【知识】插头DP

#include <iostream>
#include <cstring>
typedef long long LL;
using namespace std;
const int N = 50000, M = N*2 + 7;

int n, m,end_x,end_y;
int g[20][20], q[2][N], cnt[N];

int h[2][M];
LL v[2][M];

int find(int cur,int x){
    int t = x % M;
    while(h[cur][t]!=-1&&h[cur][t]!=x) 
        if(++t==M)
            t = 0;
    return t;
}

void insert(int cur,int state,LL w){
    int t = find(cur, state);
    if(h[cur][t]==-1){
        h[cur][t] = state, v[cur][t] = w;
        q[cur][++cnt[cur]] = t;
    }
    else
        v[cur][t] += w;
}
int get(int state,int k){       //求四进制第 k 位数字
    return state >> k * 2 & 3;  
}

int set(int k,int v){   //构造四进制的第 k 位数字为 v 的数
    return v * (1 << k * 2);
}

int main(){
    cin >> n >> m;
    for(int i = 1; i <= n;i++){
        char str[20];
        scanf("%s", str + 1);
        for (int j = 1; j <= m;j++)
            if(str[j]=='.')
                g[i][j] = 1, end_x = i, end_y = j;
    }
    LL res=0;
    memset(h, -1, sizeof(h));
    int cur = 0;
    insert(cur, 0, 1);
    for (int i = 1; i <= n;i++){
        for (int j = 1; j <= cnt[cur];j++)
            h[cur][q[cur][j]] <<= 2;
        for (int j = 1; j <= m;j++){
            int last = cur;
            cur ^= 1, cnt[cur] = 0;
            memset(h[cur], -1, sizeof(h[cur]));
            for (int k = 1; k <= cnt[last]; k++){
                int state = h[last][q[last][k]];
               
                LL w = v[last][q[last][k]];
                int x = get(state, j - 1), y = get(state, j);
                if(!g[i][j]){
                    if(!x&&!y) 
                         insert(cur, state, w);
                }
                else if(!x&&!y){
                    if(g[i+1][j]&&g[i][j+1])
                        insert(cur, state + set(j - 1, 1) + set(j, 2), w);
                }
                else if(!x&&y){
                    if(g[i][j+1])
                        insert(cur, state, w);
                    if(g[i+1][j])
                        insert(cur, state + set(j - 1, y) - set(j, y), w);
                }
                else if(x&&!y){
                    if(g[i][j+1])
                        insert(cur, state - set(j - 1, x) + set(j, x), w);
                    if(g[i+1][j])
                        insert(cur, state, w);
                }
                else if(x==1&&y==1){
                    for (int u = j + 1,s = 1;; u++){
                        int z = get(state, u);
                        if(z==1)
                            s++;
                        else if(z==2){
                            if(--s==0){
                                insert(cur,state-set(j-1,x)-set(j,y)-set(u,1),w);
                                break;
                            }
                        }
                    }
                }
                else if(x==2&&y==2){
                    for (int u = j - 2,s=1;;u--){
                        int z = get(state, u);
                        if(z==2)
                            s++;
                        else if(z==1){
                            if(--s==0){
                                insert(cur, state - set(j - 1, x) - set(j, y) + set(u, 1), w);
                                break;
                            }
                        }
                    }
                }
                else if(x==2&&y==1){
                    insert(cur, state - set(j - 1, x) - set(j, y), w);
                }
                else if(i==end_x&&j==end_y)
                    res += w;
            }
        }
    }
    cout << res << endl;
    return 0;
}