leetcode-solutions/solutions/2501-3000/2876-count-visited-nodes-in-a-directed-graph.cpp at main · Avuvos/leetcode-solutions · GitHub

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// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
template<class Fun> class y_combinator_result {
    Fun fun_;
public:
    template<class T> explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}
    template<class ...Args> decltype(auto) operator()(Args &&...args) { return fun_(std::ref(*this), std::forward<Args>(args)...); }
};
template<class Fun> decltype(auto) y_combinator(Fun &&fun) { return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun)); }

class Solution {
public:
    // http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
    struct functional_graph {
    int n = 0;
    vector<int> F;
    vector<bool> in_cycle;
    vector<int> which_cycle;
    vector<int> cycle_root;
    vector<int> cycle_position;
    vector<int> depth;
    vector<vector<int>> children;
    vector<vector<int>> cycles;
    vector<int> jump, jump_dist;

    functional_graph(const vector<int> &f = {}) {
        if (!f.empty())
            build(f);
    }

    void build(const vector<int> &f) {
        F = f;
        n = int(F.size());
        in_cycle.assign(n, false);
        which_cycle.assign(n, -1);
        cycle_root.assign(n, -1);
        cycle_position.assign(n, -1);
        depth.assign(n, -1);
        children.assign(n, {});
        cycles.clear();

        vector<int> seen(n, -1);

        for (int i = 0; i < n; i++) {
            if (seen[i] >= 0)
                continue;

            int x = i;

            do {
                seen[x] = i;
                x = F[x];
            } while (seen[x] < 0);

            if (seen[x] != i)
                continue;

            vector<int> cycle;
            int y = x;

            do {
                in_cycle[y] = true;
                cycle_position[y] = int(cycle.size());
                which_cycle[y] = int(cycles.size());
                cycle.push_back(y);
                y = F[y];
            } while (y != x);

            cycles.push_back(cycle);
        }

        seen.assign(n, 0);

        for (int i = 0; i < n; i++)
            seen[F[i]] += !in_cycle[i];

        for (int i = 0; i < n; i++)
            children[i].reserve(seen[i]);

        seen.clear();

        for (int i = 0; i < n; i++)
            if (!in_cycle[i])
                children[F[i]].push_back(i);

        jump.assign(n, -1);
        jump_dist.assign(n, -1);
        int cyc_root = -1, which_cyc = -1;

        auto dfs = y_combinator([&](auto self, int node, int parent) -> void {
            depth[node] = parent < 0 ? 0 : depth[parent] + 1;
            cycle_root[node] = cyc_root;
            which_cycle[node] = which_cyc;
            jump[node] = parent < 0 ? node : jump_dist[parent] == jump_dist[jump[parent]] ? jump[jump[parent]] : parent;
            jump_dist[node] = depth[node] - depth[jump[node]];

            for (int child : children[node])
                self(child, node);
        });

        for (int i = 0; i < n; i++)
            if (in_cycle[i]) {
                cyc_root = i;
                which_cyc = which_cycle[i];
                dfs(i, -1);
            }
    }

    int cycle_length(int node) {
        return int(cycles[which_cycle[node]].size());
    }

    int go_forward(int v, int64_t k) {
        if (k >= depth[v]) {
            int root = cycle_root[v];
            k -= depth[v];
            int cyc = which_cycle[root];
            int64_t position = (cycle_position[root] + k) % cycles[cyc].size();
            return cycles[cyc][position];
        }

        while (k > 0)
            if (jump_dist[v] <= k) {
                k -= jump_dist[v];
                v = jump[v];
            } else {
                k--;
                v = F[v];
            }

        return v;
    }
};

    vector<int> countVisitedNodes(vector<int>& edges) {
        int n = (int) edges.size();
        functional_graph fn(edges);
        vector<int> ans(n, 0);
        for (int i = 0; i < n; i++) {
            ans[i] = fn.depth[i] + fn.cycle_length(i);
        }
        return ans;


    }
};