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，
1 #include <cstdio> 2 #include <cstring> 3 #include <iostream> 4 #include <algorithm> 5 #include <cmath> 6 using namespace std; 7 #define PI acos(-1.0) 8 const int maxn=1e5+10; 9 struct cake{ 10 int r,h; 11 double V; 12 cake(){}; 13 cake(int r_,int h_):r(r_),h(h_){V=PI*r*r*h;}; 14 }; 15 struct node{ 16 int l,r; 17 double maxx; 18 int mid(){return (l+r)>>1;} 19 }; 20 node tree[maxn<<2]; 21 void pushup(int rt){ 22 tree[rt].maxx=max(tree[rt<<1].maxx,tree[rt<<1|1].maxx); 23 } 24 void build(int l,int r,int rt){ 25 tree[rt].l=l,tree[rt].r=r; 26 tree[rt].maxx=0; 27 if(l==r) return ; 28 int mid=tree[rt].mid(); 29 build(l,mid,rt<<1); 30 build(mid+1,r,rt<<1|1); 31 } 32 void update(int index,double C,int L,int R,int rt){ 33 if(L==index&&R==index){ 34 tree[rt].maxx=max(tree[rt].maxx,C); 35 return ; 36 } 37 int mid=tree[rt].mid(); 38 if(index<=mid) update(index,C,L,mid,rt<<1); 39 else update(index,C,mid+1,R,rt<<1|1); 40 pushup(rt); 41 } 42 double query(int l,int r,int L,int R,int rt){ 43 if(L>=l&&R<=r) { 44 return tree[rt].maxx; 45 } 46 double maxx=-1.0; 47 int mid=tree[rt].mid(); 48 if(l<=mid) maxx=max(maxx,query(l,r,L,mid,rt<<1)); 49 if(r>mid) maxx=max(maxx,query(l,r,mid+1,R,rt<<1|1)); 50 return maxx; 51 } 52 cake a[maxn]; 53 double v[maxn]; 54 int n; 55 void solve(){ 56 sort(v+1,v+1+n); 57 int size=unique(v+1,v+1+n)-v; 58 double ans=0; 59 build(1,size,1); 60 double tmp; 61 for(int i=1;i<=n;i++){ 62 int pos=lower_bound(v+1,v+size,a[i].V)-v; 63 tmp=0; 64 tmp=query(1,pos-1,1,size,1); 65 if(pos-1==0) tmp=0; 66 tmp+=a[i].V; 67 ans=max(ans,tmp); 68 update(pos,tmp,1,size,1); 69 } 70 printf("%.10f\n",ans); 71 } 72 int main(){ 73 while(scanf("%d",&n)!=EOF){ 74 for(int i=1;i<=n;i++){ 75 int r,h; 76 scanf("%d %d",&r,&h); 77 a[i]=cake(r,h); 78 v[i]=a[i].V; 79 } 80 solve(); 81 } 82 return 0; 83 }
