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
1 #include<cstdio> 2 #include<cstring> 3 #include<algorithm> 4 #include<vector> 5 #include<queue> 6 #include<cmath> 7 #define inf 0x3f3f3f3f 8 #define LL long long int 9 using namespace std; 10 const int maxn=50050; 11 12 inline LL rd(){ 13 LL x=0;char c=getchar();int neg=1; 14 while(c<'0'||c>'9'){if(c=='-') neg=-1;c=getchar();} 15 while(c>='0'&&c<='9') x=x*10+c-'0',c=getchar(); 16 return x*neg; 17 } 18 19 int N; 20 LL co[maxn],sm[maxn],f[maxn],L; 21 int q[maxn],h,t; 22 23 inline LL pw2(LL x){return x*x;} 24 25 inline bool judge1(int j1,int j2,int i){ 26 return f[j1]+pw2(j1+sm[j1])-f[j2]-pw2(j2+sm[j2])<(2*i+2*sm[i]-2*L-2)*(j1+sm[j1]-j2-sm[j2]); 27 } 28 inline bool judge2(int j1,int j2,int j3){ 29 return (f[j1]+pw2(j1+sm[j1])-f[j2]-pw2(j2+sm[j2]))*(j2+sm[j2]-j3-sm[j3])< 30 (f[j2]+pw2(j2+sm[j2])-f[j3]-pw2(j3+sm[j3]))*(j1+sm[j1]-j2-sm[j2]); 31 } 32 33 int main(){ 34 int i,j,k; 35 N=rd();L=rd(); 36 for(i=1;i<=N;i++)co[i]=rd(),sm[i]=sm[i-1]+co[i]; 37 h=t=1;q[1]=0; 38 for(i=1;i<=N;i++){ 39 while(h<t&&!judge1(q[h],q[h+1],i)) h++; 40 f[i]=f[q[h]]+pw2(i-q[h]-1+sm[i]-sm[q[h]]-L); 41 while(h<t&&!judge2(q[t-1],q[t],i)) t--; 42 q[++t]=i; 43 }printf("%lld\n",f[N]); 44 45 return 0; 46 }
