Light OJ 1068

数位DP

#include <cstdio>

#include <cstring>

using namespace std;



const int MAX_DIGIT = 15;

const int MAX_K = 10005;



long long n;

int f[MAX_DIGIT];

long long memoize[MAX_DIGIT][MAX_DIGIT * 9][MAX_DIGIT * 9];

int k;



int to_digits(long long a)

{

    int ret = 0;

    while (a > 0)

    {

        f[ret++] = a % 10;

        a /= 10;

    }

    return ret;

}



long long dfs(int digit, bool less, int sum, int remainder)

{

    if (digit < 0)

    {

        return sum == 0 && remainder == 0;

    }

    if (less && memoize[digit][sum][remainder] != -1)

    {

        return memoize[digit][sum][remainder];

    }

    int limit = less ? 9 : f[digit];

    long long ret = 0;

    for (int i = 0; i <= limit; i++)

    {

        ret += dfs(digit - 1, less || i < f[digit], (sum + i) % k, (remainder * 10 + i) % k);

    }

    if (less)

    {

        memoize[digit][sum][remainder] = ret;

    }

    return ret;

}



long long work(long long n)

{

    if (n < 0)

    {

        return 0;

    }

    if (n == 0)

    {

        return 1;

    }

    int len = to_digits(n);

    if (k >= MAX_DIGIT * 9)

    {

        return 0;

    }

    return dfs(len - 1, false, 0, 0);

}



int main()

{

    int t;

    scanf("%d", &t);

    for (int i = 1; i <= t; i++)

    {

        int a, b;

        scanf("%d%d%d", &a, &b, &k);

        memset(memoize, -1, sizeof(memoize));

        printf("Case %d: %lld\n", i, work(b) - work(a - 1));

    }

    return 0;

}

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