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f[i][j]表示第i天有j只股票最多赚多少钱 \\

  1. 直接买 f[i][j] = -ap[i] \times j
  2. 不买不卖

    f[i][j] =f[i-1][j]

  3. 买股

    f[i][j] = f[i-w-1][k] - ap[i] \times (j-k) (j-as[i] \le k \le j)

  4. 卖股

    f[i][j] = f[i-w-1][k] + bp[i] \times (k-j) (j \le k \le j + bs[i])

但是这样还是O(n^3)的复杂度,得想办法降到O(n^2)

看一下f[i][j] = f[i-w-1][k] - ap[i] \times (j-k) (j-as[i] \le k \le j)

可以化为f[i][j] = (f[i-w-1][k] + ap[i] \times k) - ap[i] \times j (j-as[i] \le k \le j)

于是就可以单调队列了 OωO

    #include<bits/stdc++.h>
    namespace ZDY{
        #pragma GCC optimize(3)
        #define il __inline__ __attribute__ ((always_inline))
        #define rg register
        #define ll long long
        #define ull unsigned long long
        #define db double
        #define sht short
        #define MB template <class T>il
        #define Fur(i,x,y) for(int i=x;i<=y;i++)
        #define Fdr(i,x,y) for(int i=x;i>=y;i--)
        #define fl(i,x) for(int i=head[x],to;to=e[i].to,i;i=e[i].nxt)
        #define clr(x,y) memset(x,y,sizeof(x))
        #define cpy(x,y) memcpy(x,y,sizeof(x))
        #define fin(s) freopen(s".in","r",stdin)
        #define fout(s) freopen(s".out","w",stdout)
        #define fcin ios::sync_with_stdio(false)
        #define l2(n) (int(log2(n)))
        #define inf 0x3f3f3f3f
        MB T ABS(T x){return x>0?x:-x;}
        MB T MAX(T x,T y){return x>y?x:y;}
        MB T MIN(T x,T y){return x<y?x:y;}
        MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
        MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
    }using namespace ZDY;using namespace std;
    namespace IO{const char* ln="\n";const int str=1<<20;struct IN{char buf[str],*s,*t;bool _;IN():s(buf),t(buf),_(0){}il char gc(){return s==t&&((t=(s=buf)+fread(buf,1,str,stdin))==s)?EOF:(*s++);}IN&operator>>(char&ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)_=1;else ch=c;return *this;}IN& operator>>(char* ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)_=1;return *this;}IN& operator>>(string& ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)_=1;return *this;}template<typename T>IN&operator>>(T&x){if(_)return *this;char c=gc();bool ff=0;while(c!=EOF&&(c<'0'||c>'9'))ff^=(c=='-'),c=gc();if(c==EOF){_=1;return *this;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=(x<<3)+(x<<1)+c-48,c=gc();if(c==EOF)_=1;if(ff)x=-x;return *this;}}in;struct OUT{char buf[str],*s,*t;OUT():s(buf),t(buf+str){}~OUT(){fwrite(buf,1,s-buf,stdout);}void pt(char c){(s==t)?(fwrite(s=buf,1,str,stdout),*s++=c):(*s++=c);}OUT&operator<<(const char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(string s){for(int i=0;s[i];i++)pt(s[i]);return *this;}template<typename T>OUT&operator<<(T x){if(!x)return pt('0'),*this;if(x<0)pt('-'),x=-x;char a[30],t=0;while(x)a[t++]=x%10,x/=10;while(t--)pt(a[t]+'0');return *this;}}out;}using namespace IO;
    #define N 2001
    int n,p,w,ap,bp,as,bs,f[N][N],q[N],ans=0;
    int main(){
        in>>n>>p>>w;
        clr(f,128);
        Fur(i,1,n){
            in>>ap>>bp>>as>>bs;
            Fur(j,0,as)f[i][j]=-ap*j;
            Fur(j,0,p)f[i][j]=MAX(f[i][j],f[i-1][j]);
            if(i<=w)continue;
            int l=1,r=0;
            Fur(j,0,p){
                while(l<=r&&q[l]<j-as)l++;
                while(l<=r&&f[i-w-1][q[r]]+q[r]*ap<=f[i-w-1][j]+j*ap)r--;
                q[++r]=j;
                if(l<=r)f[i][j]=MAX(f[i][j],f[i-w-1][q[l]]+q[l]*ap-j*ap);
            }
            l=1,r=0;
            Fdr(j,p,0){
                while(l<=r&&q[l]>j+bs)l++;
                while(l<=r&&f[i-w-1][q[r]]+q[r]*bp<=f[i-w-1][j]+j*bp)r--;
                q[++r]=j;
                if(l<=r)f[i][j]=MAX(f[i][j],f[i-w-1][q[l]]+q[l]*bp-j*bp);
            }
        }
        Fur(i,0,p)ans=MAX(ans,f[n][i]);
        out<<ans<<ln;
    }
LG 2569 [SCOI2010]股票交易
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