hdu 3652 B-number

求$[1,n]$中有多少个整数是$13$的倍数且十进制下的表示中存在$13$这个子串

$1 \le n \le 10^9$

依旧是数位$dp$，不光要记录一下是否有$13$，还要记录一下模$13$的值

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 20;
ll n, dig[N], f[N][4][N];

int nxt(int st, int i) {
    if(st == 0) return i == 1;
    if(st == 1) return i == 3 ? 2 : i == 1;
    return st;
}

ll dfs(int pos, int st, int md, int bd) {
    if(pos == 0) {
        return st == 2 && md == 0;
    } else if(!bd && f[pos][st][md] != -1) {
        return f[pos][st][md];
    } else {
        int top = bd ? dig[pos] : 9;
        ll sum = 0;
        for(int i = 0 ; i <= top ; ++ i)
            sum += dfs(pos - 1, nxt(st, i), (md * 10 + i) % 13, bd && i == top);
        if(!bd) f[pos][st][md] = sum;
        return sum;
    }
}

void sol() {
    memset(f, -1, sizeof f);
    int pos = 0; while(n) dig[++ pos] = n % 10, n /= 10;
    cout << dfs(pos, 0, 0, 1) << endl;
} 

int main() {
    while(cin >> n) sol(); 
}