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2019-12-21 19:47:00
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f[st][sta]表示起点是st,当前节点是否访问过的状态二进制下是sta

顺便记录d[st][sta]表示f[st][sta]最小时每个节点距离st的距离

我们可以用填表法向前推进

f[st][sta'] = \min(f[st][sta'],f[st][sta]+(d[st][sta][x]+1)\times L) (sta' = sta | 2^{to-1})

最坏情况下复杂度: \Theta(n \times 2^n \times n^2)

#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define rg register
    #define ll long long
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i=x;i<=y;++i)
    #define Fdr(i,x,y) for(int i=x;i>=y;--i)
    #define fl(i,x) for(int i=head[x],to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) ((int)(log2(n)))
    #define inf 0x3f3f3f3f
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const char* ln="\n";const int str=1<<20;struct IN{char buf[str],*s,*t;bool _;IN():s(buf),t(buf),_(0){}il char gc(){return s==t&&((t=(s=buf)+fread(buf,1,str,stdin))==s)?EOF:(*s++);}IN&operator>>(char&ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)_=1;else ch=c;return *this;}IN& operator>>(char* ch){clr(ch,0);if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)_=1;return *this;}IN& operator>>(string& ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)_=1;return *this;}template<typename T>IN&operator>>(T&x){if(_)return *this;char c=gc();bool ff=0;while(c!=EOF&&(c<'0'||c>'9'))ff^=(c=='-'),c=gc();if(c==EOF){_=1;return *this;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=(x<<3)+(x<<1)+c-48,c=gc();if(c==EOF)_=1;if(ff)x=-x;return *this;}}in;struct OUT{char buf[str],*s,*t;OUT():s(buf),t(buf+str){}~OUT(){fwrite(buf,1,s-buf,stdout);}void pt(char c){(s==t)?(fwrite(s=buf,1,str,stdout),*s++=c):(*s++=c);}OUT&operator<<(const char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(string s){for(int i=0;s[i];i++)pt(s[i]);return *this;}template<typename T>OUT&operator<<(T x){if(!x)return pt('0'),*this;if(x<0)pt('-'),x=-x;char a[30],t=0;while(x)a[t++]=x%10,x/=10;while(t--)pt(a[t]+'0');return *this;}}out;}using namespace IO;
#define N 13
int n,m,head[N],cnt=0;
struct edge{
    int to,nxt,w;
}e[2011];
void add(int x,int y,int w){
    e[++cnt].to=y;e[cnt].w=w;e[cnt].nxt=head[x];head[x]=cnt;
}
int f[N][1<<N],d[N][1<<N][N];
void init(){
    in>>n>>m;
    int x,y,w;
    Fur(i,1,m){
        in>>x>>y>>w;
        add(x,y,w),add(y,x,w);
    }
    Fur(st,1,n)
        Fur(sta,0,(1<<n)-1)
            f[st][sta]=inf;
    Fur(st,1,n)
        Fur(sta,0,(1<<n)-1)
            Fur(i,1,n)
            d[st][sta][i]=inf;

    Fur(st,1,n){
        f[st][1<<(st-1)]=0;
        d[st][1<<(st-1)][st]=1;
    }
}
#define chk(x) (sta&(1<<(x-1)))
int main(){
    init();
    Fur(st,1,n)
        Fur(sta,1,(1<<n)-1)
        if(f[st][sta]!=inf){
            Fur(x,1,n)
            if(chk(x)){
                fl(i,x)
                if(!chk(to)){
                    int ne=sta|(1<<(to-1));
                    if(f[st][sta]+d[st][sta][x]*e[i].w<f[st][ne]){
                        f[st][ne]=f[st][sta]+d[st][sta][x]*e[i].w;
                        Fur(j,1,n)
                            d[st][ne][j]=d[st][sta][j];
                        d[st][ne][to]=d[st][sta][x]+1;
                    }
                }
            }
        }
    int ans=inf;
    Fur(st,1,n)ans=MIN(ans,f[st][(1<<n)-1]);
    out<<ans<<ln;
}
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