Distinct Paths

Posted 2021-03-08 leiyuanze

代码

#include<cstdio>
using namespace std;

const int N = 20 , mod = 1e9 + 7 , K = 10;
int f[N + 5][N + 5] , map[N + 5][N + 5] , vis[K + 5] , n , m , k;

inline int dfs(int x , int y)
{
    if (y == m + 1) return dfs(x + 1 , 1);
    if (x == n + 1) return 1;
    
    f[x][y] = f[x - 1][y] | f[x][y - 1];
    int num = 0 , sum = 0 , res = 0 , bz = 0;
    
    for(register int i = 1; i <= k; i++)
    if (!(f[x][y] & (1 << i - 1))) num++;
    if (num < n + m - x - y + 1) return 0;
    
    if (!map[x][y])
    {
        for(register int i = 1; i <= k; i++)
        if (!(f[x][y] & (1 << i - 1)))
        {
            if (!vis[i])
            {
                if (bz == 1) 
                {
                    res = (res + sum) % mod;
                    continue;
                }
                else 
                {
                    bz = 1;
                    vis[i]++;
                    f[x][y] |= 1 << i - 1;
                    sum = dfs(x , y + 1);
                    res = (res + sum) % mod;
                    f[x][y] ^= 1 << i - 1;
                    vis[i]--;
                }
                continue;
            }
            vis[i]++;
            f[x][y] |= 1 << i - 1;
            res = (res + dfs(x , y + 1)) % mod;
            f[x][y] ^= 1 << i - 1;
            vis[i]--;
        }
    }
    else if (!(f[x][y] & (1 << map[x][y] - 1)))
    {
        f[x][y] |= 1 << map[x][y] - 1;
        res = (res + dfs(x , y + 1)) % mod;
        f[x][y] ^= 1 << map[x][y] - 1;
    }
    return res;
}

int main()
{
    scanf("%d%d%d" , &n , &m , &k);
    if (n + m - 1 > k) 
    {
        printf("0");
        return 0;
    }
    for(register int i = 1; i <= n; i++)
        for(register int j = 1; j <= m; j++)
        {
            scanf("%d" , &map[i][j]);
            vis[map[i][j]]++;
        }
    printf("%d" , dfs(1 , 1));
}