2286: [Sdoi2011]消耗战
2286: [Sdoi2011]消耗战
分析
虚树练习题。
构建虚树，在虚树上DP。
跟着gxb学虚-tree。。。
代码
1 #include <cstdio> 2 #include <algorithm> 3 #include <cstring> 4 #include <iostream> 5 #include <cmath> 6 #include <cctype> 7 8 using namespace std; 9 10 const int N = 250100; 11 const int INF = 1e9; 12 13 int head[N<<1],nxt[N<<1],to[N<<1],w[N<<1],TotE; 14 int deth[N],val[N],siz[N],dfn[N],fa[N],son[N],bel[N],sk[N<<1],top,Time_index; 15 int A[N]; 16 17 inline int read() { 18 int x = 0,f = 1;char ch =getchar(); 19 for (; !isdigit(ch); ch=getchar()) if (ch=='-') f=-1; 20 for (; isdigit(ch); ch=getchar()) x = x*10+ch-'0'; 21 return x * f; 22 } 23 bool cmp(const int &a,const int &b) { 24 return dfn[a] < dfn[b]; 25 } 26 void Add_edge(int u,int v,int c) { 27 ++TotE;to[TotE] = v;w[TotE] = c;nxt[TotE] = head[u];head[u] = TotE; 28 ++TotE;to[TotE] = u;w[TotE] = c;nxt[TotE] = head[v];head[v] = TotE; 29 } 30 void add_edge(int u,int v) { 31 ++TotE;to[TotE] = v;nxt[TotE] = head[u];head[u] = TotE; 32 } 33 void dfs1(int u,int mn) { 34 val[u] = mn; 35 siz[u] = 1; 36 for (int i=head[u]; i; i=nxt[i]) { 37 int v = to[i]; 38 if (v==fa[u]) continue; 39 fa[v] = u; 40 deth[v] = deth[u] + 1; 41 dfs1(v,min(w[i],mn)); 42 siz[u] += siz[v]; 43 if (!son[u] || siz[v] > siz[son[u]]) son[u] = v; 44 } 45 } 46 void dfs2(int u,int top) { 47 bel[u] = top; 48 dfn[u] = ++Time_index; 49 if (!son[u]) return; 50 dfs2(son[u],top); 51 for (int i=head[u]; i; i=nxt[i]) { 52 int v = to[i]; 53 if (v==fa[u] || v==son[u]) continue; 54 dfs2(v,v); 55 } 56 } 57 int Lca(int u,int v) { 58 while (bel[u] != bel[v]) { 59 if (deth[bel[u]] < deth[bel[v]]) swap(u,v); 60 u = fa[bel[u]]; 61 } 62 if (deth[u] < deth[v]) return u; 63 return v; 64 } 65 void Insert(int p) { 66 int x = sk[top]; 67 if (x==1) {sk[++top] = p;return ;} 68 int lca = Lca(p,x); 69 if (lca == x) return; // 此题构建虚树不同的是，若x==lca，不加入p。 70 while (lca != x) { 71 int y = sk[--top]; 72 if (dfn[y] < dfn[lca]) { 73 add_edge(lca,x); 74 sk[++top] = lca; 75 break; 76 } 77 add_edge(y,x); 78 x = sk[top]; 79 } 80 sk[++top] = p; 81 } 82 long long DP(int u) { 83 if (!head[u]) return val[u]; 84 long long ans = 0; 85 for (int i=head[u]; i; i=nxt[i]) ans += DP(to[i]); 86 head[u] = 0; 87 return min(ans,(long long)val[u]); 88 } 89 int main() { 90 int n = read(); 91 for (int i=1; i<n; ++i) { 92 int u = read(),v = read(),w = read(); 93 Add_edge(u,v,w); 94 } 95 deth[1] = 1; 96 dfs1(1,INF); 97 dfs2(1,1); 98 TotE = 0; 99 memset(head,0,sizeof(head)); 100 101 int m = read(); 102 while (m--) { 103 TotE = 0;sk[top = 1] = 1; 104 105 int k = read(); 106 for (int i=1; i<=k; ++i) A[i] = read(); 107 sort(A+1,A+k+1,cmp); 108 for (int i=1; i<=k; ++i) Insert(A[i]); 109 while (--top) add_edge(sk[top],sk[top+1]); 110 111 long long ans = 0; 112 for (int i=head[1]; i; i=nxt[i]) ans += DP(to[i]); // 单独处理1的情况，否则val[1]设为很大的longlong数，INF不够。 113 printf("%lld\n",ans); 114 head[1] = 0; 115 } 116 return 0; 117 }
