bzoj3437 小P的牧场

题目

斜率优化第一题。。。

其实熟悉之后，发现其实并没有什么难度，就是数学推公式就好了

朴素dp

    for(register LL i=1;i<=n;i++)scanf("%lld",&a[i]);    for(register LL i=1;i<=n;i++)scanf("%lld",&b[i]);    for(register LL i=1;i<=n;i++)A[i]=A[i-1]+b[i];    for(register LL i=1;i<=n;i++)B[i]=B[i-1]+b[i]*i;    memset(f,63,sizeof(f));    f[1]=a[1];    for(register LL i=2;i<=n;i++)        for(register LL j=1;j<i;j++)            f[i]=min(f[i],f[j]+i*(A[i]-A[j])-(B[i]-B[j])+a[i]);    cout<<f[n];

之后推一推斜率
((f[i]-f[j])+(B[i]-B[j]))/(double)(A[i]-A[j])

套个模板就好了。

顺便粘个模板吧。。

#include<bits/stdc++.h>#define N 1000000#define LL long longusing namespace std;LL f[N+1],A[N+1],B[N+1];LL a[N+1],b[N+1];LL n;LL q[N+1],l,r;double slope(LL i,LL j){    return (double)((f[i]-f[j])+(B[i]-B[j]))/(double)(A[i]-A[j]);}int main(){    scanf("%lld",&n);    for(register LL i=1;i<=n;i++)scanf("%lld",&a[i]);    for(register LL i=1;i<=n;i++)scanf("%lld",&b[i]);    for(register LL i=1;i<=n;i++)A[i]=A[i-1]+b[i];    for(register LL i=1;i<=n;i++)B[i]=B[i-1]+b[i]*i;/*    memset(f,63,sizeof(f));    f[1]=a[1];    for(register LL i=2;i<=n;i++)        for(register LL j=1;j<i;j++)            f[i]=min(f[i],f[j]+i*(A[i]-A[j])-(B[i]-B[j])+a[i]);    cout<<f[n];*/    l=1,r=0,q[++r]=0;    for(register LL i=1;i<=n;i++)    {        while(l<r&&slope(q[l+1],q[l])<=i)l++;        LL tmp=q[l];        f[i]=f[tmp]+i*(A[i]-A[tmp])-(B[i]-B[tmp])+a[i];        while(l<r&&slope(i,q[r])<slope(q[r],q[r-1]))r--;        q[++r]=i;    }    cout<<f[n];    return 0;}