【PAT甲级】1087 All Roads Lead to Rome (30 分)（MAP【int，string】，邻接表，DFS，模拟，SPFA）
代码：
#include<bits/stdc++.h>
using namespace std;
map<string,int>city;
map<int,string>rcity;
map<int,vector<pair<int,int> > >edge;//对比string要比对比int慢很多，所以转换映射
int dis[207],path[207],hcount[207],happ[207],fstep[207],f[207];//源点到各点的最短距离，最短路径数量，快乐总数，快乐，经过点的个数，前一个点
int vis[207];
int main(){
memset(dis,-1,sizeof(dis));
memset(hcount,-1,sizeof(hcount));
std::ios::sync_with_stdio(false);//关闭同步
int n,k,i,d,s;
string st,u,v;
cin>>n>>k>>st;
city[st]=0;//编号
rcity[0]=st;//反编号
happ[0]=0;
dis[0]=0;
hcount[0]=0;
fstep[0]=0;
path[0]=1;//init
f[0]=0;
for(i=1;i<n;++i){
f[i]=i;
cin>>u;
rcity[i]=u;
city[u]=i;
cin>>happ[i];
}
for(i=0;i<k;++i){
cin>>u>>v>>d;
edge[city[u]].push_back(make_pair(city[v],d));//建邻接表
edge[city[v]].push_back(make_pair(city[u],d));
}
s=0;
vector<pair<int,int> >::iterator it;
int next;
while(s!=city["ROM"]){
vis[s]=1;
for(it=edge[s].begin();it!=edge[s].end();++it){
next=it->first;
if(dis[next]==-1||dis[next]>dis[s]+it->second){//松弛
dis[next]=dis[s]+it->second;
hcount[next]=hcount[s]+happ[next];
path[next]=path[s];
fstep[next]=fstep[s]+1;
f[next]=s;
}
else{
if(dis[next]==dis[s]+it->second){
path[next]+=path[s];
if(hcount[next]<hcount[s]+happ[next]){
hcount[next]=hcount[s]+happ[next];
fstep[next]=fstep[s]+1;
f[next]=s;
}
else{
if(hcount[next]==hcount[s]+happ[next]){
if(fstep[next]>fstep[s]+1){
fstep[next]=fstep[s]+1;
f[next]=s;
}
}
}
}
}
}
int mindis=-1,minnum;
for(i=1;i<n;i++){
if(dis[i]==-1)//如果当前边到不了初始点，直接pass
continue;
if(!vis[i]&&(mindis==-1||(dis[i]<mindis))){
mindis=dis[i];
minnum=i;
}
}
s=minnum;//找到当前距离源点最近的一个点向下搜索
}
cout<<path[s]<<" "<<dis[s]<<" "<<hcount[s]<<" "<<hcount[s]/fstep[s]<<endl;
int p=s;
stack<int>ss;
while(p){
ss.push(p);
p=f[p];
}
cout<<rcity[p];
while(!ss.empty()){
cout<<"->"<<rcity[ss.top()];
ss.pop();
}
return 0;
}
/*#include<bits/stdc++.h>
using namespace std;
const int INF = 1e9 ;
typedef struct node{
int v;//节点编号
int cost;//边权值
};
int N;//城市数量
int K;//道路条数
string start;//起始点城市名字
int happy[207];//存放各个城市的快乐值
map<string,int>stringToInt;//城市名字->编号
map<int,string>intToString;//编号->城市名字
vector<node>graph[207];//邻接表
int d[207];//记录从起始城市到达点i的最少花费值
vector<int>pre[207];//记录前一个节点
vector<int>path,tempPath;
int optHappy=0;
double optAverageHappy=0;
int cnt=0;//记录最短路径条数
int inq[207];//记录节点是否在队列中
void spfa(int s){
for(int i=0;i<N;++i)
d[i]=INF;
d[s]=0;
queue<int>q;
q.push(s);
inq[s]=1;
while(!q.empty()){
int u=q.front();
q.pop();
inq[u]=0;
for(int j=0;j<graph[u].size();++j){
int v=graph[u][j].v;
int cost=graph[u][j].cost;
if(!v)
continue;
if(d[u]+cost<d[v]){
d[v]=d[u]+cost;
pre[v].clear();
pre[v].push_back(u);
if(!inq[v]){
q.push(v);
inq[v]=1;
}
}
else if(d[u]+cost==d[v])
pre[v].push_back(u);
}
}
}
void dfs(int nowVisit){
if(!nowVisit){
cnt++;
tempPath.push_back(nowVisit);
int happyValue=0;
for(int i=tempPath.size()-2;i>=0;--i)
happyValue+= happy[tempPath[i]];
double averageHappyValue=1.0*happyValue/(tempPath.size()-1);
if(happyValue>optHappy){
optHappy=happyValue;
optAverageHappy=averageHappyValue;
path=tempPath;
}
else if(happyValue==optHappy&&averageHappyValue>optAverageHappy){
optAverageHappy=averageHappyValue;
path=tempPath;
}
tempPath.pop_back();
return;
}
tempPath.push_back(nowVisit);
for(auto&it:pre[nowVisit])
dfs(it);
tempPath.pop_back();
}
int main(){
std::ios::sync_with_stdio(false);//关闭同步
cin>>N>>K>>start;
stringToInt[start]=0; //起始城市编号为0
intToString[0]=start;
string city;
int happyness;
for(int i=1;i<N;++i){
cin>>city>>happyness;
stringToInt[city]=i;
intToString[i]=city;
happy[i]=happyness;
}
string city1,city2;
int cost;
for(int i=0;i<K;++i){
cin>>city1>>city2>>cost;
int id1=stringToInt[city1];
int id2=stringToInt[city2];
node x,y;
x.v=id2;
x.cost=cost;
y.v=id1;
y.cost=cost;
graph[id1].push_back(x);
graph[id2].push_back(y);
}
int destination=stringToInt["ROM"];
spfa(0);
dfs(destination);
cout<<cnt<<" "<<d[destination]<<" "<<optHappy<<" "<<(int)optAverageHappy<<endl;
for(int i=path.size()-1;i>=0;--i) {
cout<<intToString[path[i]];
if(i)
cout<<"->";
}
return 0;
}*/
//SPFA先处理再DFS
