[BZOJ 1010][HNOI 2008] 玩具装箱toy

比较基础的斜率优化DP详见以下2篇博客

http://www.cnblogs.com/proverbs/archive/2012/10/06/2713109.html

http://blog.163.com/myq_952/blog/static/863906320112711750378/

主要总结斜率优化时的步骤

　　1.证明较优决策点对后续状态影响的持续性

　　2.求斜率方程:一般化为左边是J，K，右边是I的形式

　　3.规定队列的维护规则

　　4.看决策是否又单调性，没有的话有应该怎样维护

本题的代码

 1 #include<cstdio>
 2 #define N 50100
 3 #define LL long long
 4
 5 int n;
 6 int q[N],h,t;
 7 LL f[N],c[N],sum[N],g[N],l;
 8
 9 LL sqr(LL a){return a*a;}
10 LL X(int a,int b){return f[a]-f[b]+sqr(g[a]+l)-sqr(g[b]+l);}
11 LL Y(int a,int b){return 2*(g[a]-g[b]);}
12
13 int main()
14 {
15     scanf("%d%lld",&n,&l);
16     l++;
17     for (int i=1;i<=n;i++) scanf("%lld",c+i);
18     for (int i=1;i<=n;i++) sum[i]=sum[i-1]+c[i];
19     for (int i=1;i<=n;i++) g[i]=sum[i]+(LL)i;
20     for (int i=1;i<=n;i++)
21     {
22         while (h<t&&X(q[h],q[h+1])>=Y(q[h],q[h+1])*g[i]) h++;
23         f[i]=f[q[h]]+sqr(g[i]-g[q[h]]-l);
24         while (h<t&&X(q[t-1],q[t])*Y(q[t],i)>=X(q[t],i)*Y(q[t-1],q[t])) t--;
25         q[++t]=i;
26     }
27     printf("%lld\n",f[n]);
28     return 0;
29 }