bzoj4016: [FJOI2014]最短路径树问题

题目链接

bzoj4016: [FJOI2014]最短路径树问题

题解

对于建树
dij建出最短路图
在最短路图上dfs，先走字典序最小的可达点

得到最短路树
然后就是经典的点分治了
维护每个深度的最远距离合并就好了

代码

#include<queue> 
#include<vector> 
#include<cstdio> 
#include<cstring> 
#include<algorithm> 

const int maxn  = 30007; 
#define mp std::make_pair

#define pr std::pair<int,int>

std::vector<int>v[maxn];
#define INF 0x3f3f3f3f 

int hh[maxn] , tt[maxn << 2]  , ww[maxn << 2] , nn[maxn << 2] , cc = 1 , vv[maxn] , Dis[maxn] , uu[maxn];
int n , k , head[maxn] , to[maxn << 1] , w[maxn << 1] , next[maxn << 1] , cnt;
int vis[maxn] , root , sum , son[maxn] , F[maxn] ,f[maxn],g[maxn] ,Depdis[maxn] ,sg[maxn],md,deep[maxn] , dis[maxn] , ans , num;

void Add(int x , int y , int z) {  tt[++cc] = y,ww[cc] = z,nn[cc] = hh[x],hh[x] = cc; } 
void add_edge(int x , int y , int z) {  to[++cnt] = y,w[cnt] = z,next[cnt] = head[x],head[x] = cnt; } 

std::priority_queue<pr> q;  
void dijkstra() {  
    memset(Dis,0x3f,sizeof(Dis));  
    Dis[1] = 0 , q.push(mp(0 , 1));  
    while(!q.empty()) { 
        int x = q.top().second;q.pop();  
        if(vv[x]) continue;  
        vv[x] = 1;  
        for(int i = hh[x];i;i = nn[i])  
            if(Dis[x] == Dis[tt[i]] + ww[i])  
                v[tt[i]].push_back(i ^ 1);  
        for(int i = hh[x] ; i ; i = nn[i]) 
            if(Dis[tt[i]] > Dis[x] + ww[i])  
                Dis[tt[i]] = Dis[x] + ww[i] , q.push(mp(-Dis[tt[i]] , tt[i]));  
    } 
} 
inline bool cmp(int a ,int b) { return tt[a] < tt[b]; }  
 
void dfs(int x)  { 
    std::sort(v[x].begin(),v[x].end(),cmp); 
    for(int i = 0;i < v[x].size();i ++ ) 
        if(!uu[tt[v[x][i]]]) { 
            uu[tt[v[x][i]]] = 1; 
			add_edge(x,tt[v[x][i]],ww[v[x][i]]); 
			add_edge(tt[v[x][i]],x,ww[v[x][i]]); 
			dfs(tt[v[x][i]]); 
	} 
} 
void getroot(int x,int fa) { 
    F[x] = 0,son[x] = 1;
    for(int i = head[x] ;i;i = next[i])
        if(!vis[to[i]] && to[i] != fa)
            getroot(to[i],x),son[x] += son[to[i]],F[x] = std::max(F[x],son[to[i]]); 
    F[x] = std::max(F[x] , sum - son[x]); 
    if(F[x] < F[root]) root = x;
} 
void getdeep(int x,int fa) { 
    for(int i = head[x] ; i ; i = next[i]) { 
        if(!vis[to[i]] && to[i] != fa) { 
            deep[to[i]] = deep[x] + 1,dis[to[i]] = dis[x] + w[i],md = std::max(md,deep[to[i]]); 
            if(dis[to[i]] > f[deep[to[i]]]) f[deep[to[i]]] = dis[to[i]],Depdis[deep[to[i]]] = 1; 
            else if(dis[to[i]] == f[deep[to[i]]]) Depdis[deep[to[i]]] ++ ; 
            getdeep(to[i],x); 
        } 
    } 
} 
void solve(int x,int sm = 0) { 
    vis[x] = 1;  
    for(int i = head[x] ; i ; i = next[i]) {  
        if(!vis[to[i]]) {  
            md = deep[to[i]] = 1,dis[to[i]] = w[i],f[1] = w[i],Depdis[1] = 1,getdeep(to[i],x);  
            for(int j = 1;j <= md && j <= k;j ++ ) {  
                if(ans < f[j] + g[k - j]) ans = f[j] + g[k - j],num = Depdis[j] * sg[k - j];  
                else if(ans == f[j] + g[k - j])num += Depdis[j] * sg[k - j];  
            }  
            for(int j = 1;j <= md && j <= k;j ++ ) {  
                if(g[j] < f[j]) g[j] = f[j] , sg[j] = Depdis[j]; 
                else if(g[j] == f[j]) sg[j] += Depdis[j]; 
            } 
            for(int j = 1;j <= md;j ++ ) f[j] = -INF , Depdis[j] = 0; 
            sm = std::max(sm,md); 
        } 
    } 
    for(int i = 1;i <= sm && i <= k;i ++ ) g[i] = -INF , sg[i] = 0; 
    for(int i = head[x];i;i = next[i])
        if(!vis[to[i]]) { 
            root = 0; 
			sm = son[to[i]];  
			getroot(to[i] , x); 
			solve(root); 
		} 
} 
int main() { 
    int m;  
    scanf("%d%d%d",&n,&m,&k); 
	k -- ;
    for(int x,y,z,i = 1;i <= m ;i ++) scanf("%d%d%d",&x,&y,&z),Add(x,y,z),Add(y,x,z); 
    dijkstra(),uu[1] = 1,dfs(1); 
	memset(f,0xc0,sizeof(f)) ; memset(g,0xc0,sizeof(g)),g[0] = 0,sg[0] = 1; 
    F[0] = INF,sum = n;  
	getroot(1,0);  
	solve(root); 
    printf("%d %d\n", ans,num); 
    return 0; 
}