luogu3195/bzoj1010 玩具装箱(斜率优化dp)

推出来式子然后斜率优化水过去就完事了

 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<vector>
 #include<queue>
 #include<cmath>
 #define inf 0x3f3f3f3f
 #define LL long long int
 using namespace std;
 const int maxn=;
 
 inline LL rd(){
     LL x=;char c=getchar();int neg=;
     while(c<''||c>''){if(c=='-') neg=-;c=getchar();}
     while(c>=''&&c<='') x=x*+c-'',c=getchar();
     return x*neg;
 }
 
 int N;
 LL co[maxn],sm[maxn],f[maxn],L;
 int q[maxn],h,t;
 
 inline LL pw2(LL x){return x*x;}
 
 inline bool judge1(int j1,int j2,int i){
     return f[j1]+pw2(j1+sm[j1])-f[j2]-pw2(j2+sm[j2])<(*i+*sm[i]-*L-)*(j1+sm[j1]-j2-sm[j2]);
 }
 inline bool judge2(int j1,int j2,int j3){
     return (f[j1]+pw2(j1+sm[j1])-f[j2]-pw2(j2+sm[j2]))*(j2+sm[j2]-j3-sm[j3])<
            (f[j2]+pw2(j2+sm[j2])-f[j3]-pw2(j3+sm[j3]))*(j1+sm[j1]-j2-sm[j2]);
 }
 
 int main(){
     int i,j,k;
     N=rd();L=rd();
     for(i=;i<=N;i++)co[i]=rd(),sm[i]=sm[i-]+co[i];
     h=t=;q[]=;
     for(i=;i<=N;i++){
         while(h<t&&!judge1(q[h],q[h+],i)) h++;
         f[i]=f[q[h]]+pw2(i-q[h]-+sm[i]-sm[q[h]]-L);
         while(h<t&&!judge2(q[t-],q[t],i)) t--;
         q[++t]=i;
     }printf("%lld\n",f[N]);
 
     return ;
 }