数位DPCF55D Beautiful numbers

Posted zhenglw

tags:

篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了数位DPCF55D Beautiful numbers相关的知识,希望对你有一定的参考价值。

$dp[x][p][pp]$表示第x位,当前已有数字mod 2520(1~9数字的lcm)为p,当前各位数字的lcm为pp

观察到数组太大,考虑压缩,第三维lcm最多只有9个数字,打表发现最多只有48个状态,压掉第三维即可

打表用一个状压然后set维护(广搜也可以)即可

有一个坑点:题目里似乎没有说关于0的事情(即数字里出现0)但是有人在CF上打这个比赛的时候问了出题人,碰到0不要管即可!!!

打表代码:

 1 set<int>s;
 2 inline void Make(int x){
 3     int ans=1;
 4     for(int i=0;i<9;i++){
 5         if(((1<<i)&x)) ans=lcm(ans,i+1);
 6     }s.insert(ans);
 7 }
 8 inline void States_Maker(){
 9     int ans=1;
10     for(int i=0;i<(1<<9);i++)Make(i);
11     while(!s.empty()){
12         cout<<*s.begin()<<",";
13         s.erase(s.begin());
14     }    
15 }

解题代码:

 1 #include<bits/stdc++.h>
 2 #define int long long
 3 #define writeln(x)  write(x),puts("")
 4 #define writep(x)   write(x),putchar(‘ ‘)
 5 using namespace std;
 6 inline int read(){
 7     int ans=0,f=1;char chr=getchar();
 8     while(!isdigit(chr)){if(chr==-) f=-1;chr=getchar();}
 9     while(isdigit(chr)){ans=(ans<<3)+(ans<<1)+chr-48;chr=getchar();}
10     return ans*f;
11 }void write(int x){
12     if(x<0) putchar(-),x=-x;
13     if(x>9) write(x/10);
14     putchar(x%10+0);
15 }const int M = 20,State = 50;
16 int f[M][2521][State],T,n,a[M],l,r,Pos[2521],S[State]={0,1,2,3,4,5,6,7,8,9,10,12,14,15,18,20,21,24,28,30,35,36,40,42,45,56,60,63,70,72,84,90,105,120,126,140,168,180,210,252,280,315,360,420,504,630,840,1260,2520};
17 inline int gcd(int x,int y){return __gcd(x,y);}
18 inline int lcm(int x,int y){if(x==0)return y;if(y==0)return x;return x*y/gcd(x,y);}
19 int dfs(int x,int p,int pp,bool lim){
20     if(!x)return (p%pp==0)?(1):(0);
21     if(!lim&&p!=-1&&pp!=-1&&f[x][p][Pos[pp]]!=-1)return f[x][p][Pos[pp]];
22     int ans=0,up=lim?a[x]:9;
23     for(int i=0;i<=up;i++)ans+=dfs(x-1,(p*10+i)%2520,lcm(pp,i),lim&&a[x]==i);
24     if(!lim)f[x][p][Pos[pp]]=ans;
25     return ans;
26 }
27 inline int Solve(int x){
28     int len=0;
29     while(x)a[++len]=x%10,x/=10;
30     return dfs(len,0,1,1);
31 }
32 signed main(){
33     memset(f,-1,sizeof(f));
34     for(int i=1;i<=48;i++)Pos[S[i]]=i;
35     T=read();
36     while(T--)l=read(),r=read(),writeln(Solve(r)-Solve(l-1));
37     return 0;
38 }

 

以上是关于数位DPCF55D Beautiful numbers的主要内容,如果未能解决你的问题,请参考以下文章

CodeForces 55D - Beautiful numbers - [数位DP+离散化]

[暑假集训--数位dp]cf55D Beautiful numbers

CodeForces - 55D - Beautiful numbers(数位DP,离散化)

CodeForces 55D Beautiful numbers(数位dp)

Codeforces 55D - Beautiful numbers 数位dp

Codeforces 55D Beautiful numbers(数位dp)