DFS (充分考虑对称性)

#include <iostream>

using namespace std;

int ans;
bool vis[10][10];

const int dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};

void dfs(int x, int y)
{
    if (x == 0 || x == 6 || y == 0 || y == 6)
    {
        ans ++;
        return;
    }

    for (int i = 0; i < 4; i ++)
    {
        int newx = x + dx[i], newy = y + dy[i];
        if (!vis[newx][newy])
        {
            vis[newx][newy] = true;
            vis[6 - newx][6 - newy] = true;
            dfs(newx, newy);
            vis[newx][newy] = false;
            vis[6 - newx][6 - newy] = false;
        }
    }
}

int main()
{
    vis[3][3] = true;
    dfs(3, 3);

    cout << ans / 4 << endl;

    return 0;
}