### Brief description:

給定一棵 n 個點的點權樹，同時結點分為黑點和白點兩類。

要求找到一條長度最大的路徑，使得路徑上經過的黑點數不超過 k 個。

### Analysis:

點分治 + 動態規劃）

。。。有待分析。

const int MOD = 1000000007; const int INF = 0x7fffffff; const int N = 200000 + 9, M = N * 2; int a[M], b[M], w[M], prd[M], suc[M]; // edge .. int dist[N], max_dep[N], dep[N], sz[N], hd[N]; bool isBlack[N]; // vertx .. int L[N], Ln, F[N], Fn, G[N], Gn; // core .. int n, n_, m, k, _c, c, ans; inline void remove(int x){ if (x == hd[a[x]]) prd[hd[a[x]] = suc[x]] = 0; else suc[prd[suc[x]] = prd[x]] = suc[x]; } #define v b[i] inline void dfs1(int u, int p){ max_dep[u] = dep[u]; if (!p){ for(int i=hd[u];i;i=suc[i]){ remove(i^1), dist[v] = dist[u] + w[i], dep[v] = dep[u] + isBlack[v]; dfs1(v, u), checkMax(max_dep[u], max_dep[v]), L[Ln++] = v; } } else { for(int i=hd[u];i;i=suc[i]) if (v != p){ dist[v] = dist[u] + w[i], dep[v] = dep[u] + isBlack[v]; dfs1(v, u), checkMax(max_dep[u], max_dep[v]); } } } inline void dfs2(int u, int p){ if (dep[u] >= Gn) return; checkMax(G[dep[u]], dist[u]); for(int i=hd[u];i;i=suc[i]) if (v != p){ dfs2(v, u); } } inline void find_center(int u, int p){ int blc = 0; sz[u] = 1; for(int i=hd[u];i;i=suc[i]) if (v != p){ find_center(v, u), sz[u] += sz[v]; checkMax(blc, sz[v]); } checkMax(blc, n_ - sz[u]); if (blc <= _c) _c = blc, c = u; } inline bool shller(int a, int b){ return max_dep[a] < max_dep[b]; } inline void stat(bool rt){ if (!rt || k){ sort(L, L+Ln, shller); Fn = 1; REP(i, Ln){ Gn = min(max_dep[L[i]] + 1, k + !rt), dfs2(L[i], 0); FOR(j, 1, Gn) checkMax(G[j], G[j-1]); FOR(j, 0, Fn) { int t = k - j - rt; checkMax(ans, F[j] + (t<Gn?G[t]:G[Gn-1])); } checkMax(Fn, Gn); REP(j, Fn) checkMax(F[j], G[j]); //REP(i, Gn) G[i] = 0; fill(G, G+Gn, 0); } //REP(i, Fn) F[i] = 0; fill(F, F+Fn, 0); } Ln = 0; } inline void solve(int u = 1){ _c = INF, find_center(u, 0), u = c; dep[u] = dist[u] = 0, dfs1(u, 0), stat(isBlack[u]); for(int i=hd[u];i;i=suc[i]){ n_ = sz[v], solve(v); } } int main(){ //freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); //ios::sync_with_stdio(false); RD(n, k, m); DO(m) isBlack[RD()] = true; for (int i=2;i<n<<1;++i){ RD(a[i], b[i]); RD_S(w[i]), a[i|1] = b[i], b[i|1] = a[i], w[i|1] = w[i]; prd[hd[a[i]]] = i, suc[i] = hd[a[i]], hd[a[i]] = i; ++i; prd[hd[a[i]]] = i, suc[i] = hd[a[i]], hd[a[i]] = i; } n_ = n, solve(), printf("%d\n", ans); }