HDU 5787：K-wolf Number（数位DP）

题目链接：http://acm.split.hdu.edu.cn/showproblem.php?pid=5787

题意：要求相邻的K个位的数不能相同，在[L,R]区间有多少个这样的数.

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

int bit[20];
long long dp[20][11][11][11][11];
int k;

//考虑前导零:d = 10代表前一位是0, 当(d == 10 && u == 0)表示当前这位为0并且前4位都是0

bool check(int a, int b, int c, int d, int u)
{
    if(k == 2) return u != d;
    else if(k == 3) return u != d && u != c;
    else if(k == 4) return u != d && u != c && u != b;
    else return u != d && u != c && u != b && u != a;
}

long long dfs(int pos, int a, int b, int c, int d, bool flag)
{
    if(pos <= 0) return d != 10;
    long long res = dp[pos][a][b][c][d];
    if(flag && res != -1) return res;
    long long ans = 0;
    int up = flag ? 9 : bit[pos];
    for(int u = 0; u <= up; u++) {
        if(d == 10 && u == 0) {
            ans += dfs(pos - 1, a, b, c, d, flag || u != up);
        } else if(check(a, b, c, d, u)) {
            ans += dfs(pos - 1, b, c, d, u, flag || u != up);
        }
    }
    if(flag) dp[pos][a][b][c][d] = ans;
    return ans;
}

long long solve(long long x)
{
    int len = 0;
    while(x) {
        bit[++len] = x % 10;
        x /= 10;
    }
    return dfs(len, 10, 10, 10, 10, 0);
}

int main()
{
    long long l, r;
    while(~scanf("%I64d%I64d%d", &l, &r, &k)) {
        memset(dp, -1, sizeof(dp));
        printf("%I64d
", solve(r) - solve(l - 1));
    }
    return 0;
}

另一种：

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

int bit[20];
long long dp[20][11][11][11][11][2];
int k;

//考虑前导零:d = 10代表前一位是0, 当(d == 10 && u == 0)表示当前这位为0并且前4位都是0

bool check(int a, int b, int c, int d, int u)
{
    if(k == 2) return u != d;
    else if(k == 3) return u != d && u != c;
    else if(k == 4) return u != d && u != c && u != b;
    else return u != d && u != c && u != b && u != a;
}

long long dfs(int pos, int a, int b, int c, int d, bool flag, bool zero)
{
    if(pos <= 0) return zero;
    long long res = dp[pos][a][b][c][d][zero];
    if(flag && res != -1 && zero) return res;
    long long ans = 0;
    int up = flag ? 9 : bit[pos];
    for(int u = 0; u <= up; u++) {
        if(!zero && u == 0) {
            ans += dfs(pos - 1, a, b, c, d, flag || u != up, 0);
        } else if(check(a, b, c, d, u)) {
            ans += dfs(pos - 1, b, c, d, u, flag || u != up, 1);
        }
    }
    if(flag) dp[pos][a][b][c][d][zero] = ans;
    return ans;
}

long long solve(long long x)
{
    int len = 0;
    while(x) {
        bit[++len] = x % 10;
        x /= 10;
    }
    return dfs(len, 10, 10, 10, 10, 0, 0);
}

int main()
{
    long long l, r;
    while(~scanf("%I64d%I64d%d", &l, &r, &k)) {
        memset(dp, -1, sizeof(dp));
        printf("%I64d
", solve(r) - solve(l - 1));
    }
    return 0;
}