Tree Diameter

// Time:  O(|V| + |E|)
// Space: O(|E|)

// iterative dfs
class Solution {
public:
    int treeDiameter(vector<vector<int>>& edges) {
        vector<vector<int>> adj(size(edges) + 1);
        for (const auto& e : edges) {
            adj[e[0]].emplace_back(e[1]);
            adj[e[1]].emplace_back(e[0]);
        }
        int result = 0;
        const auto& iter_dfs = [&]() {
            int result = 0;
            using RET = int;
            RET ret{};
            vector<tuple<int, int, int, shared_ptr<RET>, RET *>> stk = {{1, 0, -1, nullptr, &ret}};
            while (!empty(stk)) {
                const auto [step, u, p, ret2, ret] = stk.back(); stk.pop_back();
                if (step == 1) {
                    for (const auto& v : adj[u]) {
                        if (v == p) {
                            continue;
                        }
                        const auto& ret2 = make_shared<RET>();
                        stk.emplace_back(2, -2, -2, ret2, ret);
                        stk.emplace_back(1, v, u, nullptr, ret2.get());
                    }
                } else if (step == 2) {
                    result = max(result, *ret + (*ret2 + 1));
                    *ret = max(*ret, *ret2 + 1);
                }
            }
            return result;
        };

        return iter_dfs();
    }
};

// Time:  O(|V| + |E|)
// Space: O(|E|)
// dfs
class Solution2 {
public:
    int treeDiameter(vector<vector<int>>& edges) {
        vector<vector<int>> adj(size(edges) + 1);
        for (const auto& e : edges) {
            adj[e[0]].emplace_back(e[1]);
            adj[e[1]].emplace_back(e[0]);
        }
        int result = 0;
        const function<int (int, int)> dfs = [&](int u, int p) {
            int mx = 0;
            for (const auto& v : adj[u]) {
                if (v == p) {
                    continue;
                }
                const int curr = dfs(v, u);
                result = max(result, mx + (curr + 1));
                mx = max(mx, curr + 1);
            }
            return mx;
        };

        dfs(0, -1);
        return result;
    }
};

// Time:  O(|V| + |E|)
// Space: O(|E|)
// bfs, tree dp
class Solution3 {
public:
    int treeDiameter(vector<vector<int>>& edges) {
        vector<vector<int>> adj(size(edges) + 1);
        for (const auto& e : edges) {
            adj[e[0]].emplace_back(e[1]);
            adj[e[1]].emplace_back(e[0]);
        }
        int result = 0;
        const auto& bfs = [&]() {
            int result = 0;
            vector<int> dp(size(adj));
            vector<int> degree(size(adj));
            vector<int> q;
            for (int u = 0; u < size(adj); ++u) {
                degree[u] = size(adj[u]);
                if (degree[u] == 1) {
                    q.emplace_back(u);
                }
            }
            while (!empty(q)) {
                vector<int> new_q;
                for (const auto& u : q) {
                    if (degree[u] == 0) {
                        continue;
                    }
                    --degree[u];
                    for (const auto& v : adj[u]) {
                        if (degree[v] == 0) {
                            continue;
                        }
                        result = max(result, dp[v] + (dp[u] + 1));
                        dp[v] = max(dp[v], dp[u] + 1);
                        if (--degree[v] == 1) {
                            new_q.emplace_back(v);
                        }
                    }
                }
                q = move(new_q);
            }
            return result;
        };

        return bfs();
    }
};

// Time:  O(|V| + |E|)
// Space: O(|E|)
// bfs
class Solution4 {
public:
    int treeDiameter(vector<vector<int>>& edges) {
        vector<vector<int>> adj(size(edges) + 1);
        for (const auto& e : edges) {
            adj[e[0]].emplace_back(e[1]);
            adj[e[1]].emplace_back(e[0]);
        }
        int result = 0;
        const auto& bfs = [&](int root) {
            int d = -1, new_root = -1;
            vector<bool> lookup(size(adj));
            lookup[root] = true;
            vector<int> q = {root};
            while (!empty(q)) {
                ++d;
                new_root = q[0];
                vector<int> new_q;
                for (const auto& u : q) {
                    for (const auto& v : adj[u]) {
                        if (lookup[v]) {
                            continue;
                        }
                        lookup[v] = true;
                        new_q.emplace_back(v);
                    }
                }
                q = move(new_q);
            }
            return pair(d, new_root);
        };

        const auto& [_, root] = bfs(0);
        const auto& [d, __] = bfs(root);
        return d;
    }
};