LC2556 AC

class Solution {
    using pii = pair<int, int>;
    vector<int> dfn, low;
    int ts, m, n, cc;
    bool ans;
    set<pii> vis;
    stack<pii> st;
    map<pii, int> id;
    map<int, int> cut;
    int root;

    void tarjan(int x, int y, const vector<vector<int>> &g) {
        int u = x * n + y;
        dfn[u] = low[u] = ++ts;
        int dir[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
        vis.insert({x, y});
        int flag = 0;

        for (int i = 0; i < 4; ++i) {
            int nx = x + dir[i][0], ny = y + dir[i][1];
            if (nx >= 0 && nx < m && ny >= 0 && ny < n && g[nx][ny] == 1) {
                int v = nx * n + ny;
                if (dfn[v] == 0) {
                    tarjan(nx, ny, g);
                    low[u] = min(low[u], low[v]);
                    if (dfn[u] <= low[v]) {
                        flag++;
                        if (u != root || flag > 1) {
                            cut[u] = true;
                        }
                    }
                } else
                    low[u] = min(low[u], dfn[v]);
            }
        }
    }
public:
    bool isPossibleToCutPath(vector<vector<int>>& grid) {
        m = grid.size(), n = grid[0].size();
        if (m == 2 && n == 1 || m == 1 && n == 2) return false;

        dfn = low = vector<int>(m * n);
        ts = 0; ans = false; cc = 1;

        for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) {
            int u = i * n + j;
            if (!dfn[i]) root = u, tarjan(i, j, grid);
        }
        // tarjan(0, 0, grid);
        cout << "id0: " << id[{0, 0}] << " idlast: " << id[{m-1,n-1}] << endl;
        cout << "cut.size(): " << cut.size() << endl;
        // return id[{0, 0}] != id[{m-1, n-1}];
        return cut.size() != 0 || vis.count({m -1, n -1}) == 0;
    }
};