BZOJ 2599: [IOI2011]Race

点分治，定权值，求另一关键字最小

不满足前缀加减性

可以按序遍历，用一数组$t[] 来维护路径为i的最小边数$

再对于一个直系儿子对应的子树，先算距离求答案再更新$t数组，这样就不会重复$

 #include <bits/stdc++.h>
 using namespace std;

 #define N 200010
 #define M 1000010
 #define INF 0x3f3f3f3f
 int n, k;
 struct Graph
 {
     struct node
     {
         int to, nx, w;
         node() {}
         node(int to, int nx, int w) : to(to), nx(nx), w(w) {}
     }a[N << ];
     int head[N], pos;
     void init()
     {
         memset(head, , sizeof head);
         pos = ;
     }
     void add(int u, int v, int w)
     {
         a[++pos] = node(v, head[u], w); head[u] = pos;
         a[++pos] = node(u, head[v], w); head[v] = pos;
     }
 }G;
 #define erp(u) for (int it = G.head[u], v = G.a[it].to, w = G.a[it].w; it; it = G.a[it].nx, v = G.a[it].to, w = G.a[it].w)

 int vis[N];
 int sum, root, sze[N], f[N];
 void getroot(int u, int fa)
 {
     f[u] = , sze[u] = ;
     erp(u) if (v != fa && !vis[v])
     {
         getroot(v, u);
         sze[u] += sze[v];
         f[u] = max(f[u], sze[v]);
     }
     f[u] = max(f[u], sum - sze[u]);
     if (f[u] < f[root]) root = u;
 }

 int dist[N], deep[N], t[M], res;
 void getdeep(int u, int fa)
 {
     if (dist[u] <= k) res = min(res, deep[u] + t[k - dist[u]]);
     erp(u) if (v != fa && !vis[v])
     {
         dist[v] = dist[u] + w;
         deep[v] = deep[u] + ;
         getdeep(v, u);
     }
 }

 void add(int u, int fa, int flag)
 {
     if (dist[u] <= k)
     {
         if (flag) t[dist[u]] = min(t[dist[u]], deep[u]);
         else t[dist[u]] = INF;
     }
     erp(u) if (v != fa && !vis[v])
         add(v, u, flag);
 }

 void solve(int u)
 {
     vis[u] = ; t[] = ;
     erp(u) if (!vis[v])
     {
         deep[v] = , dist[v] = w;
         getdeep(v, u); add(v, u, );
     }
     erp(u) if (!vis[v]) add(v, u, );
     erp(u) if (!vis[v])
     {
         sum = f[] = sze[v]; root = ;
         getroot(v, );
         solve(root);
     }
 }

 void Run()
 {
     while (scanf("%d%d", &n, &k) != EOF)
     {
         G.init(); res = INF;
         memset(t, 0x3f, sizeof t);
         for (int i = , u, v, w; i < n; ++i)
         {
             scanf("%d%d%d", &u, &v, &w);
             ++u, ++v;
             G.add(u, v, w);
         }
         sum = f[] = n; root = ;
         getroot(, );
         solve(root);
         printf("%d\n", res == INF ? - : res);
     }
 } 

 int main()
 {
     #ifdef LOCAL
         freopen("Test.in", "r", stdin);
     #endif 

     Run();
     return ;
 }