BZOJ 2125 最短路

树剖LCA+SPFA+tarjan找简单环

静态仙人掌最短路

没啥好说的，要分类讨论，细节要处理清楚…（我这个SB细节没弄好WA飞了）
膜：http://blog.youkuaiyun.com/popoqqq/article/details/43876907

#include<cstdio>
#include<queue>
#include<cstring>
#define cmin(u,v) (u)>(v)?(u)=(v):0
#define iabs(x) (x)>0?(x):-(x)
#define N 10005
#define M 300005
#define H 17
using namespace std;
struct edge{int next,to,val;}e[M<<1];
struct pdge{int u, v, val;}s[M];
int n, m, Q, ecnt=1, last[N], dis[N], dfn[N], low[N], timer, top, fa[N][H], bell, dep[N], belong[N], sum[N], pre[N];
bool inq[N], vis[N];
void addedge(int a, int b, int c)
{
    e[++ecnt]=(edge){last[a],b,c};
    last[a]=ecnt;
}
void SPFA(int s)
{
    memset(dis,63,sizeof(dis));
    queue<int> q;
    dis[s]=0;
    q.push(s);
    while(!q.empty())
    {
        int x = q.front(); q.pop();
        inq[x]=0;
        for(int i = last[x]; i; i=e[i].next)
        {
            int y=e[i].to;
            if(dis[x]+e[i].val<dis[y])
            {
                dis[y]=dis[x]+e[i].val;
                if(!inq[y])
                {
                    inq[y]=1;
                    q.push(y);
                }
            }
        }
    }
}
void pushout(int fat)
{
    ++bell;
    for(;s[top].u!=fat;top--)
    {
        int u = s[top].u, v = s[top].v, w = s[top].val;
        sum[bell]+=w;
        pre[u]=pre[v]+w;
        fa[v][0]=fat,belong[v]=bell;
        fa[u][0]=fat,belong[u]=bell;
    }
    int u = s[top].u, v = s[top].v, w = s[top].val;
    belong[v]=bell;
    sum[bell]+=w;
    pre[u]=pre[v]+w;
    fa[v][0]=fat;
    top--;
}
void tarjan(int x, int from)
{
    //存边tarjan 
    dfn[x]=low[x]=++timer;
    for(int i = last[x]; i; i=e[i].next)
    {
        if(i==from)continue;
        int y=e[i].to;
        if(!dfn[y])
        {
            s[++top]=(pdge){x,y,e[i].val};
            tarjan(y,i^1);
            if(low[y]<low[x])low[x]=low[y];
            if(low[y]>=dfn[x])//环顶 或 只是更新儿子 
            {
                pushout(x);
            }
        }
        else if(dfn[y]<low[x]){cmin(low[x],dfn[y]); s[++top]=(pdge){x,y,e[i].val};}//返祖边 
    }
}
void make_edge()
{
    memset(last,0,sizeof(last));
    ecnt=1;
    for(int i = 2; i <= n; i++)
    {
        addedge(fa[i][0],i,0);      
    }
}
void dfs(int x)
{
    dep[x]=dep[fa[x][0]]+1;
    for(int i = 1; 1<<i <= dep[x]; i++)
        fa[x][i]=fa[fa[x][i-1]][i-1];
    for(int i = last[x]; i; i=e[i].next)
    {
        int y=e[i].to;
        if(dep[y])continue;
        fa[y][0]=x;
        dfs(y);
    }
}
int LCA(int a,int b,int &c,int &d)
{
    int past=0;
    if(dep[a]<dep[b]) swap(a,b);
    past=dis[a]+dis[b];  c=d=b;
    for(int i=H-1;i>=0;i--) if(dep[fa[a][i]]>=dep[b]) a=fa[a][i];
    if(a==b) return past-2*dis[b];
    //如果a,b为祖先关系，那么用dis一定可以更新 

    for(int i=H-1;i>=0;i--) 
        if(fa[a][i]!=fa[b][i]) a=fa[a][i],b=fa[b][i];
    c=a; d=b;
    //如果a,b不是祖先关系， 就判LCA是不是属于环即可 
    return past-2*dis[fa[a][0]];
}
int main()
{
    scanf("%d%d%d",&n,&m,&Q);
    for(int i = 1; i <= m; i++)
    {
        int a, b, c;
        scanf("%d%d%d",&a,&b,&c);
        addedge(a,b,c);
        addedge(b,a,c);
    }
    SPFA(1);
    tarjan(1,0);
    make_edge();
    dfs(1);
    for(;Q--;)
    {
        int a, b, c, d;
        scanf("%d%d",&a,&b);
        int tmp = LCA(a,b,c,d);
        if(belong[c]==belong[d] && belong[c])
        {
            int ans = dis[a]+dis[b]-dis[c]-dis[d];
            int l1=iabs(pre[c]-pre[d]), l2=sum[belong[c]]-l1;             
            printf("%d\n",ans+min(l1,l2));
        }
        else
        {
            printf("%d\n",tmp);
        }
    }
}