教主泡嫦娥[有趣的dp状态设计]

//非常有可能被卡常，且有可能卡WA
//期望得分：100 
//实际得分：80-100 
#include<ctime>
#include<cmath>
#include<cstdio>
#include<cstdlib>
#include<iostream>
#define pf(x) ((ll)(x)*(ll)(x))
#define OPT __attribute__((optimize("O2")))
using namespace std;
typedef long long ll;
const int N=10005;
ll f[N][2],ans[N];
int n,m,a[N<<1],b[N],tp[30];
OPT inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
    while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
    return x*f;
}
OPT inline ll DP(int start){
    if(ans[start]) return ans[start];
    for(int cnt=0,i=start;i<=start+n;i++) b[++cnt]=a[i];
    f[1][0]=f[1][1]=0;
    for(int i=2;i<=n+1;i++){
        if(b[i]>b[i-1]){
            f[i][1]=min(f[i-1][0]+m+b[i]-b[i-1],f[i-1][1]+b[i]-b[i-1]);
            f[i][0]=min(f[i-1][1]+m+pf(b[i]-b[i-1]),f[i-1][0]+pf(b[i]-b[i-1]));
        }
        else{
            f[i][0]=min(f[i-1][1]+m+b[i-1]-b[i],f[i-1][0]+b[i-1]-b[i]);
            f[i][1]=min(f[i-1][0]+m+pf(b[i]-b[i-1]),f[i-1][1]+pf(b[i]-b[i-1]));
        }
    }
    return ans[start]=min(f[n+1][1],f[n+1][0]);
}
OPT int main(){
    srand(time(0));
    n=read();m=read();
    for(int i=1;i<=n;i++) a[i+n]=a[i]=read();
    for(int i=1;i<=18;i++) tp[i]=rand()%n+1;
    for(double T=n;T>=10;T*=0.5){
        for(int i=1,now;i<=18;i++){
            for(int j=1;j<=21;j++){
                now=tp[i]+sin((double)(rand()%10000)/10000)*T;
                if(now<=0||now>n) continue;
                if(DP(now)>=DP(tp[i])) continue;
                tp[i]=now;
            }
        }
    }
    ll Ans=0x7fffffffffffffffLL;
    for(int i=1;i<=18;i++) Ans=min(Ans,ans[tp[i]]);
    cout<<Ans;
    return 0;
}

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#define pf(x) (1LL*(x)*(x))
using namespace std;
typedef long long ll;
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
    while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
    return x*f;
}
const int N=10005;
int n,m,a[N<<1];
ll f[N][2][2],Ans;
void DP(){
    for(int i=1;i<=n;i++){
        for(int j=0;j<2;j++){
            if((a[i]<a[i-1])^j){
                f[i][j][0]=f[i-1][j][0]+abs(a[i]-a[i-1]);
                f[i][j][1]=min(f[i-1][j][1],
                           min(f[i-1][j^1][0],f[i-1][j^1][1])+m)+abs(a[i]-a[i-1]);
            }
            else{
                f[i][j][0]=f[i-1][j][0]+pf(a[i]-a[i-1]);
                f[i][j][1]=min(f[i-1][j][1],
                           min(f[i-1][j^1][0],f[i-1][j^1][1])+m)+pf(a[i]-a[i-1]);
            }
        }
    }
}
int main(){
    n=read();m=read();
    for(int i=0;i<n;i++) a[i]=read();a[n]=a[0];
    //情况1、2 
    memset(f,0,sizeof f);memset(f[0],0x3f,sizeof f[0]);
    f[0][0][0]=f[0][1][0]=0;;
    DP();
    Ans=min(min(f[n][0][0],f[n][0][1]),min(f[n][1][0],f[n][1][1]));
    //情况3
    memset(f,0,sizeof f);memset(f[0],0x3f,sizeof f[0]);
    f[0][0][0]=0;
    DP();Ans=min(Ans,f[n][0][1]-m);
    //情况3
    memset(f,0,sizeof f);memset(f[0],0x3f,sizeof f[0]);
    f[0][1][0]=0;
    DP();Ans=min(Ans,f[n][1][1]-m);
    
    cout<<Ans;
    return 0;
}