HDU 4718 The LCIS on the Tree （动态树LCT）

The LCIS on the Tree

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 175    Accepted Submission(s): 40

Problem Description

For a sequence S₁, S₂, ... , S_N, and a pair of integers (i, j), if 1 <= i <= j <= N and S_i < S_i+1 < S_i+2 < ... < S_j-1 < S_j , then the sequence S_i, S_i+1, ... , S_j is a CIS(Continuous Increasing Subsequence). The longest CIS of a sequence is called the LCIS (Longest Continuous Increasing Subsequence).
Now we consider a tree rooted at node 1. Nodes have values. We have Q queries, each with two nodes u and v. You have to find the shortest path from u to v. And write down each nodes' value on the path, from u to v, inclusive. Then you will get a sequence, and please show us the length of its LCIS.

 

Input

The first line has a number T (T <= 10) , indicating the number of test cases.
For each test case, the first line is a number N (N <= 10⁵), the number of nodes in the tree.
The second line comes with N numbers v1, v2, v3 ... , v_N, describing the value of node 1 to node N. (1 <= v_i <= 10⁹)
The third line comes with N - 1 numbers p₂, p₃, p₄ ... , p_N, describing the father nodes of node 2 to node N. Node 1 is the root and will have no father.
Then comes a number Q, it is the number of queries. (Q <= 10⁵)
For next Q lines, each with two numbers u and v. As described above.

 

Output

For test case X, output "Case #X:" at the first line.
Then output Q lines, each with an answer to the query.
There should be a blank line *BETWEEN* each test case.

 

Sample Input

1
5
1 2 3 4 5
1 1 3 3
3
1 5
4 5
2 5

 

Sample Output

Case #1:
3
2
3

 

Source

2013 ACM/ICPC Asia Regional Online —— Warmup2

 

Recommend

zhuyuanchen520

 

用动态树把这题A掉了，

感觉很爽，一写就A了。

只有用动态树，splay维护最长连续上升子序列，注意更新操作

 /* ***********************************************
 Author        :kuangbin
 Created Time  :2013-9-13 21:03:22
 File Name     :HDU4718.cpp
 ************************************************ */

 #pragma comment(linker, "/STACK:1024000000,1024000000")
 #include <stdio.h>
 #include <string.h>
 #include <iostream>
 #include <algorithm>
 #include <vector>
 #include <queue>
 #include <set>
 #include <map>
 #include <string>
 #include <math.h>
 #include <stdlib.h>
 #include <time.h>
 using namespace std;
 #define REP(I, N) for (int I=0;I<int(N);++I)
 #define FOR(I, A, B) for (int I=int(A);I<int(B);++I)
 #define DWN(I, B, A) for (int I=int(B-1);I>=int(A);--I)
 #define REP_1(I, N) for (int I=1;I<=int(N);++I)
 #define FOR_1(I, A, B) for (int I=int(A);I<=int(B);++I)
 #define DWN_1(I, B, A) for (int I=int(B);I>=int(A);--I)
 #define REP_C(I, N) for (int N____=int(N),I=0;I<N____;++I)
 #define FOR_C(I, A, B) for (int B____=int(B),I=A;I<B____;++I)
 #define DWN_C(I, B, A) for (int A____=int(A),I=B-1;I>=A____;--I)
 #define REP_1_C(I, N) for (int N____=int(N),I=1;I<=N____;++I)
 #define FOR_1_C(I, A, B) for (int B____=int(B),I=A;I<=B____;++I)
 #define DWN_1_C(I, B, A) for (int A____=int(A),I=B;I>=A____;--I)
 #define DO(N) while(N--)
 #define DO_C(N) int N____ = N; while(N____--)
 #define TO(i, a, b) int s_=a<b?1:-1,b_=b+s_;for(int i=a;i!=b_;i+=s_)
 #define TO_1(i, a, b) int s_=a<b?1:-1,b_=b;for(int i=a;i!=b_;i+=s_)
 #define SQZ(I, J, A, B) for (int I=int(A),J=int(B)-1;I<J;++I,--J)
 #define SQZ_1(I, J, A, B) for (int I=int(A),J=int(B);I<=J;++I,--J)

 const int MAXN = ;
 int ch[MAXN][], pre[MAXN], key[MAXN];
 int rev[MAXN];
 int size[MAXN];
 int la[MAXN], ra[MAXN], ma[MAXN];//递增的长度
 int ls[MAXN], rs[MAXN], ms[MAXN];//递减的长度
 int lv[MAXN], rv[MAXN];
 bool rt[MAXN];

 void Update_Rev(int r)
 {
     if(!r)return;
     swap(ch[r][],ch[r][]);
     swap(lv[r],rv[r]);
     swap(la[r],rs[r]);
     swap(ls[r],ra[r]);
     swap(ma[r],ms[r]);
     rev[r] ^= ;
 }
 void push_down(int r)
 {
     if(rev[r])
     {
         Update_Rev(ch[r][]);
         Update_Rev(ch[r][]);
         rev[r] = ;
     }
 }
 void push_up(int r)
 {
     size[r] = size[ch[r][]] + size[ch[r][]] + ;
     if(ch[r][])lv[r] = lv[ch[r][]];
     else lv[r] = key[r];
     if(ch[r][])rv[r] = rv[ch[r][]];
     else rv[r] = key[r];

     if(ch[r][] == )
     {
         if(ch[r][] == )
         {
             la[r] = ;
             ls[r] = ;
         }
         else
         {
             if(key[r] < lv[ch[r][]])
                 la[r] = +la[ch[r][]];
             else la[r] = ;
             if(key[r] > lv[ch[r][]])
                 ls[r] =  + ls[ch[r][]];
             else ls[r] = ;
         }
     }
     else
     {
         if(la[ch[r][]] == size[ch[r][]])
         {
             if(rv[ch[r][]] < key[r])
             {
                 if(ch[r][] == )
                     la[r] = la[ch[r][]] + ;
                 else
                 {
                     if(key[r] < lv[ch[r][]])
                         la[r] = la[ch[r][]] +  + la[ch[r][]];
                     else la[r] = la[ch[r][]] + ;
                 }
             }
             else la[r] = la[ch[r][]];
         }
         else la[r] = la[ch[r][]];

         if(ls[ch[r][]] == size[ch[r][]])
         {
             if(rv[ch[r][]] > key[r])
             {
                 if(ch[r][] == )
                     ls[r] = ls[ch[r][]] + ;
                 else
                 {
                     if(key[r] > lv[ch[r][]])
                         ls[r] = ls[ch[r][]] +  + ls[ch[r][]];
                     else ls[r] = ls[ch[r][]] + ;
                 }
             }
             else ls[r] = ls[ch[r][]];
         }
         else ls[r] = ls[ch[r][]];

     }

     if(ch[r][] == )
     {
         if(ch[r][] == )
         {
             ra[r] = ;
             rs[r] = ;
         }
         else
         {
             if(key[r] > rv[ch[r][]])
                 ra[r] = ra[ch[r][]] + ;
             else ra[r] = ;
             if(key[r] < rv[ch[r][]])
                 rs[r] = rs[ch[r][]] + ;
             else rs[r] = ;
         }
     }
     else
     {
         if(ra[ch[r][]] == size[ch[r][]])
         {
             if(key[r] < lv[ch[r][]])
             {
                 if(ch[r][] == )
                     ra[r] = ra[ch[r][]] + ;
                 else
                 {
                     if(key[r] > rv[ch[r][]])
                         ra[r] = ra[ch[r][]] +  + ra[ch[r][]];
                     else ra[r] = ra[ch[r][]] + ;
                 }
             }
             else ra[r] = ra[ch[r][]];
         }
         else ra[r] = ra[ch[r][]];

         if(rs[ch[r][]] == size[ch[r][]])
         {
             if(key[r] > lv[ch[r][]])
             {
                 if(ch[r][] == )
                     rs[r] = rs[ch[r][]] + ;
                 else
                 {
                     if(key[r] < rv[ch[r][]])
                         rs[r] = rs[ch[r][]] +  + rs[ch[r][]];
                     else rs[r] = rs[ch[r][]] + ;
                 }
             }
             else rs[r] = rs[ch[r][]];
         }
         else rs[r] = rs[ch[r][]];

     }

     ma[r] = max(ma[ch[r][]],ma[ch[r][]]);
     ms[r] = max(ms[ch[r][]],ms[ch[r][]]);
     int tmp = ;
     if(ch[r][] && key[r] > rv[ch[r][]])
         tmp += ra[ch[r][]];
     if(ch[r][] && key[r] < lv[ch[r][]])
         tmp += la[ch[r][]];
     ma[r] = max(ma[r],tmp);
     tmp= ;
     if(ch[r][] && key[r] < rv[ch[r][]])
         tmp += rs[ch[r][]];
     if(ch[r][] && key[r] > lv[ch[r][]])
         tmp += ls[ch[r][]];
     ms[r] = max(ms[r],tmp);

 }
 void Rotate(int x)
 {
     int y = pre[x], kind = ch[y][]==x;
     ch[y][kind] = ch[x][!kind];
     pre[ch[y][kind]] = y;
     pre[x] = pre[y];
     pre[y] = x;
     ch[x][!kind] = y;
     if(rt[y])
         rt[y] = false, rt[x] = true;
     else
         ch[pre[x]][ch[pre[x]][]==y] = x;
     push_up(y);
 }
 void P(int r)
 {
     if(!rt[r])P(pre[r]);
     push_down(r);
 }
 void Splay(int r)
 {
     P(r);
     while( !rt[r] )
     {
         int f = pre[r], ff = pre[f];
         if(rt[f])
             Rotate(r);
         else if( (ch[ff][]==f) == (ch[f][]==r) )
             Rotate(f), Rotate(r);
         else
             Rotate(r), Rotate(r);
     }
     push_up(r);
 }
 int Access(int x)
 {
     int y = ;
     for( ; x ; x = pre[y=x])
     {
         Splay(x);
         rt[ch[x][]] = true, rt[ch[x][]=y] = false;
         push_up(x);
     }
     return y;
 }
 int mroot(int r)
 {
     Access(r);
     Splay(r);
     Update_Rev(r);
 }

 int main()
 {
     //freopen("in.txt","r",stdin);
     //freopen("out.txt","w",stdout);
     int T;
     int n;
     int Q;
     int u,v;
     scanf("%d",&T);
     int iCase = ;
     while(T--)
     {
         iCase++;
         scanf("%d",&n);
         for(int i = ;i <= n;i++)
         {
             pre[i] = ;
             ch[i][] = ch[i][] = ;
             rev[i] = ;
             rt[i] = true;
             la[i] = ra[i] = ma[i] = ;
             ls[i] = rs[i] = ms[i] = ;
             size[i] = ;
         }
         pre[] = ;
         ch[][] = ch[][] = ;
         rev[] = ;
         rt[] = true;
         la[] = ra[] = ma[] = ;
         ls[] = rs[] = ms[] = ;
         size[] = ;

         for(int i = ;i <= n;i++)
         {
             scanf("%d",&key[i]);
             lv[i] = rv[i] = key[i];
         }
         for(int i = ;i <= n;i++)
             scanf("%d",&pre[i]);

         printf("Case #%d:\n",iCase);
         scanf("%d",&Q);
         while(Q--)
         {
             scanf("%d%d",&u,&v);
             mroot(u);
             Access(v);
             Splay(v);
             printf("%d\n",ma[v]);
         }
         if(T > )printf("\n");

     }
     return ;
 }