B-number
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 1658 Accepted Submission(s): 906
Problem Description
A wqb-number, or B-number for short, is a non-negative integer whose decimal form contains the sub- string "13" and can be divided by 13. For example, 130 and 2613 are wqb-numbers, but 143 and 2639 are not. Your task is to calculate how many wqb-numbers from 1 to n for a given integer n.
Input
Process till EOF. In each line, there is one positive integer n(1 <= n <= 1000000000).
Output
Print each answer in a single line.
Sample Input
13
100
200
1000
Sample Output
1
1
2
2
含有数字13且能够被13整除的数的个数
#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <cmath>
#include <algorithm>
#include <vector>
#include <map>
#include <string>
#include <stack>
using namespace std;
typedef long long ll;
#define PI 3.1415926535897932
#define E 2.718281828459045
#define INF 0x3f3f3f3f
#define mod 100000007
const int M=1005;
int n,m;
int cnt;
int sx,sy,sz;
int mp[1000][1000];
int pa[M*10],rankk[M];
int head[M*6],vis[M*100];
int dis[M*100];
ll prime[M*1000];
bool isprime[M*1000];
int lowcost[M],closet[M];
char st1[5050],st2[5050];
int len[M*6];
typedef pair<int ,int> ac;
//vector<int> g[M*10];
int dp[50][50][20][10];
int has[10500];
int month[13]= {0,31,59,90,120,151,181,212,243,273,304,334,0};
int dir[8][2]= {{0,1},{0,-1},{-1,0},{1,0},{1,1},{1,-1},{-1,1},{-1,-1}};
void getpri()
{
ll i;
int j;
cnt=0;
memset(isprime,false,sizeof(isprime));
for(i=2; i<1000000LL; i++)
{
if(!isprime[i])prime[cnt++]=i;
for(j=0; j<cnt&&prime[j]*i<1000000LL; j++)
{
isprime[i*prime[j]]=1;
if(i%prime[j]==0)break;
}
}
}
struct node
{
int v,w;
node(int vv,int ww)
{
v=vv;
w=ww;
}
};
vector<int> g[M*100];
string str[1000];
int bit[50];
/*
//dp[i][j][k][z]:i:处理的数位,j:该数对13取模以后的值,k:是否已经包含13,z结尾的数(dp[i][j]表示i为高位且i位为数字j时满足题意的种数)
int dfs(int cur,int s,bool h13,int pre,int e,int z){
if(cur<0) return h13&&(s==0);//return 1;含有数字13且能够被13整除的数
if(!e&&!z&&dp[cur][s][h13][pre]!=-1) return dp[cur][s][h13][pre];//dp[cur][pre]不能变,相当于模板的dp[cur][s],因为是交事件,加两项
int endx=e?bit[cur]:9;
int ans=0;
for(int i=0;i<=endx;i++){
//if(!z&&abs(i-s)<2)continue;
if(z&&!i) ans+=dfs(cur-1,(s*10+i),h13,i,e&&i==endx,1);
else ans+=dfs(cur-1,(s*10+i),h13||(pre==1&&i==3),i,e&&i==endx,0);
}
if(!e&&!z) dp[cur][s][h13][pre]=ans;
return ans;
}
int dp[15][15][3],s[15];//dp[i][j][k],i表示位数,j表示余数,k表示末尾是1、末尾不是1、含有13.
int dfs(int pos, int mod, int have, int lim)//前三个数对应数组dp,lim表示上限
{
int num,ans,mod_x,have_x;
if (pos <= 0)
return mod==0&&have==2;
if (!lim && dp[pos][mod][have]!=-1) //没有上限且被访问过
return dp[pos][mod][have];
ans = 0;
num = lim?s[pos]:9;//如果有上限,只能取到当前位数,如果没上限,可取到9
//假设该位是2,下一位是3,如果现在算到该位为1,那么下一位是能取到9的,如果该位为2,下一位只能取到3
for (int i=0; i<=num; i++)
{
mod_x = (mod*10+i);//该位的每种情况对13取模
have_x = have;
if (have==0 && i==1)//末尾加1
have_x=1;
if (have==1 && i!=1)//末尾已经为1了
have_x=0;
if (have==1 && i==3)//末尾是1,现在加3
have_x=2;
ans+=dfs(pos-1, mod_x, have_x, lim&&i==num);//如果i==num,下一位能取的最大数就为s[pos-1],i!=num,下一位能取到9
}
if (!lim)
dp[pos][mod][have] = ans;
return ans;
}*/
//压缩版
int get(int t,int i){
if(t==2||(t==1&&i==3))return 2; //2是含有13
if(i==1)return 1; //当前为一,对下个状态而言,上一位就是1
return 0; //其他数
}
int dfs(int pos,int s,int h13,int flag ){ //pre
if(cur<0)return s==0&&h13==2;
if(!flag&&dp[cur][s][h13]!=-1)return dp[cur][s][h13];
int ans=0,u=flag?pri[cur]:9;
for(int i=0;i<=u;i++){
ans+=dfs(cur-1,(s*10+i),get(h13,i),flag&&i==u);
//printf("%d %d %d\n",ans,pos,i);
}
return flag?ans:dp[cur][s][h13]=ans;
}
int solve(int n){
int len=0;
while(n){
bit[len++]=n;
n/=10;
}
return dfs(len-1,0,0,0,1,1);
}
int main()
{
int i,j,k,t;
int l,r;
while(~scanf("%d",&r))
{
memset(dp,-1,sizeof(dp));
printf("%d\n",solve(r));
}
return 0;
}
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