[国家集训队]旅游

Posted 2021-01-09 mrclr

嘟嘟嘟

 

这其实就是一道树剖板子题，只不过就是写的长了一点。

还是叨叨几点吧：

1.区间取相反数：开一个标记数组，每一次亦或1，然后对应的sum取相反数，Max, Min交换，并且取相反数。

2.题目中给的是边权，但要转化成点权：这条边的边权转化成儿子节点的点权，然后每一次链上操作的时候，x, y的LCA不要管。实现的时候就是当x,y跳到同一条链的时候，对[dfsx[y] + 1, dfsx[x]]（假设dfsx[y] < dfsx[x]）操作即可，因为同一条链上的dfs序是连续的。

耐着性子写完吧~

  1 #include<cstdio>
  2 #include<iostream>
  3 #include<cmath>
  4 #include<algorithm>
  5 #include<cstring>
  6 #include<cstdlib>
  7 #include<cctype>
  8 #include<vector>
  9 #include<stack>
 10 #include<queue>
 11 using namespace std;
 12 #define enter puts("") 
 13 #define space putchar(‘ ‘)
 14 #define Mem(a, x) memset(a, x, sizeof(a))
 15 #define rg register
 16 typedef long long ll;
 17 typedef double db;
 18 const int INF = 0x3f3f3f3f;
 19 const db eps = 1e-8;
 20 const int maxn = 1e5 + 5;
 21 inline ll read()
 22 {
 23     ll ans = 0;
 24     char ch = getchar(), last = ‘ ‘;
 25     while(!isdigit(ch)) {last = ch; ch = getchar();}
 26     while(isdigit(ch)) {ans = ans * 10 + ch - ‘0‘; ch = getchar();}
 27     if(last == ‘-‘) ans = -ans;
 28     return ans;
 29 }
 30 inline void write(ll x)
 31 {
 32     if(x < 0) x = -x, putchar(‘-‘);
 33     if(x >= 10) write(x / 10);
 34     putchar(x % 10 + ‘0‘);
 35 }
 36 
 37 int n, m, a[maxn];
 38 
 39 vector<int> v[maxn], c[maxn];
 40 bool vis[maxn];
 41 int dep[maxn], fa[maxn], siz[maxn], son[maxn];
 42 void dfs1(int now)
 43 {
 44     vis[now] = 1; siz[now] = 1;
 45     for(int i = 0; i < (int)v[now].size(); ++i)
 46     {
 47         if(!vis[v[now][i]])
 48         {
 49             a[v[now][i]] = c[now][i];
 50             dep[v[now][i]] = dep[now] + 1;
 51             fa[v[now][i]] = now;
 52             dfs1(v[now][i]);
 53             siz[now] += siz[v[now][i]];
 54             if(!son[now] || siz[son[now]] < siz[v[now][i]]) son[now] = v[now][i];
 55         }
 56     }
 57 }
 58 int dfsx[maxn], pos[maxn], top[maxn], cnt = 0;
 59 void dfs2(int now)
 60 {
 61     vis[now] = 1;
 62     dfsx[now] = ++cnt; pos[cnt] = now;
 63     if(son[now])
 64     {
 65         top[son[now]] = top[now];
 66         dfs2(son[now]);
 67     }
 68     for(int i = 0; i < (int)v[now].size(); ++i)
 69     {
 70         if(!vis[v[now][i]] && v[now][i] != son[now])
 71         {
 72             top[v[now][i]] = v[now][i];
 73             dfs2(v[now][i]);
 74         }
 75     }
 76 }
 77 
 78 int l[maxn << 2], r[maxn << 2], sum[maxn << 2], Max[maxn << 2], Min[maxn << 2];
 79 int lzy[maxn << 2];             //相反数标记
 80 void pushup(int now)
 81 {
 82     sum[now] = sum[now << 1] + sum[now << 1 | 1];
 83     Max[now] = max(Max[now << 1], Max[now << 1 | 1]);
 84     Min[now] = min(Min[now << 1], Min[now << 1 | 1]);    
 85 }
 86 void build(int L, int R, int now)
 87 {
 88     l[now] = L; r[now] = R;
 89     if(L == R) {sum[now] = Max[now] = Min[now] = a[pos[L]]; return;}
 90     int mid = (L + R) >> 1;
 91     build(L, mid, now << 1);
 92     build(mid + 1, R, now << 1 | 1);
 93     pushup(now);
 94 }
 95 void pushdown(int now)
 96 {
 97     if(lzy[now])
 98     {
 99         sum[now << 1] = -sum[now << 1]; sum[now << 1 | 1] = -sum[now << 1 | 1];
100         swap(Max[now << 1], Min[now << 1]); swap(Max[now << 1 | 1], Min[now << 1 | 1]);
101         Max[now << 1] = -Max[now << 1]; Max[now << 1 | 1] = -Max[now << 1 | 1];
102         Min[now << 1] = -Min[now << 1]; Min[now << 1 | 1] = -Min[now << 1 | 1];
103         lzy[now << 1] ^= 1; lzy[now << 1 | 1] ^= 1;
104         lzy[now] = 0;
105     }
106     
107 }
108 void update_sin(int now, int idx, int d)
109 {
110     if(l[now] == r[now]) 
111     {
112         sum[now] = Max[now] = Min[now] = d; 
113         return;
114     }
115     pushdown(now);
116     int mid = (l[now] + r[now]) >> 1;
117     if(idx <= mid) update_sin(now << 1, idx, d);
118     else update_sin(now << 1 | 1, idx, d);
119     pushup(now);
120 }
121 void update_opp(int L, int R, int now)
122 {
123     if(L == l[now] && R == r[now])
124     {
125         sum[now] = -sum[now];
126         swap(Max[now], Min[now]);
127         Max[now] = -Max[now];
128         Min[now] = -Min[now];
129         lzy[now] ^= 1;
130         return;
131     }
132     pushdown(now);
133     int mid = (l[now] + r[now]) >> 1;
134     if(R <= mid) update_opp(L, R, now << 1);
135     else if(L > mid) update_opp(L, R, now << 1 | 1);
136     else update_opp(L, mid, now << 1), update_opp(mid + 1, R, now << 1 | 1);
137     pushup(now);
138 }
139 int query_sum(int L, int R, int now)
140 {
141     if(L == l[now] && R == r[now]) return sum[now];
142     pushdown(now);
143     int mid = (l[now] + r[now]) >> 1;
144     if(R <= mid) return query_sum(L, R, now << 1);
145     else if(L > mid) return query_sum(L, R, now << 1 | 1);
146     else return query_sum(L, mid, now << 1) + query_sum(mid + 1, R, now << 1 | 1);
147 }
148 int query_M(int L, int R, int now, bool flg)
149 {
150     if(L == l[now] && R == r[now]) return flg ? Max[now] : Min[now];
151     pushdown(now);
152     int mid = (l[now] + r[now]) >> 1;
153     if(R <= mid) return query_M(L, R, now << 1, flg);
154     else if(L > mid) return query_M(L, R, now << 1 | 1, flg);
155     else
156     {
157         if(flg) return max(query_M(L, mid, now << 1, flg), query_M(mid + 1, R, now << 1 | 1, flg));
158         else return min(query_M(L, mid, now << 1, flg), query_M(mid + 1, R, now << 1 | 1, flg));
159     }
160 }
161 
162 void update_path(int x, int y)
163 {
164     while(top[x] != top[y])
165     {
166         if(dep[top[x]] < dep[top[y]]) swap(x, y);
167         update_opp(dfsx[top[x]], dfsx[x], 1);
168         x = fa[top[x]];
169     }
170     if(dfsx[x] < dfsx[y]) swap(x, y);
171     if(x == y) return;
172     update_opp(dfsx[y] + 1, dfsx[x], 1);
173 }
174 int queryS_path(int x, int y)
175 {
176     int ret = 0;
177     while(top[x] != top[y])
178     {
179         if(dep[top[x]] < dep[top[y]]) swap(x, y);
180         ret += query_sum(dfsx[top[x]], dfsx[x], 1);
181         x = fa[top[x]];
182     }
183     if(dfsx[x] < dfsx[y]) swap(x, y);
184     if(x != y) ret += query_sum(dfsx[y] + 1, dfsx[x], 1);    
185     return ret;
186 }
187 int queryM_path(int x, int y, int flg)
188 {
189     int ret = flg ? -INF : INF;
190     while(top[x] != top[y])
191     {
192         if(dep[top[x]] < dep[top[y]]) swap(x, y);
193         if(flg) ret = max(ret, query_M(dfsx[top[x]], dfsx[x], 1, flg));
194         else ret = min(ret, query_M(dfsx[top[x]], dfsx[x], 1, flg));
195         x = fa[top[x]];
196     }
197     if(dfsx[x] < dfsx[y]) swap(x, y);
198     if(x != y)
199     {
200         if(flg) ret = max(ret, query_M(dfsx[y] + 1, dfsx[x], 1, flg));
201         else ret = min(ret, query_M(dfsx[y] + 1, dfsx[x], 1, flg));
202     }
203     return ret;
204 }
205 
206 char ch[5];
207 
208 int main()
209 {
210     n = read();
211     for(int i = 1; i < n; ++i)
212     {
213         int x = read() + 1, y = read() + 1, co = read();
214         v[x].push_back(y); c[x].push_back(co);
215         v[y].push_back(x); c[y].push_back(co);
216     }
217     dfs1(1); 
218     Mem(vis, 0); top[1] = 1; dfs2(1);
219     build(1, cnt, 1);
220     m = read();
221     for(int i = 1; i <= m; ++i)
222     {
223         scanf("%s", ch); int x = read() + 1, y = read() + 1;
224         if(ch[0] == ‘C‘) update_sin(1, dfsx[x], y - 1);
225         else if(ch[0] == ‘N‘) update_path(x, y);
226         else if(ch[0] == ‘S‘) write(queryS_path(x, y)), enter;
227         else if(ch[1] == ‘A‘) write(queryM_path(x, y, 1)), enter;
228         else write(queryM_path(x, y, 0)), enter;
229     }
230     return 0;
231 }

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