Minimum Transport Cost

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7007 Accepted Submission(s): 1791


Problem Description These are N cities in Spring country. Between each pair of cities there may be one transportation track or none. Now there is some cargo that should be delivered from one city to another. The transportation fee consists of two parts:
The cost of the transportation on the path between these cities, and

a certain tax which will be charged whenever any cargo passing through one city, except for the source and the destination cities.

You must write a program to find the route which has the minimum cost.

Input First is N, number of cities. N = 0 indicates the end of input.

The data of path cost, city tax, source and destination cities are given in the input, which is of the form:

a11 a12 ... a1N
a21 a22 ... a2N
...............
aN1 aN2 ... aNN
b1 b2 ... bN

c d
e f
...
g h

where aij is the transport cost from city i to city j, aij = -1 indicates there is no direct path between city i and city j. bi represents the tax of passing through city i. And the cargo is to be delivered from city c to city d, city e to city f, ..., and g = h = -1. You must output the sequence of cities passed by and the total cost which is of the form:

Output From c to d :
Path: c-->c1-->......-->ck-->d
Total cost : ......
......

From e to f :
Path: e-->e1-->..........-->ek-->f
Total cost : ......

Note: if there are more minimal paths, output the lexically smallest one. Print a blank line after each test case.


Sample Input

5
0 3 22 -1 4
3 0 5 -1 -1
22 5 0 9 20
-1 -1 9 0 4
4 -1 20 4 0
5 17 8 3 1
1 3
3 5
2 4
-1 -1
0

Sample Output

From 1 to 3 :
Path: 1-->5-->4-->3
Total cost : 21

From 3 to 5 :
Path: 3-->4-->5
Total cost : 16

From 2 to 4 :
Path: 2-->1-->5-->4
Total cost : 17

Source Asia 1996, Shanghai (Mainland China)

最基本的floyd最短路,難點在記錄字典序最小的路徑.....

有兩種路徑記錄方法:

出始化: fa[a][b]=a 則 fa[a][b]=c 表示 a....c->b

出始化: fa[a][b]=b 則 fa[a][b]=c 表示 a->c....b

根據題意,要選擇第二種

#include 
#include 
#include 
#include 
#include 

using namespace std;

const int INF=0x3f3f3f3f;

int n;
int g[110][110],b[110];
int fa[110][110];

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        memset(g,63,sizeof(g));
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=n;j++)
            {
                scanf("%d",&g[i][j]);
                if(g[i][j]==-1)
                    g[i][j]=INF;
            }
        }

        for(int i=1;i<=n;i++)
            scanf("%d",&b[i]);

        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++)
                fa[i][j]=j;

        for(int k=1;k<=n;k++)
        {
            for(int i=1;i<=n;i++)
            {
                for(int j=1;j<=n;j++)
                {
                    if(g[i][j]>g[i][k]+g[k][j]+b[k])
                    {
                        g[i][j]=g[i][k]+g[k][j]+b[k];
                        fa[i][j]=fa[i][k];
                    }
                    else if(g[i][j]==g[i][k]+g[k][j]+b[k])
                    {
                        fa[i][j]=min(fa[i][j],fa[i][k]);
                    }
                }
            }
        }

        int s,t;
        while(scanf("%d%d",&s,&t)!=EOF)
        {
            if(s==-1&&t==-1) break;
            printf("From %d to %d :\nPath: ",s,t);
            int next=fa[s][t];
            printf("%d",s);
            if(s!=t)
            {
                while(next!=t)
                {
                    printf("-->");
                    printf("%d",next);
                    next=fa[next][t];
                }
                printf("-->%d",t);
            }
            printf("\nTotal cost : %d\n\n",g[s][t]);
        }
    }
    return 0;
}