include<cstdio>
#include<stack> 
#include<queue>
#include<vector>
#include<algorithm>
#include<cstring>
#include<string>
#include<cmath>
#include<set>
#include<map>
#include<cctype>
#include<cstdlib>