Luogu P3928 SAC E#1 - 一道简单题 Sequence2

Posted 2020-10-09 ONION_CYC

【题目】洛谷10月月赛R1 提高组

【算法】递推DP+树状数组

【题解】列出DP递推方程，然后用树状数组维护前后缀和。

#include<cstdio>
#include<cstring>
#include<cctype>
#include<cmath>
#include<algorithm>
#define lowbit(x) (x&-x)
#define ll long long
using namespace std;
int read(){
    char c;int s=0,t=1;
    while(!isdigit(c=getchar()))if(c==‘-‘)t=-1;
    do{s=s*10+c-‘0‘;}while(isdigit(c=getchar()));
    return s*t;
}
int min(int a,int b){return a<b?a:b;}
int max(int a,int b){return a<b?b:a;}
int abs(int x){return x>0?x:-x;}
//void insert(int u,int v){tot++;e[tot].v=v;e[tot].from=first[u];first[u]=tot;}
/*------------------------------------------------------------*/
const int inf=0x3f3f3f3f,maxn=300010;

int n,a[maxn][3],f[maxn][4],ans,tot,c[5][maxn],b[maxn];

void modify(int d,int x,int k){if(d&1)x=tot-x+1;for(int i=x;i<=tot;i+=lowbit(i))c[d][i]=max(c[d][i],k);}
int ask(int d,int x){if(d&1)x=tot-x+1;int as=0;for(int i=x;i>=1;i-=lowbit(i))as=max(as,c[d][i]);return as;}
int main(){
    n=read();tot=0;
    for(int i=1;i<=n;i++)a[i][0]=read(),f[i][0]=1,b[++tot]=a[i][0];
    for(int i=1;i<=n;i++)a[i][1]=read(),f[i][1]=1,b[++tot]=a[i][1];
    for(int i=1;i<=n;i++)a[i][2]=read(),f[i][2]=f[i][3]=1,b[++tot]=a[i][2];
    sort(b+1,b+tot+1);
    tot=unique(b+1,b+tot+1)-b-1;
    for(int i=1;i<=n;i++)a[i][0]=lower_bound(b+1,b+tot+1,a[i][0])-b;
    for(int i=1;i<=n;i++)a[i][1]=lower_bound(b+1,b+tot+1,a[i][1])-b;
    for(int i=1;i<=n;i++)a[i][2]=lower_bound(b+1,b+tot+1,a[i][2])-b;
    modify(0,a[1][0],1);modify(0,a[1][1],1);modify(0,a[1][2],1);
    modify(1,a[1][0],1);modify(1,a[1][1],1);modify(1,a[1][2],1);
    modify(2,a[1][0],1);modify(2,a[1][1],1);modify(2,a[1][2],1);
    modify(3,a[1][0],1);modify(3,a[1][1],1);modify(3,a[1][2],1);
    for(int i=2;i<=n;i++){
        f[i][0]=max(f[i][0],ask(0,a[i][0])+1);ans=max(ans,f[i][0]);
        f[i][1]=max(f[i][1],ask(1,a[i][1])+1);ans=max(ans,f[i][1]);
        f[i][2]=max(f[i][2],ask(2,a[i][2])+1);ans=max(ans,f[i][2]);
        f[i][3]=max(f[i][3],ask(3,a[i][2])+1);ans=max(ans,f[i][3]);
        modify(0,a[i][0],f[i][0]);modify(0,a[i][1],f[i][1]);modify(0,a[i][2],max(f[i][2],f[i][3]));
         modify(1,a[i][0],f[i][0]);modify(1,a[i][1],f[i][1]);modify(1,a[i][2],max(f[i][2],f[i][3]));
        modify(2,a[i][0],f[i][0]);modify(2,a[i][1],f[i][1]);modify(2,a[i][2],f[i][2]);
        modify(3,a[i][0],f[i][0]);modify(3,a[i][1],f[i][1]);modify(3,a[i][2],f[i][3]);//
    }
    printf("%d",ans);
    return 0;
}

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