暑期留校——状态压缩DP-板子题

第一道题：

 

 

 

 

 朴素写法，1000ms

#include 
#include 
#include 
 
using namespace std;
 
const int N = 12, M = 1 << N;
 
int n, m;
long long f[N][M];
bool st[M];
 
int main()
{
    while (cin >> n >> m, n || m)
    {
        for (int i = 0; i < 1 << n; i ++ )
        {
            int cnt = 0;
            st[i] = true;
            for (int j = 0; j < n; j ++ )
                if (i >> j & 1)
                {
                    if (cnt & 1) st[i] = false;
                    cnt = 0;
                }
                else cnt ++ ;
            if (cnt & 1) st[i] = false;
        }
 
        memset(f, 0, sizeof f);
        f[0][0] = 1;
        for (int i = 1; i <= m; i ++ )
            for (int j = 0; j < 1 << n; j ++ )
                for (int k = 0; k < 1 << n; k ++ )
                    if ((j & k) == 0 && st[j | k])
                        f[i][j] += f[i - 1][k];
 
        cout << f[m][0] << endl;
    }
    return 0;
}

去除无效状态的优化写法，230ms

#include 
#include 
#include 
#include 
 
using namespace std;
 
typedef long long LL;
 
const int N = 12, M = 1 << N;
 
int n, m;
LL f[N][M];
vector<int> state[M];
bool st[M];
 
int main()
{
    while (cin >> n >> m, n || m)
    {
        for (int i = 0; i < 1 << n; i ++ )
        {
            int cnt = 0;
            bool is_valid = true;
            for (int j = 0; j < n; j ++ )
                if (i >> j & 1)
                {
                    if (cnt & 1)
                    {
                        is_valid = false;
                        break;
                    }
                    cnt = 0;
                }
                else cnt ++ ;
            if (cnt & 1) is_valid = false;
            st[i] = is_valid;
        }
 
        for (int i = 0; i < 1 << n; i ++ )
        {
            state[i].clear();
            for (int j = 0; j < 1 << n; j ++ )
                if ((i & j) == 0 && st[i | j])
                    state[i].push_back(j);
        }
 
        memset(f, 0, sizeof f);
        f[0][0] = 1;
        for (int i = 1; i <= m; i ++ )
            for (int j = 0; j < 1 << n; j ++ )
                for (auto k : state[j])
                    f[i][j] += f[i - 1][k];
 
        cout << f[m][0] << endl;
    }
 
    return 0;
}