codeforces 628D Magic Numbers (数位dp)

 1 #include <bits/stdc++.h>
 2 
 3 using namespace std;
 4 typedef long long ll;
 5 const ll MOD = 1e9+7;
 6 const int N = 2020;
 7 
 8 char a[N], b[N];
 9 int m, n;
10 int dg[N];
11 ll f[N][N];
12 
13 inline ll add(ll x, ll y) {
14     x = x + y;
15     return x >= MOD ? x-MOD : x;
16 }
17 
18 ll dfs(int i, int s, bool flag, bool e) {  // dp[i][s] , flag 表示奇数还是偶数，e代表边界
19     if(i == -1) return s == 0;
20     if(!e && ~f[i][s]) return f[i][s];
21     ll res = 0LL;
22     int u = e ? dg[i] : 9;
23     for(int d = 0; d <= u; ++d) {
24         if(flag == 1 && d == n) continue;
25         if(flag == 0 && d != n) continue;
26         res = add(res, dfs(i-1, (s*10+d)%m, flag^1, e && d==u));
27     }
28     return e ? res : f[i][s] = res;
29 }
30 
31 void deal(int& len) {
32     for(int i = 0; i < len; ++i) {
33         if(dg[i] == 0) dg[i] = 9;
34         else {
35             --dg[i];
36             break;
37         }
38     }
39     return ;
40 }
41 
42 ll solve(char c[], bool fg) {
43     int len = strlen(c);
44     for(int i = 0; i < len; ++i) dg[i] = c[len-1-i] - ‘0‘;
45     if(fg) deal(len);
46     return dfs(len-1, 0, 1, 1);
47 }
48 
49 int main()
50 {
51     scanf("%d %d", &m, &n);
52     scanf("%s %s", a, b);
53     memset(f, -1, sizeof f);
54     printf("%I64d\n", add(solve(b, 0) - solve(a, 1), MOD));
55     return 0;
56 }