Codeforces 629D Babaei and Birthday Cakes DP+线段树

题目：http://codeforces.com/contest/629/problem/D

题意：有n个蛋糕要叠起来，能叠起来的条件是蛋糕的下标比前面的大并且体积也比前面的大，问能叠成的最大体积

思路：DP[i]表示拿到第i个蛋糕时最多能叠成的体积，转移就是这样DP[i]=max(DP[1...i])+V[i];如果直接做的话复杂度是n^2的，用线段树维护比它小的蛋糕的能叠的最大体积，事先离散化，

 #include <cstdio>
 #include <cstring>
 #include <iostream>
 #include <algorithm>
 #include <cmath>
 using namespace std;
 #define PI acos(-1.0)
 const int maxn=1e5+;
 struct cake{
     int r,h;
     double V;
     cake(){};
     cake(int r_,int h_):r(r_),h(h_){V=PI*r*r*h;};
 };
 struct node{
     int l,r;
     double maxx;
     int mid(){return (l+r)>>;}
 };
 node tree[maxn<<];
 void pushup(int rt){
     tree[rt].maxx=max(tree[rt<<].maxx,tree[rt<<|].maxx);
 }
 void build(int l,int r,int rt){
     tree[rt].l=l,tree[rt].r=r;
     tree[rt].maxx=;
     if(l==r) return ;
     int mid=tree[rt].mid();
     build(l,mid,rt<<);
     build(mid+,r,rt<<|);
 }
 void update(int index,double C,int L,int R,int rt){
     if(L==index&&R==index){
         tree[rt].maxx=max(tree[rt].maxx,C);
         return ;
     }
     int mid=tree[rt].mid();
     if(index<=mid) update(index,C,L,mid,rt<<);
     else update(index,C,mid+,R,rt<<|);
     pushup(rt);
 }
 double query(int l,int r,int L,int R,int rt){
     if(L>=l&&R<=r) {
         return tree[rt].maxx;
     }
     double maxx=-1.0;
     int mid=tree[rt].mid();
     if(l<=mid) maxx=max(maxx,query(l,r,L,mid,rt<<));
     if(r>mid) maxx=max(maxx,query(l,r,mid+,R,rt<<|));
     return maxx;
 }
 cake a[maxn];
 double v[maxn];
 int n;
 void solve(){
     sort(v+,v++n);
     int size=unique(v+,v++n)-v;
     double ans=;
     build(,size,);
     double tmp;
     for(int i=;i<=n;i++){
         int pos=lower_bound(v+,v+size,a[i].V)-v;
         tmp=;
         tmp=query(,pos-,,size,);
         if(pos-==) tmp=;
         tmp+=a[i].V;
         ans=max(ans,tmp);
         update(pos,tmp,,size,);
     }
     printf("%.10f\n",ans);
 }
 int main(){
     while(scanf("%d",&n)!=EOF){
         for(int i=;i<=n;i++){
             int r,h;
             scanf("%d %d",&r,&h);
             a[i]=cake(r,h);
             v[i]=a[i].V;
         }
         solve();
     }
     return ;
 }