Heavy Transportation
Background
Hugo Heavy is happy. After the breakdown of the Cargolifter project he can now expand business. But he needs a clever man who tells him whether there really is a way from the place his customer has build his giant steel crane to the place where it is needed on which all streets can carry the weight.
Fortunately he already has a plan of the city with all streets and bridges and all the allowed weights.Unfortunately he has no idea how to find the the maximum weight capacity in order to tell his customer how heavy the crane may become. But you surely know.
Problem
You are given the plan of the city, described by the streets (with weight limits) between the crossings, which are numbered from 1 to n. Your task is to find the maximum weight that can be transported from crossing 1 (Hugo's place) to crossing n (the customer's place). You may assume that there is at least one path. All streets can be travelled in both directions.
Input
The first line contains the number of scenarios (city plans). For each city the number n of street crossings (1 <= n <= 1000) and number m of streets are given on the first line. The following m lines contain triples of integers specifying start and end crossing of the street and the maximum allowed weight, which is positive and not larger than 1000000. There will be at most one street between each pair of crossings.
Output
The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print a single line containing the maximum allowed weight that Hugo can transport to the customer. Terminate the output for the scenario with a blank line.
Sample Input
1 3 3 1 2 3 1 3 4 2 3 5
Sample Output
Scenario #1: 4
#include <iostream>
#include <queue>
#include <stdio.h>
#include <algorithm>
#include <string.h>
#include <math.h>
using namespace std;
#define MAXV 1010
int map[MAXV][MAXV],n,m;
int vis[MAXV],d[MAXV];
int spfa(){
queue <int>q;
int v;
for(int i=1;i<=n;i++){
vis[i]=0;
d[i]=0;
}
q.push(1);
vis[1]=1;
while(!q.empty()){
v=q.front();q.pop();
vis[v]=0;
for(int i=1;i<=n;i++){
if(v==1 && map[v][i]){
d[i]=map[v][i];
q.push(i);
vis[i]=1;
continue;
}
if(d[i]<min(d[v],map[v][i])){
d[i]=min(d[v],map[v][i]);
if(!vis[i]){
vis[i]=1;
q.push(i);
}
}
}
}
return d[n];
}
int main(){
int sum,a,b,c;
scanf("%d",&sum);
for(int t=1;t<=sum;t++){
scanf("%d%d",&n,&m);
for(int i=0;i<=n;i++)
for(int j=0;j<=n;j++)
map[i][j]=0;
for(int i=1;i<=m;i++){
scanf("%d%d%d",&a,&b,&c);
map[a][b]=map[b][a]=c;
}
printf("Scenario #%d:\n",t);
printf("%d\n\n",spfa());
}
return 0;
}
/*
4128K 375MS
Dijkstra邻接矩阵
*/
#include <iostream>
using namespace std;
#define MAXV 1010
#define min(a,b) (a<b?a:b)
int map[MAXV][MAXV],n,m;
int dijkstra(){
int vis[MAXV],d[MAXV],i,j,v;
for(i=1;i<=n;i++){
vis[i]=0;
d[i]=map[1][i]; //这个时候d不代表从1到n的最短路径，而是最大承载量
}
for(i=1;i<=n;i++){
int f=-1;
for(j=1;j<=n;j++)
if(!vis[j] && d[j]>f){
f=d[j];
v=j;
}
vis[v]=1;
for(j=1;j<=n;j++)
if(!vis[j] && d[j]<min(d[v],map[v][j])){
d[j]=min(d[v],map[v][j]);
}
}
return d[n];
}
int main(){
int t,i,j,sum,a,b,c;
scanf("%d",&sum);
for(t=1;t<=sum;t++){
scanf("%d%d",&n,&m);
for(i=0;i<=n;i++)
for(j=0;j<=n;j++)
map[i][j]=0;
for(i=1;i<=m;i++){
scanf("%d%d%d",&a,&b,&c);
map[a][b]=map[b][a]=c;
}
printf("Scenario #%d:\n",t);
printf("%d\n\n",dijkstra());
}
return 0;
}
========================================================================================
/*
spfa邻接矩阵
4156K 469MS
*/
#include <iostream>
#include <queue>
using namespace std;
#define MAXV 1010
#define min(a,b) (a<b?a:b)
int map[MAXV][MAXV],n,m;
int spfa(){
queue <int>q;
int i,j,v;
int vis[MAXV],d[MAXV];
for(i=1;i<=n;i++){
vis[i]=0;
d[i]=0;
}
q.push(1);
vis[1]=1;
while(!q.empty()){
v=q.front();q.pop();
vis[v]=0;
for(i=1;i<=n;i++){
if(v==1 && map[v][i]){
d[i]=map[v][i];
q.push(i);
vis[i]=1;
continue;
}
if(d[i]<min(d[v],map[v][i])){
d[i]=min(d[v],map[v][i]);
if(!vis[i]){
vis[i]=1;
q.push(i);
}
}
}
}
return d[n];
}
int main(){
int t,i,j,sum,a,b,c;
scanf("%d",&sum);
for(t=1;t<=sum;t++){
scanf("%d%d",&n,&m);
for(i=0;i<=n;i++)
for(j=0;j<=n;j++)
map[i][j]=0;
for(i=1;i<=m;i++){
scanf("%d%d%d",&a,&b,&c);
map[a][b]=map[b][a]=c;
}
printf("Scenario #%d:\n",t);
printf("%d\n\n",spfa());
}
return 0;
}
================================================================================
/*
bellman-ford邻接矩阵
Time Limit Exceeded
*/
#include <iostream>
using namespace std;
#define MAXV 1010
#define min(a,b) (a<b?a:b)
int map[MAXV][MAXV],n,m;
int bellman_ford(){
int i,j,v,k;
int vis[MAXV],d[MAXV];
for(i=1;i<=n;i++) d[i]=map[1][i];
for(i=1;i<=n;i++){
for(j=1;j<=n;j++){
for(k=1;k<=n;k++){
if (d[k]<min(d[j],map[j][k]) && map[j][k]) d[k]=min(d[j],map[j][k]);
if (d[j]<min(d[k],map[k][j]) && map[k][j]) d[j]=min(d[k],map[k][j]);
}
}
}
return d[n];
}
int main(){
int t,i,j,sum,a,b,c;
scanf("%d",&sum);
for(t=1;t<=sum;t++){
scanf("%d%d",&n,&m);
for(i=0;i<=n;i++)
for(j=0;j<=n;j++)
map[i][j]=0;
for(i=1;i<=m;i++){
scanf("%d%d%d",&a,&b,&c);
map[a][b]=map[b][a]=c;
}
printf("Scenario #%d:\n",t);
printf("%d\n\n",bellman_ford());
}
return 0;
}
===================================================================================================
/*
760K 1532MS
bellman_ford邻接表
*/
#include <iostream>
using namespace std;
#define MAXV 1010
#define MAXE 1000010
#define min(a,b) (a<b?a:b)
struct {
int s,e,w;
}edge[MAXE];
int n,m;
int bellman_ford(){
int i,j,d[MAXV];
for(i=1;i<=n;i++) d[i]=0;
d[1]=0xffffff;
for (i=1;i<n;i++){
for (j=1;j<=m;j++){
if (d[edge[j].e]<min(d[edge[j].s],edge[j].w)) d[edge[j].e]=min(d[edge[j].s],edge[j].w);
if (d[edge[j].s]<min(d[edge[j].e],edge[j].w)) d[edge[j].s]=min(d[edge[j].e],edge[j].w);
}
}
return d[n];
}
int main(){
int t,i,sum;
scanf("%d",&sum);
for(t=1;t<=sum;t++){
scanf("%d%d",&n,&m);
for(i=1;i<=m;i++){
scanf("%d%d%d",&edge[i].s,&edge[i].e,&edge[i].w);
}
printf("Scenario #%d:\n",t);
printf("%d\n\n",bellman_ford());
}
return 0;
}
================================================================================================
/*
760K 250MS
bell_ford邻接表优化
*/#include <iostream>
using namespace std;
#define MAXV 1010
#define MAXE 1000010
#define min(a,b) (a<b?a:b)
struct {
int s,e,w;
}edge[MAXE];
int n,m;
int bellman_ford(){
int i,j,d[MAXV];
for(i=1;i<=n;i++) d[i]=0;
d[1]=0xffffff;
int flag=1;
while(flag){
flag=0;
for (j=1;j<=m;j++){
if (d[edge[j].e]<min(d[edge[j].s],edge[j].w)) {d[edge[j].e]=min(d[edge[j].s],edge[j].w);flag=1;}
if (d[edge[j].s]<min(d[edge[j].e],edge[j].w)) {d[edge[j].s]=min(d[edge[j].e],edge[j].w);flag=1;}
}
}
return d[n];
}
int main(){
int t,i,sum;
scanf("%d",&sum);
for(t=1;t<=sum;t++){
scanf("%d%d",&n,&m);
for(i=1;i<=m;i++){
scanf("%d%d%d",&edge[i].s,&edge[i].e,&edge[i].w);
}
printf("Scenario #%d:\n",t);
printf("%d\n\n",bellman_ford());
}
return 0;
}
=======================================================================================
/*
bellman-ford邻接矩阵优化
4124K 1485MS
*/
#include <iostream>
using namespace std;
#define MAXV 1010
#define min(a,b) (a<b?a:b)
int map[MAXV][MAXV],n,m;
int bellman_ford(){
int i,j,v,k;
int vis[MAXV],d[MAXV];
for(i=1;i<=n;i++) d[i]=map[1][i];
int flag=1;
while(flag){
flag=0;
for(j=1;j<=n;j++){
for(k=1;k<=n;k++){
if (d[k]<min(d[j],map[j][k]) && map[j][k]) {d[k]=min(d[j],map[j][k]);flag=1;}
if (d[j]<min(d[k],map[k][j]) && map[k][j]) {d[j]=min(d[k],map[k][j]);flag=1;}
}
}
}
return d[n];
}
int main(){
int t,i,j,sum,a,b,c;
scanf("%d",&sum);
for(t=1;t<=sum;t++){
scanf("%d%d",&n,&m);
for(i=0;i<=n;i++)
for(j=0;j<=n;j++)
map[i][j]=0;
for(i=1;i<=m;i++){
scanf("%d%d%d",&a,&b,&c);
map[a][b]=map[b][a]=c;
}
printf("Scenario #%d:\n",t);
printf("%d\n\n",bellman_ford());
}
return 0;
}
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