Codeforces-solutions/2024-2025 ICPC Asia Jakarta Regional Contest (Unrated, Online Mirror, ICPC Rules, Teams Preferred)/M. Mirror Maze.cpp

/* Problem URL: https://codeforces.com/problemset/problem/2045/M */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

const int oo = INT32_MAX >> 1;
const ll OO = INT64_MAX >> 1;


void pre()
{

}

#define TEST 0

void solve()
{
    int r, c;
    cin >> r >> c;

    V<string> a(r);
    cin >> a;

    auto getpos = [&](int i, int j, int k) {
        return i * c * 4 + j * 4 + k;
    };

    int tot = 0;

    vvi graph(r * c * 4);
    vi ty(r * c * 4, -1);
    rep(i, r) {
        rep(j, c) {
            int n = getpos(i, j, 0);
            int e = getpos(i, j, 1);
            int s = getpos(i, j, 2);
            int w = getpos(i, j, 3);

            if (i > 0) {
                int ot = getpos(i - 1, j, 2);
                graph[n].push_back(ot);
            }

            if (j > 0) {
                int ot = getpos(i, j - 1, 1);
                graph[w].push_back(ot);
            }

            if (i < r - 1) {
                int ot = getpos(i + 1, j, 0);
                graph[s].push_back(ot);
            }

            if (j < c - 1) {
                int ot = getpos(i, j + 1, 3);
                graph[e].push_back(ot);
            }

            if (a[i][j] == '.') {
                graph[e].push_back(w);
                graph[w].push_back(e);
                graph[s].push_back(n);
                graph[n].push_back(s);
                continue;
            }
            tot++;
            ty[n] = i * c + j;
            ty[e] = i * c + j;
            ty[s] = i * c + j;
            ty[w] = i * c + j;

            if (a[i][j] == '/') {
                graph[n].push_back(w);
                graph[w].push_back(n);
                graph[s].push_back(e);
                graph[e].push_back(s);
                continue;
            }

            graph[n].push_back(e);
            graph[e].push_back(n);
            graph[w].push_back(s);
            graph[s].push_back(w);
        }
    }

    V<bool> vis(r * c * 4);
    vi sz(r * c * 4, -1);

    set<int> s;
    function<void(int)> dfs = [&](int i) {
        vis[i] = true;
        if (ty[i] != -1) {
            s.insert(ty[i]);
        }

        repv(j, graph[i]) {
            if (vis[j]) {
                continue;
            }

            dfs(j);
        }
    };

    function<void(int)> dfs2 = [&](int i) {
        sz[i] = s.size();

        repv(j, graph[i]) {
            if (sz[j] != -1) {
                continue;
            }

            dfs2(j);
        }
    };

    rep(i, r) {
        rep(j, c) {
            rep(k, 4) {
                int ac = getpos(i, j, k);
                if (vis[ac]) {
                    continue;
                }

                dfs(ac);
                dfs2(ac);
                s.clear();
            }
        }
    }

    V<string> ans;
    rep(i, r) {
        int w = getpos(i, 0, 3);
        if (sz[w] == tot) {
            ans.emplace_back("W" + to_string(i + 1));
        }
        int e = getpos(i, c - 1, 1);
        if (sz[e] == tot) {
            ans.emplace_back("E" + to_string(i + 1));
        }
    }

    rep(i, c) {
        int n = getpos(0, i, 0);
        if (sz[n] == tot) {
            ans.emplace_back("N" + to_string(i + 1));
        }
        int s = getpos(r - 1, i, 2);
        if (sz[s] == tot) {
            ans.emplace_back("S" + to_string(i + 1));
        }
    }

    cout << ans.size() << '\n';
    repv(i, ans) {
        cout << i << ' ';
    }
    cout << '\n';
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    pre();

    int t;
    (TEST && cin >> t) || (t = 1);
    while (t--) {
        solve();
    }
}