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tree-diameter.cpp
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// 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;
}
};