题目链接：hdu 4734 F(x)

题目大意：给定f(x)的计算公式，现在给出n和m，求有多少个x，x <= m，并且f(x) <= f(n)

解题思路：数位dp，dp[i][j]表示到第10i内，然后f值为j的总数。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 10000;

int n, bit[15];
int dp[15][maxn];

int init () {
    int s = n = 0, a, b;
    scanf("%d%d", &a, &b);

    for (int i = 0; a; i++) {
        s += (a % 10) * (1<<i);
        a /= 10;
    }

    while (b) {
        bit[n++] = b % 10;
        b /= 10;
    }
    return s;
}

int dfs (int d, int s, int flag) {

    if (d == -1)
        return (s >= 0);

    if (flag == 0 && dp[d][s] != -1)
        return dp[d][s];

    int ret = 0, end = (flag ? bit[d] : 9);
    for (int i = 0; i <= end; i++) {
        if (s < i * (1<<d))
            continue;
        ret += dfs(d - 1, s - i * (1<<d), flag && i == end);
    }

    if (flag == 0)
        dp[d][s] = ret;
    return ret;
}

int main () {
    int cas;
    scanf("%d", &cas);
    memset(dp, -1, sizeof(dp));
    for (int kcas = 1; kcas <= cas; kcas++) {
        int f = init();
        printf("Case #%d: %d\n", kcas, dfs(n - 1, f, 1));
    }
    return 0;
}

hdu 4734 F(x)(数位dp)