Luogu2542 AHOI2005 航线规划 树链剖分、线段树

传送门

先把删完边之后的图拆一个生成树出来，然后考虑非树边的影响。实际上非树边就是让树上的一条路径的权值从$1$变为了$0$，而每一个询问就是一条路径上的权值之和。使用树链剖分+线段树维护权值即可。

  1 #include<bits/stdc++.h>
  2 #define lch (now << 1)
  3 #define rch (now << 1 | 1)
  4 #define mid ((l + r) >> 1)
  5 //This code is written by Itst
  6 using namespace std;
  7
  8 inline int read(){
  9     int a = 0;
 10     bool f = 0;
 11     char c = getchar();
 12     while(c != EOF && !isdigit(c)){
 13         if(c == ‘-‘)
 14             f = 1;
 15         c = getchar();
 16     }
 17     while(c != EOF && isdigit(c)){
 18         a = (a << 3) + (a << 1) + (c ^ ‘0‘);
 19         c = getchar();
 20     }
 21     return f ? -a : a;
 22 }
 23
 24 const int MAXN = 30010;
 25 struct Edge{
 26     int end , upEd;
 27 }Ed[MAXN << 3];
 28 struct query{
 29     int type , s , t;
 30 }now[MAXN << 1];
 31 int head[MAXN] , sum[MAXN << 2] , mark[MAXN << 2] , ans[MAXN << 1] , N , M , cntEd , cntQ , cntAns;
 32 int top[MAXN] , dep[MAXN] , fa[MAXN] , son[MAXN] , ind[MAXN] , size[MAXN] , ts;
 33 vector < int > bef[MAXN] , del[MAXN];
 34 bool vis[MAXN];
 35
 36 inline void addEd(int a , int b){
 37     Ed[++cntEd].end = b;
 38     Ed[cntEd].upEd = head[a];
 39     head[a] = cntEd;
 40 }
 41
 42 void dfs1(int x , int f){
 43     size[x] = 1;
 44     fa[x] = f;
 45     dep[x] = dep[f] + 1;
 46     for(int i = head[x] ; i ; i = Ed[i].upEd)
 47         if(!dep[Ed[i].end]){
 48             dfs1(Ed[i].end , x);
 49             size[x] += size[Ed[i].end];
 50             if(size[Ed[i].end] > size[son[x]])
 51                 son[x] = Ed[i].end;
 52         }
 53 }
 54
 55 void dfs2(int x , int t){
 56     top[x] = t;
 57     ind[x] = ++ts;
 58     if(!son[x])
 59         return;
 60     dfs2(son[x] , t);
 61     for(int i = head[x] ; i ; i = Ed[i].upEd)
 62         if(fa[Ed[i].end] == x && Ed[i].end != son[x])
 63             dfs2(Ed[i].end , Ed[i].end);
 64 }
 65
 66 inline void pushup(int now){
 67     sum[now] = sum[lch] + sum[rch];
 68 }
 69
 70 inline void pushdown(int now , int l , int r){
 71     if(mark[now] != -1){
 72         mark[lch] = mark[now];
 73         mark[rch] = mark[now];
 74         sum[lch] = mark[now] * (mid - l + 1);
 75         sum[rch] = mark[now] * (r - mid);
 76         mark[now] = -1;
 77     }
 78 }
 79
 80 int query(int now , int l , int r , int L , int R){
 81     if(l >= L && r <= R)
 82         return sum[now];
 83     pushdown(now , l , r);
 84     int sum = 0;
 85     if(mid >= L)
 86         sum = query(lch , l , mid , L , R);
 87     if(mid < R)
 88         sum += query(rch , mid + 1 , r , L , R);
 89     return sum;
 90 }
 91
 92 void modify(int now , int l , int r , int L , int R , int num){
 93     if(l >= L && r <= R){
 94         mark[now] = num;
 95         sum[now] = num * (r - l + 1);
 96         return;
 97     }
 98     pushdown(now , l , r);
 99     if(mid >= L)
100         modify(lch , l , mid , L , R , num);
101     if(mid < R)
102         modify(rch , mid + 1 , r , L , R , num);
103     pushup(now);
104 }
105
106 inline void work(int x , int y){
107     int tx = top[x] , ty = top[y];
108     while(tx != ty){
109         if(dep[tx] < dep[ty]){
110             swap(tx , ty);
111             swap(x , y);
112         }
113         modify(1 , 1 , N , ind[tx] , ind[x] , 0);
114         x = fa[x];
115         tx = top[x];
116     }
117     if(dep[x] > dep[y])
118         swap(x , y);
119     if(dep[x] != dep[y])
120         modify(1 , 1 , N , ind[x] + 1 , ind[y] , 0);
121 }
122
123 inline int query(int x , int y){
124     int sum = 0 , tx = top[x] , ty = top[y];
125     while(tx != ty){
126         if(dep[tx] < dep[ty]){
127             swap(tx , ty);
128             swap(x , y);
129         }
130         sum += query(1 , 1 , N , ind[tx] , ind[x]);
131         x = fa[tx];
132         tx = top[x];
133     }
134     if(dep[x] > dep[y])
135         swap(x , y);
136     if(dep[x] != dep[y])
137         sum += query(1 , 1 , N , ind[x] + 1 , ind[y]);
138     return sum;
139 }
140
141 void dfs3(int now){
142     vis[now] = 1;
143     for(int i = head[now] ; i ; i = Ed[i].upEd)
144         if(fa[Ed[i].end] == now && !vis[Ed[i].end])
145             dfs3(Ed[i].end);
146         else
147             if(dep[Ed[i].end] >= dep[now])
148                 work(now , Ed[i].end);
149 }
150
151 int main(){
152 #ifndef ONLINE_JUDGE
153     freopen("2542.in" , "r" , stdin);
154     freopen("2542.out" , "w" , stdout);
155 #endif
156     memset(mark , -1 , sizeof(mark));
157     N = read();
158     M = read();
159     modify(1 , 1 , N , 1 , N , 1);
160     for(int i = 1 ; i <= M ; ++i){
161         int a = read() , b = read();
162         bef[a].push_back(b);
163         bef[b].push_back(a);
164     }
165     for(int i = 1 ; i <= N ; ++i)
166         sort(bef[i].begin() , bef[i].end());
167     int c = read();
168     while(c + 1){
169         now[++cntQ].type = c;
170         now[cntQ].s = read();
171         now[cntQ].t = read();
172         if(!c){
173             del[now[cntQ].s].push_back(now[cntQ].t);
174             del[now[cntQ].t].push_back(now[cntQ].s);
175         }
176         c = read();
177     }
178     for(int i = 1 ; i <= N ; ++i){
179         sort(del[i].begin() , del[i].end());
180         int p = 0 , sizeb = bef[i].size() , sized = del[i].size();
181         for(int j = 0 ; j < sizeb ; ++j)
182             if(p < sized && bef[i][j] == del[i][p])
183                 ++p;
184             else
185                 addEd(i , bef[i][j]);
186     }
187     dfs1(1 , 0);
188     dfs2(1 , 1);
189     dfs3(1);
190     for(int i = cntQ ; i ; --i)
191         if(now[i].type)
192             ans[++cntAns] = query(now[i].s , now[i].t);
193         else
194             work(now[i].s , now[i].t);
195     while(cntAns)
196         printf("%d\n" , ans[cntAns--]);
197     return 0;
198 }

原文地址：https://www.cnblogs.com/Itst/p/10075821.html