洛谷 P4127 [AHOI2009]同类分布

题意简述

求l~r之间各位数字之和能整除原数的数的个数。

题解思路

数位DP

代码

#include <cstdio>
#include <cstring>
typedef long long ll;
int cnt, C;
int num[20];
ll l, r;
ll dp[20][200][200];
ll dfs(int len, int sum, int rem, int mod, bool limit, ll s = 0)
{
	if (!len) return sum == mod && rem == 0;
	ll& dp = ::dp[len][sum][rem];
	if (!limit && ~dp) return dp;
	int mx = limit ? num[len] : 9;
	for (register int i = 0; i <= mx; ++i)
		s += dfs(len - 1, sum + i, (rem * 10 + i) % mod, mod, limit && (i == mx));
	if (!limit) dp = s;
	return s;
}
ll solve(ll x, ll s = 0)
{
	for (cnt = 0; x; num[++cnt] = x % 10, x = x / 10);
	C = cnt * 9;
	for (register int i = 1; i <= C; ++i)
	{
		memset(dp, -1, sizeof dp);
		s += dfs(cnt, 0, 0, i, 1);
	}
	return s;
}
int main()
{
	scanf("%lld%lld", &l, &r);
	printf("%lld\n", solve(r) - solve(l - 1));
}