[bzoj1597]: [Usaco2008 Mar]土地购买

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斜率优化dp

从今天开始练习dp,各种dp

斜率方程:slope(a,b)=(f(a)-f(b))/(y(b+1)-y(a+1))

代码:

 1 #include<bits/stdc++.h>
 2 #define ll long long
 3 using namespace std;
 4 inline int read(){
 5     int x=0;char ch=' ';int f=1;
 6     while(ch!='-'&&(ch<'0'||ch>'9'))ch=getchar();
 7     if(ch=='-'){
 8         f=-1;ch=getchar();
 9     }
10     while(ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar();
11     return x*f;
12 }
13 int n,tot;
14 ll x[50001],y[50001],f[50001];
15 int q[50001],l,r;
16 inline double slope(int a,int b){
17     return (double)(f[a]-f[b])/(double)(y[b+1]-y[a+1]);
18 }
19 struct node{
20     int x,y;
21     inline bool operator < (const node& b) const {
22         return (x==b.x)?y<b.y:x<b.x;
23     }
24 }a[50001];
25 int main(){
26     n=read();
27     for(int i=1;i<=n;i++){
28         a[i].x=read();a[i].y=read();
29     }
30     sort(a+1,a+n+1);
31     for(int i=1;i<=n;i++){
32         while(tot&&y[tot]<=a[i].y)tot--;
33         x[++tot]=a[i].x;y[tot]=a[i].y;
34     }
35     l=0,r=0;
36     for(int i=1;i<=tot;i++){
37         while(l<r&&slope(q[l],q[l+1])<x[i])l++;
38         f[i]=f[q[l]]+y[q[l]+1]*x[i];
39         while(l<r&&slope(q[r],i)<slope(q[r-1],q[r]))r--;
40         q[++r]=i;
41     }
42     printf("%lld",f[tot]);
43     return 0;
44 }

 

posted @ 2017-09-25 15:40  玫葵之蝶  阅读(143)  评论(0编辑  收藏  举报