關於石頭剪刀布和Racing那題題解很清晰，所以就不多說了。
但是，racing這一題竟然卡SPFA，吐槽不能。。。。。。
還有關於racing爲什麼是從賽道上一點走到另一賽道端點而不是中間某點的證明請看題解PPT的第11張(相信很多人都木有認真看題解)
Code
jsb racing(SPFA 60分,懶得改了)
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
bool vis[20005];
int next[2000005],w[2000005],now[20005],head[20005],d[20005],pre[20005],sta[200005],que[200005],c[2000005],link[2000005],n=0,nn=0,m=0,e=1,top=0;
bool spfa()
{
memset(d,60,sizeof(d));
memset(vis,0,sizeof(vis));
memset(pre,0,sizeof(pre));
int oo=d[0]-1;
sta[1]=n-1;
int top=0,tail=1,x=0,y=0,ne=0;
d[n-1]=0;
vis[n-1]=1;
while (top<tail)
{
x=sta[++top];
for (ne=head[x];ne;ne=next[ne])
if (w[ne] && d[x]+c[ne]<d[link[ne]])
{
y=link[ne];
d[y]=d[x]+c[ne];
pre[y]=x;
now[y]=ne;
if (!vis[y])
{
sta[++tail]=y;
vis[y]=1;
}
}
vis[x]=0;
}
if (d[n]<oo) return 1;
else
return 0;
}
int getcost()
{
int nowp=0,flows=1,ctot=0;
for (nowp=n;nowp!=n-1;nowp=pre[nowp])
{
w[now[nowp]]-=flows;
w[now[nowp]^1]+=flows;
ctot+=(flows*c[now[nowp]]);
}
return ctot;
}
int mincost()
{
int cost=0;
while (spfa())
cost+=getcost();
return cost;
}
void push(int u,int v)
{
sta[++top]=u;
que[top]=v;
}
void add(int u,int v,int ww,int cc)
{
next[++e]=head[u];
head[u]=e;
link[e]=v;
w[e]=ww;
c[e]=cc;
next[++e]=head[v];
head[v]=e;
link[e]=u;
c[e]=-cc;
}
int main()
{
freopen("jsb.in","r",stdin);
freopen("jsb.out","w",stdout);
scanf("%d",&nn);
int i=0,j=0,tmp=0,mtot=0;
n=nn;
for (i=1;i<=nn;i++)
for (j=1;j<=nn;j++)
{
scanf("%d",&tmp);
if (tmp==1)
{
d[j]++;
mtot++;
}
else
if (tmp==2 && i<j)
{
push(i,j);
mtot++;
}
}
int cost=0;
for (i=1;i<=nn;i++)
cost+=d[i]*d[i];
int nowd=0;
for (i=1;i<=top;i++)
{
++n;
add(n,sta[i],1,0);
add(n,que[i],1,0);
}
for (++n,i=nn+1;i<n;i++)
add(n,i,1,0);
for (++n,i=1;i<=nn;i++)
for (nowd=d[i];nowd<=nn;nowd++)
add(i,n,1,2*nowd+1);
cost+=mincost();
int ans=nn*(nn-1)/2*(nn-2)/3-(cost-mtot)/2;
printf("%d",ans);
return 0;
}
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
const double eps=1e-8;
double x[1005*1005],y[1005*1005],w[2005*2005],d[1005*1005];
int next[2005*2005],head[1005*1005],link[1005*1005],c[1005];
int esum=0,node=0,n=0;
double va=0,vb=0;
int sta[4005*4005];
bool vis[1005*1005];
double dis(double x,double y,double xx,double yy)
{
return sqrt((x-xx)*(x-xx)+(y-yy)*(y-yy));
}
int cmp(const void *a,const void *b)
{
double tmp=x[*(int *)a]+y[*(int *)a]-x[*(int *)b]-y[*(int *)b];
if (fabs(tmp)<eps)
return 0;
else
if (tmp>0) return 1;
else return -1;
}
void add(int u,int v,double &vv)
{
double d=dis(x[u],y[u],x[v],y[v])/vv;
next[++esum]=head[u];
head[u]=esum;
link[esum]=v;
w[esum]=d;
next[++esum]=head[v];
head[v]=esum;
link[esum]=u;
w[esum]=d;
}
void dit(double p,double q,double &xx,double &yy,int i,int j)
{
double left=0,right=1,mid1=0,mid2=0,x1=0,y1=0,x2=0,y2=0,tmp=0,d1=0,d2=0;
tmp=dis(x[i],y[i],x[i-1],y[i-1])/va;
while (left+eps<right)
{
mid1=left+(right-left)/3;
mid2=left+(right-left)*2/3;
x1=x[i-1]+(x[i]-x[i-1])*mid1;
x2=x[i-1]+(x[i]-x[i-1])*mid2;
y1=y[i-1]+(y[i]-y[i-1])*mid1;
y2=y[i-1]+(y[i]-y[i-1])*mid2;
d1=dis(x[j],y[j],x1,y1)/vb+tmp*(p+q*mid1);
d2=dis(x[j],y[j],x2,y2)/vb+tmp*(p+q*mid2);
if (d1<d2)
right=mid2;
else
left=mid1;
}
xx=x1;
yy=y1;
}
int main()
{
freopen("racing.in","r",stdin);
freopen("racing.out","w",stdout);
scanf("%d",&n);++n;
scanf("%lf%lf",&va,&vb);
int i=0,j=0;
for (i=2;i<=n;i++)
scanf("%lf%lf",&x[i],&y[i]);
int nn=n,top=0;
for (i=2;i<=nn;i++)
{
top=2;
c[1]=i-1;c[2]=i;
for (j=1;j<=nn;j++)
{
if (j<i) add(i,j,vb);
++n;
dit(0,1,x[n],y[n],i,j);
c[++top]=n;
add(j,n,vb);
++n;
dit(1,-1,x[n],y[n],i,j);
c[++top]=n;
add(j,n,vb);
}
qsort(c+1,top,sizeof(c[0]),cmp);
for (j=2;j<=top;j++)
add(c[j-1],c[j],va);
}
int ne=0,xx=0,yy=0;
d[1]=0;
for (i=2;i<=n;i++) d[i]=1e10;
top=0;
int tail=1;
sta[1]=1;vis[1]=1;
while (top<tail)
{
xx=sta[++top];
ne=head[xx];
while (ne)
{
yy=link[ne];
if (d[yy]>d[xx]+w[ne])
{
d[yy]=d[xx]+w[ne];
if (!vis[yy])
{
sta[++tail]=yy;
vis[yy]=1;
}
}
ne=next[ne];
}
vis[xx]=0;
}
printf("%.6f",d[nn]);
return 0;
}