/
divide-nodes-into-the-maximum-number-of-groups.cpp
148 lines (144 loc) · 4.34 KB
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divide-nodes-into-the-maximum-number-of-groups.cpp
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// Time: O(n^2)
// Space: O(n)
// iterative dfs, bfs
class Solution {
public:
int magnificentSets(int n, vector<vector<int>>& edges) {
vector<vector<int>> adj(n);
for (const auto& e : edges) {
adj[e[0] - 1].emplace_back(e[1] - 1);
adj[e[1] - 1].emplace_back(e[0] - 1);
}
vector<int> lookup(n, -1);
const auto& iter_dfs = [&](int u) {
vector<int> group;
vector<int> stk = {u};
lookup[u] = 0;
while (!empty(stk)) {
const auto u = stk.back(); stk.pop_back();
group.emplace_back(u);
for (const auto& v : adj[u]) {
if (lookup[v] != -1) {
if (lookup[v] == lookup[u]) { // odd-length cycle, not bipartite
return vector<int>();
}
continue;
}
lookup[v] = lookup[u] ^ 1;
stk.emplace_back(v);
}
}
return group;
};
const auto& bfs = [&](int u) {
int result = 0;
vector<bool> lookup(n);
vector<int> q = {u};
lookup[u] = true;
for (; !empty(q); ++result) {
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 result;
};
int result = 0;
for (int u = 0; u < n; ++u) {
if (lookup[u] != -1) {
continue;
}
const auto& group = iter_dfs(u);
if (empty(group)) {
return -1;
}
int mx = 0;
for (const auto& u : group) {
mx = max(mx, bfs(u));
}
result += mx;
}
return result;
}
};
// Time: O(n^2)
// Space: O(n)
// bfs
class Solution2 {
public:
int magnificentSets(int n, vector<vector<int>>& edges) {
vector<vector<int>> adj(n);
for (const auto& e : edges) {
adj[e[0] - 1].emplace_back(e[1] - 1);
adj[e[1] - 1].emplace_back(e[0] - 1);
}
vector<bool> lookup(n);
const auto& bfs = [&](int u) {
vector<int> group = {u};
vector<int> q = {u};
lookup[u] = true;
while (!empty(q)) {
vector<int> new_q;
for (const auto& u : q) {
group.emplace_back(u);
for (const auto& v : adj[u]) {
if (lookup[v]) {
continue;
}
lookup[v] = true;
new_q.emplace_back(v);
}
}
q = move(new_q);
}
return group;
};
const auto& bfs2 = [&](int u) {
int result = 0;
vector<bool> lookup(n);
unordered_set<int> q = {u};
lookup[u] = true;
for (; !empty(q); ++result) {
unordered_set<int> new_q;
for (const auto& u : q) {
for (const auto& v : adj[u]) {
if (q.count(v)) {
return 0;
}
if (lookup[v]) {
continue;
}
lookup[v] = true;
new_q.emplace(v);
}
}
q = move(new_q);
}
return result;
};
int result = 0;
for (int u = 0; u < n; ++u) {
if (lookup[u]) {
continue;
}
const auto& group = bfs(u);
int mx = 0;
for (const auto& u : group) {
const int d = bfs2(u);
if (d == 0) {
return -1;
}
mx = max(mx, d);
}
result += mx;
}
return result;
}
};