BZOJ4539 [Hnoi2016]树 【倍增 + 主席树】
2018-05-29 09:24
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题目链接
题解
我们把每次复制出来的树看做一个点,那么大树实际上也就是一棵\(O(M)\)个点的树
所以我们只需求两遍树上距离:
大树上求距离,进入同一个点后在模板树上再求一次距离
讨论好一些情况即可
然后求子树第\(k\)大的点要用主席树
没了
#include<algorithm> #include<iostream> #include<cstring> #include<cstdio> #include<cmath> #include<map> #define Redge(u) for (int k = h[u],to; k; k = ed[k].nxt) #define REP(i,n) for (int i = 1; i <= (n); i++) #define mp(a,b) make_pair<int,int>(a,b) #define cls(s) memset(s,0,sizeof(s)) #define cp pair<int,int> #define LL long long int using namespace std; const int maxn = 100005,maxm = 6000005,INF = 1000000000; inline LL read(){ LL out = 0,flag = 1; char c = getchar(); while (c < 48 || c > 57){if (c == '-') flag = -1; c = getchar();} while (c >= 48 && c <= 57){out = (out << 3) + (out << 1) + c - 48; c = getchar();} return out * flag; } LL S[maxn],R[maxn]; int n,m,Q,bin[50]; int h[maxn],ne = 1; struct EDGE{int to,nxt;}ed[maxn << 1]; inline void build(int u,int v){ ed[++ne] = (EDGE){v,h[u]}; h[u] = ne; ed[++ne] = (EDGE){u,h[v]}; h[v] = ne; } int sum[maxm],ls[maxm],rs[maxm],rt[maxn],tot; void modify(int& u,int pre,int l,int r,int pos){ sum[u = ++tot] = sum[pre] + 1; ls[u] = ls[pre]; rs[u] = rs[pre]; if (l == r) return; int mid = l + r >> 1; if (mid >= pos) modify(ls[u],ls[pre],l,mid,pos); else modify(rs[u],rs[pre],mid + 1,r,pos); } int query(int u,int v,int l,int r,LL k){ if (l == r) return l; int mid = l + r >> 1,t = sum[ls[u]] - sum[ls[v]]; if (t >= k) return query(ls[u],ls[v],l,mid,k); return query(rs[u],rs[v],mid + 1,r,k - t); } int dfn[maxn],siz[maxn],dep[maxn],Fa[maxn][18],cnt; void dfs(int u){ dfn[u] = ++cnt; siz[u] = 1; modify(rt[cnt],rt[cnt - 1],1,n,u); REP(i,17) Fa[u][i] = Fa[Fa[u][i - 1]][i - 1]; Redge(u) if ((to = ed[k].to) != Fa[u][0]){ Fa[to][0] = u; dep[to] = dep[u] + 1; dfs(to); siz[u] += siz[to]; } } int hh[maxn],nne = 1,Nxt[maxn << 1],To[maxn << 1]; int fa[maxn][18],N,lk[maxn],Dep[maxn]; LL d[maxn][18]; void DFS(int u){ for (int k = hh[u]; k; k = Nxt[k]){ Dep[To[k]] = Dep[u] + 1; DFS(To[k]); } } void Build(){ LL u,b,x,r,v; S[1] = n; R[1] = 1; N = 1; for (int i = 1; i <= m; i++){ u = read(); v = read(); b = lower_bound(S + 1,S + 1 + N,v) - S; r = R[b]; x = query(rt[dfn[r] + siz[r] - 1],rt[dfn[r] - 1],1,n,v - S[b - 1]); N++; fa [0] = b; d [0] = 1 + dep[x] - dep[r]; S = S[N - 1] + siz[u]; R = u; lk = x; nne++; Nxt[nne] = hh[b]; To[nne] = N; hh[b] = nne; } DFS(1); //REP(i,N) printf("block %d rt = %lld lk = %d d = %lld Dep = %d total = %lld\n",i,R[i],lk[i],d[i][0],Dep[i],S[i]); REP(j,17) REP(i,N){ fa[i][j] = fa[fa[i][j - 1]][j - 1]; d[i][j] = d[i][j - 1] + d[fa[i][j - 1]][j - 1]; } } LL dis(int u,int v){ if (dep[u] < dep[v]) swap(u,v); LL re = 0; for (int i = 0,D = dep[u] - dep[v]; bin[i] <= D; i++) if (D & bin[i]) re += bin[i],u = Fa[u][i]; if (u == v) return re; for (int i = 17; ~i; i--) if (Fa[u][i] != Fa[v][i]){ u = Fa[u][i]; v = Fa[v][i]; re += bin[i + 1]; } return re + 2; } LL Dis(LL a,LL b,LL x,LL y){ if (Dep[a] < Dep[b]){ swap(a,b); swap(x,y); } LL re = dep[x] - dep[R[a]] + dep[y] - dep[R[b]]; int D = Dep[a] - Dep[b],u = a,v = b; for (int i = 0; bin[i] <= D; i++) if (D & bin[i]){ re += d[u][i]; u = fa[u][i]; } if (u == v){ D = Dep[a] - Dep[b] - 1; u = a; re = dep[x] - dep[R[a]]; for (int i = 0; bin[i] <= D; i++) if (D & bin[i]){ re += d[u][i]; u = fa[u][i]; } re += 1; x = lk[u]; re += dis(x,y); } else { for (int i = 17; ~i; i--) if (fa[u][i] != fa[v][i]){ re += d[u][i] + d[v][i]; u = fa[u][i]; v = fa[v][i]; } re += 2; x = lk[u]; y = lk[v]; re += dis(x,y); } return re; } void solve(){ LL u,v,a,b,x,y; while (Q--){ u = read(); v = read(); a = lower_bound(S + 1,S + 1 + N,u) - S; b = lower_bound(S + 1,S + 1 + N,v) - S; x = query(rt[dfn[R[a]] + siz[R[a]] - 1],rt[dfn[R[a]] - 1],1,n,u - S[a - 1]); y = query(rt[dfn[R[b]] + siz[R[b]] - 1],rt[dfn[R[b]] - 1],1,n,v - S[b - 1]); //printf("(%lld,%lld) (%lld,%lld)\n",a,x,b,y); if (a == b) printf("%lld\n",dis(x,y)); else printf("%lld\n",Dis(a,b,x,y)); } } int main(){ bin[0] = 1; for (int i = 1; i <= 25; i++) bin[i] = bin[i - 1] << 1; n = read(); m = read(); Q = read(); for (int i = 1; i < n; i++) build(read(),read()); dfs(1); Build(); solve(); return 0; }
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