12.5
孔子：因为我说过的话都会被大家当做道理，所以我是说的道理。
今天学习了单调队列优化 DP。
股票交易
给定 \(T\) 天内的股票情况，求收益最大。
此题朴素 DP 复杂度似乎是 \(O(n^4)\)，可以优化成 \(O(n^3)\)，但这有什么用，显然需要单调队列优化。
动态转移方程
（不买不卖）：\(f[i][j]=f[i−1][j]\)
（买入）：$ f[i][j]=max ∑^{p<i}_{p=1}∑ ^{q<j} _ {q=0}f[p][q]−(j−q)×AP[i]$
（卖出）： $f[i][j]=max ∑ ^{p<i} _{p=1}∑ ^{q>j} _{q=0}f[p][q]+(q−j)×BP[i] $
可以用单调队列维护两次，分别维护 \(AP[i]\) 和 \(BP[i]\)。
部分代码
for(int i=1;i<=n;++i)
{
for(int j=0;j<=maxp;++j)
dp[i][j]=max(dp[i-1][j],dp[i][j]);
if(i<=w+1) continue;
int pre=i-w-1;
head=tail=0;
for(int j=0;j<=maxp;++j)
{
int mon=dp[pre][j]+j*a[i];
while(head<tail && q[tail-1].f<mon)
tail--;
q[tail].f=mon;q[tail++].noww=j;
while(head<tail && q[head].noww+as[i]<j)
head++;
dp[i][j]=max(dp[i][j],q[head].f-j*a[i]);
}
head=tail=0;
for(int j=maxp;j>=0;--j)
{
int mon=dp[pre][j]+j*b[i];
while(head<tail && q[tail-1].f<mon)
tail--;
q[tail].f=mon;q[tail++].noww=j;
while(head<tail && q[head].noww-bs[i]>j)
head++;
dp[i][j]=max(dp[i][j],q[head].f-j*b[i]);
}
}
瑰丽华尔兹
好（sb）题。
还是单调队列优化，但是要找东南西北四个方向的最大值并且维护 \(ans\)。
code
#include <bits/stdc++.h>
using namespace std;
const int N=1e6;
const int fx[5]={0,-1,1,0,0},fy[5]={0,0,0,-1,1};
#define inf 0x7ffffff
char ch[2001][2001];
int dp[210][210];
int n,m,x,y,k,ans;
struct node
{
int s,t,d;
}sh[N];
struct Node
{
int x,y,val;
}q[N];
int head=1,tail;
inline int get_dis(int ax,int ay,int bx,int by)
{
return abs(ax-bx)+abs(ay-by);
}
void find_ans(int x,int y,int opt,int len)
{
head=1,tail=0;
while(x>=1 && x<=n && y>=1 && y<=m)
{
if(ch[x][y]=='x')
head=1,tail=0;
else
{
while(head<=tail && q[tail].val+get_dis(x,y,q[tail].x,q[tail].y)<dp[x][y])
tail--;
q[++tail]=((Node){x,y,dp[x][y]});
while(head<=tail && max(abs(x-q[head].x),abs(y-q[head].y))>len)
head++;
dp[x][y]=max(dp[x][y],q[head].val+get_dis(x,y,q[head].x,q[head].y));
ans=max(ans,dp[x][y]);
}
x+=fx[opt];
y+=fy[opt];
}
}
signed main()
{
cin>>n>>m>>x>>y>>k;
for(int i=1;i<=n;++i)
scanf("%s",ch[i]+1);
memset(dp,-0x3f,sizeof(dp));
dp[x][y]=0;
for(register int i=1;i<=k;++i)
{
cin>>sh[i].s>>sh[i].t>>sh[i].d;
int len=sh[i].t-sh[i].s+1;
if(sh[i].d==1)
for(register int j=1;j<=m;++j)
find_ans(n,j,sh[i].d,len);
else if(sh[i].d==2)
for(register int j=1;j<=m;++j)
find_ans(1,j,sh[i].d,len);
else if(sh[i].d==3)
for(register int j=1;j<=n;++j)
find_ans(j,m,sh[i].d,len);
else if(sh[i].d==4)
for(register int j=1;j<=n;++j)
find_ans(j,1,sh[i].d,len);
}
cout<<ans;
}
今天旁边两位拍代码，拍了好几个小时还没拍出来呢，加油。
推歌：Lose Control -Hedley
Can I make a little toast
Can we get a little close
Can I get an amen
Can I get a hell yeah
Can I get a holy ghost
Somebody give me a beat
Let me see you on your feet
Somebody save your man
I don't give a god damn I wanna be a freak
Catch me if you can
I don't think you understand where we're going
Where we're going
When you feel it and you know
When this sh*t's about to blow
And it hits you
Ooh it hits you like
In my body
In my bones
Drop the beat and free my soul
When I hear that rock and roll
Oh my god I lose control
La la la la oh oh oh
La la la la oh oh oh
I had to let it go
Oh my god I lose control
In my body
In my bones
Drop the beat and free my soul
When I hear that rock and roll
Oh my god I lose control
La la la la oh oh oh
La la la la oh oh oh
I had to let it go
Oh my god I lose control
Like a shot to the face
Now you got a little taste
Baby never give a fuck
Get up
Stand up
Shake your buns to the bass
When you break it down
They're gonna love the sound
Everybody just stop
And bring it back around like
Catch me if you can
I don't think you understand where we're going
Where we're going
When you feel it and you know
When this sh*t's about to blow
And it hits you
Ooh it hits you like
In my body
In my bones
Drop the beat and free my soul
When I hear that rock and roll
Oh my god I lose control
La la la la oh oh oh
La la la la oh oh oh
I had to let it go
Oh my god I lose control
In my body
In my bones
Drop the beat and free my soul
When I hear that rock and roll
Oh my god I lose control
La la la la oh oh oh
La la la la oh oh oh
I had to let it go
Oh my god I lose control
Oh my god I lose control
Oh my god I lose control
Catch me if you can
I don't think you understand where we're going
When you feel it and you know
When this sh*t's about to blow
When it hits you
Hits you like
In my body
In my bones
Drop the beat and free my soul
When I hear that rock and roll
Oh my god I lose control
La la la la oh oh oh
La la la la oh oh oh
I had to let it go
Oh my god I lose control
In my body
In my bones
Drop the beat and free my soul
When I hear that rock and roll
Oh my god I lose control
La la la la oh oh oh
La la la la oh oh oh
I had to let it go
Oh my god I lose control
In my body
In my bones
Drop the beat and free my soul
When I hear that rock and roll
Oh my god I lose control
La la la la oh oh oh
La la la la oh oh oh
I had to let it go
Oh my god I lose control
Oh my god I lose control
Oh my god I lose control
非常好洗脑神曲，但是千万别看BGA。
怎么是2021年发布的，可是我2022年就已经在听了。
哎我草，本来想写数学题的，忘了写了。
喜
