POJ 1125 Floyd最短路入门

题目 

Stockbroker Grapevine

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 33238 Accepted: 18311

Description

Stockbrokers are known to overreact to rumours. You have been contracted to develop a method of spreading disinformation amongst the stockbrokers to give your employer the tactical edge in the stock market. For maximum effect, you have to spread the rumours in the fastest possible way. 

Unfortunately for you, stockbrokers only trust information coming from their "Trusted sources" This means you have to take into account the structure of their contacts when starting a rumour. It takes a certain amount of time for a specific stockbroker to pass the rumour on to each of his colleagues. Your task will be to write a program that tells you which stockbroker to choose as your starting point for the rumour, as well as the time it will take for the rumour to spread throughout the stockbroker community. This duration is measured as the time needed for the last person to receive the information.

Input

Your program will input data for different sets of stockbrokers. Each set starts with a line with the number of stockbrokers. Following this is a line for each stockbroker which contains the number of people who they have contact with, who these people are, and the time taken for them to pass the message to each person. The format of each stockbroker line is as follows: The line starts with the number of contacts (n), followed by n pairs of integers, one pair for each contact. Each pair lists first a number referring to the contact (e.g. a '1' means person number one in the set), followed by the time in minutes taken to pass a message to that person. There are no special punctuation symbols or spacing rules. 

Each person is numbered 1 through to the number of stockbrokers. The time taken to pass the message on will be between 1 and 10 minutes (inclusive), and the number of contacts will range between 0 and one less than the number of stockbrokers. The number of stockbrokers will range from 1 to 100. The input is terminated by a set of stockbrokers containing 0 (zero) people. 

Output

For each set of data, your program must output a single line containing the person who results in the fastest message transmission, and how long before the last person will receive any given message after you give it to this person, measured in integer minutes. 
It is possible that your program will receive a network of connections that excludes some persons, i.e. some people may be unreachable. If your program detects such a broken network, simply output the message "disjoint". Note that the time taken to pass the message from person A to person B is not necessarily the same as the time taken to pass it from B to A, if such transmission is possible at all.

Sample Input

32 2 4 3 52 1 2 3 62 1 2 2 253 4 4 2 8 5 31 5 84 1 6 4 10 2 7 5 202 2 5 1 50

Sample Output

3 23 10

Source

Southern African 2001

想法

最近在学最短路的算法，dijkstra算法只能求得单个起点到全图其他点的最短路。Floyd算法能求图中所有对顶点之间的最短路。

前几天复习了一下Dijkstra算法之后我便开始思考这个问题，当时还不知道Floyd算法，我坐在自习室里想如果按顺序录入所有边，直接构建邻接表，构建过程中a->b可能通过a->i->b达到.（后来发现这就是Floyd）今天学习Floyd之后发现很好理解~

代码 View Source On GitHub

#include <cstdio>#include <cstdlib>#include <cstring>using namespace std;#define MAXSTOCK 101int m[MAXSTOCK][MAXSTOCK];int main(){    int n;    while(scanf("%d",&n)==1&&n!=0)    {        memset(m,0,sizeof(int)*MAXSTOCK*MAXSTOCK);        for(int i=1;i<=n;i++)/// From i to...        {            int s;            scanf("%d",&s);            for(int j=0;j<s;j++)            {                int t,v;                scanf("%d %d",&t,&v);                /// From i to t, value=v                m[i][t]=v;            }        }        for(int k=1;k<=n;k++)        {            for(int f=1;f<=n;f++)            {                for(int t=1;t<=n;t++)                {                    if(f==t||f==k||t==k) continue;                    if(m[f][k]!=0&&m[k][t]!=0)                    {                        int total=m[f][k]+m[k][t];                        if(total<m[f][t]||m[f][t]==0)                        {                            m[f][t]=total;                        }                    }                }            }        }        /// Judge if is disjoint        bool found=false;        int FromPos=-1;        int FromPosMaxTime=-1;        for(int i=1;i<=n;i++)        {            int cnt=0;            int Max=0;            for(int j=1;j<=n;j++)            {                Max=Max>m[i][j]?Max:m[i][j];                if(m[i][j]) ++cnt;            }            if(cnt==n-1)            {                found=true;                if(FromPosMaxTime<0||FromPosMaxTime>Max)                {                    FromPos=i;                    FromPosMaxTime=Max;                }            }        }        if(!found)        {            printf("disjoint\n");        }        else        {            printf("%d %d\n",FromPos,FromPosMaxTime);        }    }    return 0;}