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find-the-last-marked-nodes-in-tree.cpp
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// Time: O(n)
// Space: O(n)
// bfs
class Solution {
public:
vector<int> lastMarkedNodes(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]);
}
const auto& bfs = [&](int root) {
int new_root = -1;
vector<int> dist(size(adj), -1);
dist[root] = 0;
vector<int> q = {root};
while (!empty(q)) {
new_root = q[0];
vector<int> new_q;
for (const auto& u : q) {
for (const auto& v : adj[u]) {
if (dist[v] != -1) {
continue;
}
dist[v] = dist[u] + 1;
new_q.emplace_back(v);
}
}
q = move(new_q);
}
return pair(dist, new_root);
};
const auto& [x, u] = bfs(0);
const auto& [dist1, v] = bfs(u);
const auto& [dist2, y] = bfs(v);
vector<int> result(size(adj));
for (int w = 0; w < size(adj); ++w) {
result[w] = dist1[w] > dist2[w] ? u : v;
}
return result;
}
};
// Time: O(n)
// Space: O(n)
// bfs
class Solution2 {
public:
vector<int> lastMarkedNodes(vector<vector<int>>& edges) {
const auto& increase = [](const auto& x) {
return pair(x.first + 1, x.second);
};
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]);
}
const auto& bfs = [&]() {
vector<vector<pair<int, int>>> dp(size(adj), vector<pair<int, int>>(2));
int new_root = -1;
for (int u = 0; u < size(dp); ++u) {
for (auto& x : dp[u]) {
x.second = u;
}
}
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) {
new_root = u;
continue;
}
--degree[u];
for (const auto& v : adj[u]) {
if (degree[v] == 0) {
continue;
}
auto curr = increase(dp[u][0]);
for (auto& x : dp[v]) {
if (curr > x) {
swap(curr, x);
}
}
if (--degree[v] == 1) {
new_q.emplace_back(v);
}
}
}
q = move(new_q);
}
return pair(dp, new_root);
};
const auto& [dp, u] = bfs();
const auto& bfs2 = [&](int root) {
vector<int> result(size(adj), -1);
vector<tuple<int, int, pair<int, int>>> q = {{root, -1, pair(0, -1)}};
while (!empty(q)) {
vector<tuple<int, int, pair<int, int>>> new_q;
for (const auto& [u, p, curr] : q) {
result[u] = max(dp[u][0], curr).second;
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
new_q.emplace_back(v, u, increase(max(dp[u][dp[u][0].second == dp[v][0].second], curr)));
}
}
q = move(new_q);
}
return result;
};
return bfs2(u);
}
};
// Time: O(n)
// Space: O(n)
// bfs
class Solution3 {
public:
vector<int> lastMarkedNodes(vector<vector<int>>& edges) {
const auto& increase = [](const auto& x) {
return pair(x.first + 1, x.second);
};
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]);
}
const auto& topological_traversal = [&]() {
vector<int> p(size(adj), -2);
p[0] = -1;
vector<int> topological_order;
topological_order.reserve(size(adj));
topological_order.emplace_back(0);
for (int idx = 0; idx < size(topological_order); ++idx) {
const auto& u = topological_order[idx];
for (const auto& v : adj[u]) {
if (p[v] != -2) {
continue;
}
p[v] = u;
topological_order.emplace_back(v);
}
}
reverse(begin(topological_order), end(topological_order));
vector<vector<pair<int, int>>> dp(size(adj), vector<pair<int, int>>(2));
for (int u = 0; u < size(dp); ++u) {
for (auto& x : dp[u]) {
x.second = u;
}
}
for (const auto& u : topological_order) {
for (const auto& v : adj[u]) {
if (v == p[u]) {
continue;
}
auto curr = increase(dp[v][0]);
for (auto& x : dp[u]) {
if (curr > x) {
swap(curr, x);
}
}
}
}
return dp;
};
const auto& dp = topological_traversal();
const auto& bfs = [&]() {
vector<int> result(size(adj), -1);
vector<tuple<int, int, pair<int, int>>> q = {{0, -1, pair(0, -1)}};
while (!empty(q)) {
vector<tuple<int, int, pair<int, int>>> new_q;
for (const auto& [u, p, curr] : q) {
result[u] = max(dp[u][0], curr).second;
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
new_q.emplace_back(v, u, increase(max(dp[u][dp[u][0].second == dp[v][0].second], curr)));
}
}
q = move(new_q);
}
return result;
};
return bfs();
}
};
// Time: O(n)
// Space: O(n)
// iterative dfs, tree dp
class Solution4 {
public:
vector<int> lastMarkedNodes(vector<vector<int>>& edges) {
const auto& increase = [](const auto& x) {
return pair(x.first + 1, x.second);
};
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]);
}
const auto& iter_dfs1 = [&]() {
vector<vector<pair<int, int>>> dp(size(adj), vector<pair<int, int>>(2));
for (int u = 0; u < size(dp); ++u) {
for (auto& x : dp[u]) {
x.second = u;
}
}
vector<tuple<int, int, int, int>> stk = {{1, 0, -1, -1}};
while (!empty(stk)) {
const auto [step, u, p, i] = stk.back(); stk.pop_back();
if (step == 1) {
stk.emplace_back(2, u, p, 0);
} else if (step == 2) {
if (i == size(adj[u])) {
continue;
}
stk.emplace_back(2, u, p, i + 1);
const int v = adj[u][i];
if (v == p) {
continue;
}
stk.emplace_back(3, v, u, -1);
stk.emplace_back(1, v, u, -1);
} else if (step == 3) {
auto curr = increase(dp[u][0]);
for (auto& x : dp[p]) {
if (curr > x) {
swap(curr, x);
}
}
}
}
return dp;
};
const auto& dp = iter_dfs1();
const auto& iter_dfs2 = [&]() {
vector<int> result(size(adj), -1);
vector<tuple<int, int, pair<int, int>>> stk = {{0, -1, pair(0, -1)}};
while (!empty(stk)) {
const auto [u, p, curr] = stk.back(); stk.pop_back();
result[u] = max(dp[u][0], curr).second;
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
stk.emplace_back(v, u, increase(max(dp[u][dp[u][0].second == dp[v][0].second], curr)));
}
}
return result;
};
return iter_dfs2();
}
};
// Time: O(n)
// Space: O(n)
// dfs, tree dp
class Solution5 {
public:
vector<int> lastMarkedNodes(vector<vector<int>>& edges) {
const auto& increase = [](const auto& x) {
return pair(x.first + 1, x.second);
};
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]);
}
vector<vector<pair<int, int>>> dp(size(adj), vector<pair<int, int>>(2));
for (int u = 0; u < size(dp); ++u) {
for (auto& x : dp[u]) {
x.second = u;
}
}
const function<void (int, int)> dfs1 = [&](int u, int p) {
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
dfs1(v, u);
auto curr = increase(dp[v][0]);
for (auto& x : dp[u]) {
if (curr > x) {
swap(curr, x);
}
}
}
};
dfs1(0, -1);
vector<int> result(size(adj), -1);
const function<void (int, int, pair<int, int>)> dfs2 = [&](int u, int p, const auto& curr) {
for (const auto& v : adj[u]) {
if (v == p) {
continue;
}
dfs2(v, u, increase(max(dp[u][dp[u][0].second == dp[v][0].second], curr)));
}
result[u] = max(dp[u][0], curr).second;
};
dfs2(0, -1, pair(0, -1));
return result;
}
};