bzoj 3991: [SDOI2015]寻宝游戏 虚树 set

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目录

• [TOC]

题目链接

bzoj 3991: [SDOI2015]寻宝游戏

题解

发现每次答案就是把虚树上的路径*2
接在同一关键点上的点的dfs序是相邻的
那么用set动态维护dfs序列
每次删点加点就好了

代码

#include<set> 
#include<cstdio> 
#include<algorithm> 
#define gc getchar()
#define pc putchar 
#define LL long long
inline int read() { 
    int x = 0,f = 1; 
    char c = gc; 
    while(c < '0' || c > '9') c = gc; 
    while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = gc; 
    return x * f;  
} 
void print(LL x) { 
    if(x < 0) { 
        pc('-'); 
        x = -x; 
    } 
    if(x >= 10) print(x / 10); 
    pc(x % 10 + '0'); 
}
const int maxn = 100007; 
int n,m;  
struct node {
    int v,next,w; 
} edge[maxn << 1]; 
int head[maxn],num = 0; 
inline void add_edge(int u,int v,int w) { 
    edge[++ num].v = v; edge[num].w = w; edge[num].next = head[u];head[u] = num; 
} 
std::set<int>s; 
std::set<int> :: iterator it,qi,ho;  
int deep[maxn],top[maxn],fa[maxn],son[maxn],siz[maxn]; 
LL dis[maxn]; 
void dfs1(int x,int f) { 
    deep[x] = deep[f] + 1,fa[x] = f; 
    siz[x] = 1; 
    for(int i = head[x];i;i = edge[i].next) { 
        int v = edge[i].v; 
        if(v != f) { 
            dis[v] = dis[x] + edge[i].w; 
            dfs1(v,x); 
            if(siz[v] > siz[son[x]]) son[x] = v; 
            siz[x] += siz[v]; 
        } 
    } 
} 
int cnt = 0,dfn[maxn],ra[maxn]; 
void dfs2(int x,int tp) { 
    top[x] = tp; dfn[x] = ++ cnt;ra[cnt] = x; 
    if(son[x]) dfs2(son[x],tp); 
    for(int i = head[x];i;i = edge[i].next) { 
        int v = edge[i].v; 
        if(v == fa[x] || v == son[x]) continue; 
        dfs2(v,v); 
    } 
} 
int lca(int x,int y) { 
    while(top[x] != top[y]) { 
        if(deep[top[x]] > deep[top[y]]) x = fa[top[x]]; 
        else y = fa[top[y]]; 
    } 
    return deep[x] > deep[y] ? y : x; 
} 
LL query(int x) {
    it = s.find(dfn[x]); 
    if(it == s.begin()) {qi = s.end();qi --; } 
    else {qi = it ;qi --; }  
    ho = it;ho ++; 
    if(ho == s.end()) ho = s.begin(); 
    return dis[ra[* ho]] + dis[ra[* it]] * 2 + dis[ra[* qi]] - dis[lca(ra[* ho],ra[* it])] * 2 - dis[lca(ra[* it],ra[* qi])] * 2;       
} 
bool vis[maxn]; 
LL work(int x) {
    it = s.find(dfn[x]); 
    if(it == s.begin()) {qi = s.end();qi --; } 
    else {qi = it; qi --;} 
    ho = it;ho ++; 
    if(ho == s.end()) ho = s.begin(); 
    return dis[ra[*ho]] + dis[ra[*qi]] - 2 * dis[lca(ra[*qi],ra[*ho])]; 
} 
int main() { 
    n = read(),m = read(); 
    for(int u,v,w,i = 1;i < n;++ i) { 
        u = read(),v = read(),w = read(); 
        add_edge(u,v,w); add_edge(v,u,w); 
    } 
    LL ans = 0; 
    dfs1(1,0); 
    dfs2(1,1); 
    for(int i = 1;i <= m;++ i) { 
        int x = read(); 
        if(vis[x]) { 
            ans -= query(x); 
            ans += work(x); 
            s.erase(dfn[x]),vis[x] = 0; 
        } else { 
            vis[x] = 1; 
            s.insert(dfn[x]); 
            ans -= work(x); 
            ans += query(x); 
        } 
        printf("%lld
",ans); 
    } 
    return 0; 
}