HDU X mod f(x) (数位DP)

Posted 2020-08-12 dwtfukgv

题意：求一个区间内各位数字之和能被该数整除的个数。

析：数位DP，dp[i][j][k][l] 表示前 i 位和为 j，对 k 取模为 l，然后就好做了。

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <cctype>
#include <cmath>
#include <stack>
//#include <tr1/unordered_map>
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;
//using namespace std :: tr1;

typedef long long LL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const double inf = 0x3f3f3f3f3f3f;
const LL LNF = 0x3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int maxn = 1e5 + 5;
const LL mod = 10000000000007;
const int N = 1e6 + 5;
const int dr[] = {-1, 0, 1, 0, 1, 1, -1, -1};
const int dc[] = {0, 1, 0, -1, 1, -1, 1, -1};
const char *Hex[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};
inline LL gcd(LL a, LL b){  return b == 0 ? a : gcd(b, a%b); }
int n, m;
const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
inline int Min(int a, int b){ return a < b ? a : b; }
inline int Max(int a, int b){ return a > b ? a : b; }
inline LL Min(LL a, LL b){ return a < b ? a : b; }
inline LL Max(LL a, LL b){ return a > b ? a : b; }
inline bool is_in(int r, int c){
    return r >= 0 && r < n && c >= 0 && c < m;

}
int dp[12][85][85][85];
int a[12];

int dfs(int pos, int val, int x, int y, bool ok){
    if(!pos)  return y == 0 && val == x;
    int &ans = dp[pos][val][x][y];
    if(!ok && ans >= 0)  return ans;

    int res = 0, n = ok ? a[pos] : 9;
    for(int i = 0; i <= n; ++i)
        res += dfs(pos-1, val+i, x, (y*10+i)%x, ok && i == n);
    if(!ok)  ans = res;
    return res;
}

int solve(int n){
    int len = 0;
    int k = 0;
    while(n){
        a[++len] = n % 10;
        k += a[len];
        n /= 10;
    }

    int ans = 0;
    for(int i = 1; i < 82; ++i)
        ans += dfs(len, 0, i, 0, true);
    return ans;
}

int main(){
    int T;  cin >> T;
    memset(dp, -1, sizeof dp);
    for(int kase = 1; kase <= T; ++kase){
        scanf("%d %d", &m, &n);
        printf("Case %d: %d\n", kase, solve(n) - solve(m-1));
    }
    return 0;
}