CodeForces 55D Beautiful numbers(数位dp)

CodeForces 55D

题目

思路

代码

#include<iostream>
#include<cstring>
#include<cstdio>
#include<vector>
#include<queue>
#include<algorithm>
#include<stack>

using namespace std;

typedef  long long ll;
int index[2530];
int dis[30];
ll dp[30][2520][50];

void init()
{
int num=0;
for(int i=1; i<=2520; i++)
if(2520%i==0)
index[i]=num++;
}

int gcd(int a, int b)
{
return b == 0 ? a : gcd(b, a%b);
}

int lcm(int a, int b)
{
return a/gcd(a, b)*b;
}

ll dfs(int len,int sum,int lc ,int lim)
{
if(len==-1) return sum%lc==0?1:0;
if(!lim&&dp[len][sum][index[lc]]!=-1) return dp[len][sum][index[lc]];
ll res=0;
int u=lim?dis[len]:9;
for(int i=0; i<=u; i++)
{
int ssum=(sum*10+i)%2520;
int llc=lc;
if(i)
llc=lcm(lc,i);
res+=dfs(len-1,ssum,llc,lim&&i==u);
}
if(lim) return res;
else return dp[len][sum][index[lc]]=res;
}

ll solve(ll x)
{
int len=0;
while(x)
{
dis[len++]=x%10;
x/=10;
}
return dfs(len-1,0,1,1);
}

ll a,b;

int main()
{
int T;
scanf("%d",&T);
init();
memset(dp,-1,sizeof(dp));
while(T--)
{
scanf("%I64d %I64d",&a,&b);
printf("%I64d\n",solve(b)-solve(a-1));
}
}