Minimum Transport Cost

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

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,难点在记录字典序最小的路径.....

有两种路径记录方法:

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

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

根据题意,要选择第二种

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>

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;
}

HDOJ 1385 Minimum Transport Cost