Codeforces Round #425 (Div. 2) Problem D Misha, Grisha and Underground (Codeforces 832D) - 树链剖分 - 树状

Posted 2020-09-29 阿波罗2003

Misha and Grisha are funny boys, so they like to use new underground. The underground has n stations connected with n - 1 routes so that each route connects two stations, and it is possible to reach every station from any other.

The boys decided to have fun and came up with a plan. Namely, in some day in the morning Misha will ride the underground from station s to station f by the shortest path, and will draw with aerosol an ugly text "Misha was here" on every station he will pass through (including s and f). After that on the same day at evening Grisha will ride from station t to station f by the shortest path and will count stations with Misha‘s text. After that at night the underground workers will wash the texts out, because the underground should be clean.

The boys have already chosen three stations a, b and c for each of several following days, one of them should be station s on that day, another should be station f, and the remaining should be station t. They became interested how they should choose these stations s, f, t so that the number Grisha will count is as large as possible. They asked you for help.

Input

The first line contains two integers n and q (2 ≤ n ≤ 10⁵, 1 ≤ q ≤ 10⁵) — the number of stations and the number of days.

The second line contains n - 1 integers p₂, p₃, ..., p_n (1 ≤ p_i ≤ n). The integer p_i means that there is a route between stations p_i and i. It is guaranteed that it‘s possible to reach every station from any other.

The next q lines contains three integers a, b and c each (1 ≤ a, b, c ≤ n) — the ids of stations chosen by boys for some day. Note that some of these ids could be same.

Output

Print q lines. In the i-th of these lines print the maximum possible number Grisha can get counting when the stations s, t and f are chosen optimally from the three stations on the i-th day.

Examples

Input

3 2
1 1
1 2 3
2 3 3

Output

2 3

Input

4 1
1 2 3
1 2 3

Output

2

Note

In the first example on the first day if s = 1, f = 2, t = 3, Misha would go on the route 1 2, and Grisha would go on the route 3 1 2. He would see the text at the stations 1 and 2. On the second day, if s = 3, f = 2, t = 3, both boys would go on the route 3 1 2. Grisha would see the text at 3 stations.

In the second examle if s = 1, f = 3, t = 2, Misha would go on the route 1 2 3, and Grisha would go on the route 2 3 and would see the text at both stations.

---

　　题目大意 给定一个有n个点的树，有m个询问，每个询问给出3个点，你需要分别选出一个点作为s，f，t，如果将s到f的路径上的所有点权加1，计算t到f的路径上的点权和，问可能的点权和最大为多少。

　　显然树链剖分。

　　枚举6种可能，然后取个max。然后水完了。

　　然而比赛最后30分钟发现这特么是道水题，早知道该先写D题(内心崩溃...)。然后最后30分钟内20分钟写了出来，然后gdb挂了。。

　　然后在没gdb的情况下，今天上午把它改出来(不可思议)，然后发现，不会线段树区间lazy标记如何赋初值，树链剖分数组开始滥用。

　　另外线段树似乎容易被卡常，所以我就改用树状数组了（动态new点，能不TLE就怪了）。

Code

  1 /**
  2  * Codeforces
  3  * Problem#832D
  4  * Accepted
  5  * Time:1466ms
  6  * Memory:14200k
  7  */
  8 #include <iostream>
  9 #include <cstdio>
 10 #include <ctime>
 11 #include <cmath>
 12 #include <cctype>
 13 #include <cstring>
 14 #include <cstdlib>
 15 #include <fstream>
 16 #include <sstream>
 17 #include <algorithm>
 18 #include <map>
 19 #include <set>
 20 #include <stack>
 21 #include <queue>
 22 #include <vector>
 23 #include <stack>
 24 #ifndef WIN32
 25 #define Auto "%lld"
 26 #else
 27 #define Auto "%I64d"
 28 #endif
 29 using namespace std;
 30 typedef bool boolean;
 31 const signed int inf = (signed)((1u << 31) - 1);
 32 const signed long long llf = (signed long long)((1ull << 61) - 1);
 33 const double eps = 1e-9;
 34 const int binary_limit = 256;
 35 #define smin(a, b) a = min(a, b)
 36 #define smax(a, b) a = max(a, b)
 37 #define max3(a, b, c) max(a, max(b, c))
 38 #define min3(a, b, c) min(a, min(b, c))
 39 template<typename T>
 40 inline boolean readInteger(T& u){
 41     char x;
 42     int aFlag = 1;
 43     while(!isdigit((x = getchar())) && x != ‘-‘ && x != -1);
 44     if(x == -1) {
 45         ungetc(x, stdin);    
 46         return false;
 47     }
 48     if(x == ‘-‘){
 49         x = getchar();
 50         aFlag = -1;
 51     }
 52     for(u = x - ‘0‘; isdigit((x = getchar())); u = (u << 1) + (u << 3) + x - ‘0‘);
 53     ungetc(x, stdin);
 54     u *= aFlag;
 55     return true;
 56 }
 57 
 58 #define LL int
 59 #define lowbit(x) (x & (-x))
 60 
 61 typedef class IndexedTree {
 62     public:
 63         LL* a;
 64         int s;
 65         IndexedTree():a(NULL), s(0) {        }
 66         IndexedTree(int n):s(n) {
 67             a = new LL[(n + 1)];
 68             memset(a, 0, sizeof(LL) * (n + 1));
 69         }
 70         
 71         inline void add(int idx, LL val) {
 72             for(; idx <= s; idx += lowbit(idx))
 73                 a[idx] += val;
 74         }
 75         
 76         inline LL getSum(int idx) {
 77             LL rt = 0;
 78             for(; idx; idx -= lowbit(idx))
 79                 rt += a[idx];
 80             return rt;
 81         }
 82 }IndexedTree;
 83 
 84 typedef class SegmentableIndexedTree {
 85     public:
 86         IndexedTree s;            // sum
 87         IndexedTree us;            // unique sum
 88         stack< pair<int, int> > bs;
 89         
 90         SegmentableIndexedTree() {        }
 91         SegmentableIndexedTree(int n) {
 92             s = IndexedTree(n + 1);
 93             us = IndexedTree(n + 1);
 94         }
 95         
 96         inline void add(int l, int r, LL val) {
 97             s.add(l, val), us.add(l, l * val);
 98             s.add(r + 1, -val), us.add(r + 1, -(r + 1) * val);
 99             if(val > 0)
100                 bs.push(pair<int, int>(l, r));
101         }
102         
103         inline LL getSum(int idx) {
104             return (idx + 1) * s.getSum(idx) - us.getSum(idx);
105         }
106         
107         inline LL getSum(int l, int r) {
108             return getSum(r) - getSum(l - 1);
109         }
110         
111         inline void reset() {
112             pair<int, int> p;
113             while(!bs.empty()) {
114                 p = bs.top();
115                 bs.pop();
116                 add(p.first, p.second, -1);
117             }
118         }
119 }SegmentableIndexedTree;
120 
121 const int maxn = 1e5 + 5;
122 int n, m;
123 vector<int> g[maxn];
124 
125 inline void init() {
126     readInteger(n);
127     readInteger(m);
128     for(int i = 1, x; i < n; i++) {
129         readInteger(x);
130         g[x].push_back(i + 1);
131     }
132 }
133 
134 int cnt = 0;
135 int visitID[maxn], size[maxn], fa[maxn];
136 int zson[maxn], dep[maxn], top[maxn];
137 SegmentableIndexedTree st;
138 
139 void dfs1(int node, int last) {
140     dep[node] = dep[last] + 1;
141     size[node] = 1;
142     fa[node] = last;
143     int maxs = 0, maxid = 0;
144     for(int i = 0; i < (signed)g[node].size(); i++) {
145         int& e = g[node][i];
146         if(e == last)    continue;
147         dfs1(e, node);
148         size[node] += size[e];
149         if(size[e] > maxs)    maxs = size[e], maxid = e;//if(siz[son[u]] < siz[v]) son[u] = v;
150     }
151     zson[node] = maxid;
152 }
153 
154 void dfs2(int node, int last, boolean iszson) {
155     top[node] = (iszson) ? (top[last]) : (node);
156     visitID[node] = ++cnt;
157     if(zson[node] != 0)    dfs2(zson[node], node, true);
158     for(int i = 0; i < (signed)g[node].size(); i++) {
159         int& e = g[node][i];
160         if(e == last || e == zson[node])    continue;
161         dfs2(e, node, false);
162     }
163 }
164 
165 void update(int a, int b){
166 //    cout << st.query(st.root, 1, n, 1, n) << endl;
167     while(top[a] != top[b]){
168         int& d = (dep[top[a]] > dep[top[b]]) ? (a) : (b);
169         st.add(visitID[top[d]], visitID[d], 1);
170         d = fa[top[d]];
171     }
172     if(visitID[a] > visitID[b])    swap(a, b);
173     st.add(visitID[a], visitID[b], 1);
174 //    cout << st.query(st.root, 1, n, 1, n) << endl;
175 }
176 
177 int query(int a, int b) {
178     int ret = 0;
179     while(top[a] != top[b]){
180         int& d = (dep[top[a]] > dep[top[b]]) ? (a) : (b);
181         ret += st.getSum(visitID[top[d]], visitID[d]);
182         d = fa[top[d]];
183     }
184     if(visitID[a] > visitID[b])    swap(a, b);
185     ret += st.getSum(visitID[a], visitID[b]); 
186 //    cout << ret << endl;
187 //    cout << "============================" << endl;
188     return ret;
189 }
190 
191 int query(int s, int t, int f) {
192     st.reset();
193     update(s, f);
194     return query(t, f);
195 }
196 
197 inline void solve() {
198     int a, b, c;
199     dfs1(1, 0);
200     dfs2(1, 0, false); 
201     st = SegmentableIndexedTree(n);
202 //    for(int i = 1; i <= n; i++)
203 //        cout << zson[i] << " ";
204     while(m--) {
205         readInteger(a);
206         readInteger(b);
207         readInteger(c);
208         int res = query(a, b, c);
209         smax(res, query(b, a, c));
210         smax(res, query(b, c, a));
211         smax(res, query(b, a, c));
212         smax(res, query(c, a, b));
213         smax(res, query(c, b, a));
214         printf("%d\n", res);
215     }
216 }
217 
218 int main() {
219     init();
220     solve();
221     return 0;
222 }

 

  1 /**
  2  * Codeforces
  3  * Problem#832D
  4  * Accepted
  5  * Time:1466ms
  6  * Memory:14200k
  7  */
  8 #include <iostream>
  9 #include <cstdio>
 10 #include <ctime>
 11 #include <cmath>
 12 #include <cctype>
 13 #include <cstring>
 14 #include <cstdlib>
 15 #include <fstream>
 16 #include <sstream>
 17 #include <algorithm>
 18 #include <map>
 19 #include <set>
 20 #include <stack>
 21 #include <queue>
 22 #include <vector>
 23 #include <stack>
 24 #ifndef WIN32
 25 #define Auto "%lld"
 26 #else
 27 #define Auto "%I64d"
 28 #endif
 29 using namespace std;
 30 typedef bool boolean;
 31 const signed int inf = (signed)((1u << 31) - 1);
 32 const signed long long llf = (signed long long)((1ull << 61) - 1);
 33 const double eps = 1e-9;
 34 const int binary_limit = 256;
 35 #define smin(a, b) a = min(a, b)
 36 #define smax(a, b) a = max(a, b)
 37 #define max3(a, b, c) max(a, max(b, c))
 38 #define min3(a, b, c) min(a, min(b, c))
 39 template<typename T>
 40 inline boolean readInteger(T& u){
 41     char x;
 42     int aFlag = 1;
 43     while(!isdigit((x = getchar())) && x != ‘-‘ && x != -1);
 44     if(x == -1) {
 45         ungetc(x, stdin);    
 46         return false;
 47     }
 48     if(x == ‘-‘){
 49         x = getchar();
 50         aFlag = -1;
 51     }
 52     for(u = x - ‘0‘; isdigit((x = getchar())); u = (u << 1) + (u << 3) + x - ‘0‘);
 53     ungetc(x, stdin);
 54     u *= aFlag;
 55     return true;
 56 }
 57 
 58 #define LL int
 59 #define lowbit(x) (x & (-x))
 60 
 61 typedef class IndexedTree {
 62     public:
 63         LL* a;
 64         int s;
 65         IndexedTree():a(NULL), s(0) {        }
 66         IndexedTree(int n):s(n) {
 67             a = new LL[(n + 1)];
 68             memset(a, 0, sizeof(LL) * (n + 1));
 69         }
 70         
 71         inline void add(int idx, LL val) {
 72             for(; idx <= s; idx += lowbit(idx))
 73                 a[idx] += val;
 74         }
 75         
 76         inline LL getSum(int idx) {
 77             LL rt = 0;
 78             for(; idx; idx -= lowbit(idx))
 79                 rt += a[idx];
 80             return rt;
 81         }
 82 }IndexedTree;
 83 
 84 typedef class SegmentableIndexedTree {
 85     public:
 86         IndexedTree s;            // sum
 87         IndexedTree us;            // unique sum
 88         stack< pair<int, int> > bs;
 89         
 90         SegmentableIndexedTree() {        }
 91         SegmentableIndexedTree(int n) {
 92             s = IndexedTree(n + 1);
 93             us = IndexedTree(n + 1);
 94         }
 95         
 96         inline void add(int l, int r, LL val) {
 97             s.add(l, val), us.add(l, l * val);
 98             s.add(r + 1, -val), us.add(r + 1, -(r + 1) * val);
 99             if(val > 0)
100                 bs.push(pair<int, int>(l, r));
101         }
102         
103         inline LL getSum(int idx) {
104             return (idx + 1) * s.getSum(idx) - us.getSum(idx);
105         }
106         
107         inline LL getSum(int l, int r) {
108             return getSum(r) - getSum(l - 1);
109         }
110         
111         inline void reset() {
112             pair<int, int> p;
113             while(!bs.empty()) {
114                 p = bs.top();
115                 bs.pop();
116                 add(p.first, p.second, -1);
117             }
118         }
119 }SegmentableIndexedTree;
120 
121 const int maxn = 1e5 + 5;
122 int n, m;
123 vector<int> g[maxn];
124 
125 inline void init() {
126     readInteger(n);
127     readInteger(m);
128     for(int i = 1, x; i < n; i++) {
129         readInteger(x);
130         g[x].push_back(i + 1);
131     }
132 }
133 
134 int cnt = 0;
135 int visitID[maxn], size[maxn], fa[maxn];
136 int zson[maxn], dep[maxn], top[maxn];
137 SegmentableIndexedTree st;
138 
139 void dfs1(int node, int last) {
140     dep[node] = dep[last] + 1;
141     size[node] = 1;
142     fa[node] = last;
143     int maxs = 0, maxid = 0;
144     for(int i = 0; i < (signed)g[node].size(); i++) {
145         int& e = g[node][i];
146         if(e == last)    continue;
147         dfs1(e, node);
148         size[node] += size[e];
149         if(size[e] > maxs)    maxs = size[e], maxid = e;//if(siz[son[u]] < siz[v]) son[u] = v;
150     }
151     zson[node] = maxid;
152 }
153 
154 void dfs2(int node, int last, boolean iszson) {
155     top[node] = (iszson) ? (top[last]) : (node);
156     visitID[node] = ++cnt;
157     if(zson[node] != 0)    dfs2(zson[node], node, true);
158     for(int i = 0; i < (signed)g[node].size(); i++) {
159         int& e = g[node][i];
160         if(e == last || e == zson[node])    continue;
161         dfs2(e, node, false);
162     }
163 }
164 
165 void update(int a, int b){
166 //    cout << st.query(st.root, 1, n, 1, n) << endl;
167     while(top[a] != top[b]){
168         int& d = (dep[top[a]] > dep[top[b]]) ? (a) : (b);
169         st.add(visitID[top[d]], visitID[d], 1);
170         d = fa[top[d]];
171     }
172     if(visitID[a] > visitID[b])    swap(a, b);
173     st.add(visitID[a], visitID[b], 1);
174 //    cout << st.query(st.root, 1, n, 1, n) << endl;
175 }
176 
177 int query(int a, int b) {
178     int ret = 0;
179     while(top[a] != top[b]){
180         int& d = (dep[top[a]] > dep[top[b]]) ? (a) : (b);
181         ret += st.getSum(visitID[top[d]], visitID[d]);
182         d = fa[top[d]];
183     }
184     if(visitID[a] > visitID[b])    swap(a, b);
185     ret += st.getSum(visitID[a], visitID[b]); 
186 //    cout << ret << endl;
187 //    cout << "============================" << endl;
188     return ret;
189 }
190 
191 int query(int s, int t, int f) {
192     st.reset();
193     update(s, f);
194     return query(t, f);
195 }
196 
197 inline void solve() {
198     int a, b, c;
199     dfs1(1, 0);
200     dfs2(1, 0, false); 
201     st = SegmentableIndexedTree(n);
202 //    for(int i = 1; i <= n; i++)
203 //        cout << zson[i] << " ";
204     while(m--) {
205         readInteger(a);
206         readInteger(b);
207         readInteger(c);
208         int res = query(a, b, c);
209         smax(res, query(b, a, c));
210         smax(res, query(b, c, a));
211         smax(res, query(b, a, c));
212         smax(res, query(c, a, b));
213         smax(res, query(c, b, a));
214         printf("%d\n", res);
215     }
216 }
217 
218 int main() {
219     init();
220     solve();
221     return 0;
222 }