10.4 PAT A1003 Emergency (25 分)(最短路径及最大点权——Bellman算法实现）

1003 Emergency (25 分)

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, C​1​​ and C​2​​ - 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 c​1​​, c​2​​ 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 C​1​​ to C​2​​.

Output Specification:

For each test case, print in one line two numbers: the number of different shortest paths between C​1​​ and C​2​​, 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:

5 6 0 2
1 2 1 5 3
0 1 1
0 2 2
0 3 1
1 2 1
2 4 1
3 4 1

Sample Output:

2 4

参考代码：

#include 
#include 
#include 
#include 
#include 
using namespace std;
const int maxv=520;
const int INF=0x3fffffff;
struct node{
	int v,dis;
	node(int _v,int _dis): v(_v) ,dis(_dis) //构造函数 
	{}
}; 
vector G[maxv];

int n,m,start,End,weight[maxv]; 
//n为顶点数，m为边数，start和End分别为起点和终点，wieght[]记录点权
int d[maxv],w[maxv],num[maxv];
//d[]记录最短距离，w[]记录最大点权之和，num[]记录最短路径条数
set pre[maxv]; //前驱

void Bellman(int s)
{
	fill(d,d+maxv,INF);
	memset(num,0,sizeof(num));
	memset(w,0,sizeof(w));
	d[s]=0;
	w[s]=weight[s];
	num[s]=1;
	//以下为求解数组d的部分
	for(int i=0;iw[v]) //以u为中介点时点权之和更大 
						w[v]=w[u]+weight[v]; //w[v]继承自w[u] 
					pre[v].insert(u); //将u加入pre 
					num[v]=0; //重新统计num[v] 
					set ::iterator it;
					for(it=pre[v].begin();it!=pre[v].end();++it)
					{
						num[v]+=num[*it];
					}
				}
			}
		}
	 } 
 } 
 
 int main()
 {
 	scanf("%d%d%d%d",&n,&m,&start,&End);
 	for(int i=0;i