BZOJ.1010.[HNOI2008]玩具装箱toy(DP 斜率优化/单调队列 决策单调性)
题目链接
斜率优化 不说了 网上很多 这的比较详细->Click Here or Here
//1700kb 60ms
#include<cstdio>
#include<cctype>
//#define gc() getchar()
#define gc() (SS==TT&&(TT=(SS=IN)+fread(IN,1,MAXIN,stdin),SS==TT)?EOF:*SS++)
typedef long long LL;
const int N=5e4+5,MAXIN=1e5;
int n,C,S[N],q[N];
char IN[MAXIN],*SS=IN,*TT=IN;
LL f[N];
inline int read()
{
int now=0,f=1;register char c=gc();
for(;!isdigit(c);c=gc()) if(c=='-') f=-1;
for(;isdigit(c);now=now*10+c-'0',c=gc());
return now*f;
}
inline LL Squ(LL x){
return x*x;
}
inline LL X(int j,int k){
return (S[j]-S[k])<<1;
}
inline LL Y(int j,int k){
return f[j]+Squ(S[j]+C)-(f[k]+Squ(S[k]+C));
}
int main()
{
n=read(),C=read()+1;
for(int i=1;i<=n;++i) S[i]=S[i-1]+read()+1;
// for(int i=1;i<=n;++i) S[i]+=i;
int h=1,t=1; q[1]=0;
for(int i=1;i<=n;++i)
{
while(h<t && Y(q[h+1],q[h])<=S[i]*X(q[h+1],q[h])) ++h;
f[i]=f[q[h]]+Squ(S[i]-S[q[h]]-C);
while(h<t && Y(i,q[t])*X(q[t],q[t-1])<=Y(q[t],q[t-1])*X(i,q[t])) --t;
q[++t]=i;
}
printf("%lld",f[n]);
return 0;
}
由决策单调,单调队列写法:\(\mathcal O(n\log n)\)
//2288kb 140ms
#include <cstdio>
#include <cctype>
#include <algorithm>
//#define gc() getchar()
#define MAXIN 100000
#define gc() (SS==TT&&(TT=(SS=IN)+fread(IN,1,MAXIN,stdin),SS==TT)?EOF:*SS++)
typedef long long LL;
const int N=50005;
int n,L;
LL sum[N],f[N];
char IN[MAXIN],*SS=IN,*TT=IN;
struct Node{
int l,r,pos;//pos是区间[l,r]的最优转移点
}q[N];
inline int read()
{
int now=0;register char c=gc();
for(;!isdigit(c);c=gc());
for(;isdigit(c);now=now*10+c-'0',c=gc());
return now;
}
inline LL Squ(LL x){
return x*x;
}
inline LL Cost(int i,int p){//在i之前,分割p处
return f[p]+Squ((LL)(i-p-1+sum[i]-sum[p]-L));
}
int Find(Node t,int x)
{
int l=t.l, r=t.r, mid;
while(l<=r)
if(mid=l+r>>1, Cost(mid,x)<Cost(mid,t.pos)) r=mid-1;
else l=mid+1;
return l;
}
int main()
{
n=read(), L=read();
for(int i=1; i<=n; ++i) sum[i]=sum[i-1]+read();
int h=1,t=1; q[1]=(Node){0,n,0};
for(int i=1; i<=n; ++i)
{
if(i>q[h].r) ++h;
f[i]=Cost(i,q[h].pos);
if(Cost(n,i)<Cost(n,q[t].pos))//为什么要拿n比??不解。
{
while(h<=t && Cost(q[t].l,i)<Cost(q[t].l,q[t].pos)) --t;//队尾区间的l用i都比pos更优了,而决策点是单调的,所以[l,r]肯定都要不选pos而选i了
if(h>t) q[++t]=(Node){i,n,i};
else
{
int Pos=Find(q[t],i);
q[t].r=Pos-1, q[++t]=(Node){Pos,n,i};
}
}
}
printf("%lld",f[n]);
return 0;
}
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很久以前的奇怪但现在依旧成立的签名
attack is our red sun $$\color{red}{\boxed{\color{red}{attack\ is\ our\ red\ sun}}}$$ ------------------------------------------------------------------------------------------------------------------------
很久以前的奇怪但现在依旧成立的签名
attack is our red sun $$\color{red}{\boxed{\color{red}{attack\ is\ our\ red\ sun}}}$$ ------------------------------------------------------------------------------------------------------------------------