/*
* powered by ANDRIY POPYK
* in honor of MYSELF and SEGMENT DECOMPOSITION and N^(log(N)) and (Harry Potter and the Methods of Rationality) and Monkie D. Luffy
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
//#pragma GCC optimize("O3")
//#pragma GCC target("avx,avx2,fma")
//#pragma GCC optimization ("unroll-loops")
//#pragma GCC target("avx,avx2,sse,sse2,sse3,sse4,popcnt")
using namespace std;
using namespace __gnu_pbds;
#define int long long
#define float long double
#define elif else if
#define endl "\n"
#define mod 1000000007
#define pi acos(-1)
#define eps 0.000000001
#define inf 1000'000'000'000'000'000LL
#define FIXED(a) cout << fixed << setprecision(a)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define time_init auto start = std::chrono::high_resolution_clock::now()
#define time_report \
auto end = std::chrono::high_resolution_clock::now(); \
std::cout << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count() << " ms" << endl
#define debug(x) \
{ cerr << #x << " = " << x << endl; }
#define len(x) (int) x.size()
#define sqr(x) ((x) * (x))
#define cube(x) ((x) * (x) * (x))
#define bit(x, i) (((x) >> (i)) & 1)
#define set_bit(x, i) ((x) | (1LL << (i)))
#define clear_bit(x, i) ((x) & (~(1LL << (i))))
#define toggle_bit(x, i) ((x) ^ (1LL << (i)))
#define low_bit(x) ((x) & (-(x)))
#define count_bit(x) __builtin_popcountll(x)
#define srt(x) sort(all(x))
#define rsrt(x) sort(rall(x))
#define mp make_pair
#define maxel(x) (*max_element(all(x)))
#define minel(x) (*min_element(all(x)))
#define maxelpos(x) (max_element(all(x)) - x.begin())
#define minelpos(x) (min_element(all(x)) - x.begin())
#define sum(x) (accumulate(all(x), 0LL))
#define product(x) (accumulate(all(x), 1LL, multiplies<int>()))
#define gcd __gcd
#define lcm(a, b) ((a) / gcd(a, b) * (b))
#define rev(x) (reverse(all(x)))
#define shift_left(x, k) (rotate(x.begin(), x.begin() + k, x.end()))
#define shift_right(x, k) (rotate(x.rbegin(), x.rbegin() + k, x.rend()))
#define is_sorted(x) (is_sorted_until(all(x)) == x.end())
#define is_even(x) (((x) &1) == 0)
#define is_odd(x) (((x) &1) == 1)
#define pow2(x) (1LL << (x))
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T>
using max_heap = priority_queue<T, vector<T>, less<T>>;
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T>
using ordered_multiset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T>
using matrix = vector<vector<T>>;
template<typename T>
using graph = vector<vector<T>>;
using hashmap = gp_hash_table<int, int, custom_hash>;
template<typename T>
vector<T> vect(int n, T val) {
return vector<T>(n, val);
}
template<typename T>
vector<vector<T>> vect(int n, int m, T val) {
return vector<vector<T>>(n, vector<T>(m, val));
}
template<typename T>
vector<vector<vector<T>>> vect(int n, int m, int k, T val) {
return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, val)));
}
template<typename T>
vector<vector<vector<vector<T>>>> vect(int n, int m, int k, int l, T val) {
return vector<vector<vector<vector<T>>>>(n, vector<vector<vector<T>>>(m, vector<vector<T>>(k, vector<T>(l, val))));
}
template<typename T>
matrix<T> new_matrix(int n, int m, T val) {
return matrix<T>(n, vector<T>(m, val));
}
template<typename T>
graph<T> new_graph(int n) {
return graph<T>(n);
}
template<class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template<class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
template<typename T>
using vec = vector<T>;
using pII = pair<int, int>;
template<typename T>
using enumerated = pair<T, int>;
struct BlockCutTree {
public:
graph<int> g;
int timer, n;
vec<int> fup, tin;
vec<bool> used;
vec<vec<pII>> edge_components;
vec<int> components;
vec<int> comp_vertices;
vec<int> cut_points;
vec<bool> is_cut_point;
stack<pII> buffer;
int component_cnt;
void dfs(int v, int p) {
tin[v] = fup[v] = timer++;
used[v] = true;
bool is_cut = false;
int child_cnt = 0;
for (auto u: g[v]) {
if (u == p)
continue;
if (!used[u]) {
child_cnt++;
buffer.emplace(v, u);
dfs(u, v);
if (fup[u] >= tin[v]) {
is_cut = true;
edge_components.emplace_back();
while (true) {
auto [a, b] = buffer.top();
buffer.pop();
edge_components.back().emplace_back(a, b);
if (a == v && b == u) {
break;
}
}
}
chmin(fup[v], fup[u]);
} else {
chmin(fup[v], tin[u]);
if (tin[u] < tin[v]) {
buffer.emplace(v, u);
}
}
}
if (p == -1) {
is_cut = child_cnt > 1;
}
if (p == -1 and child_cnt == 0) {
is_cut = true;
}
if (is_cut) {
cut_points.push_back(v);
is_cut_point[v] = true;
}
}
void build_components() {
for (int i = 0; i < n; ++i) {
if (!used[i]) {
dfs(i, -1);
}
}
components = vec<int>(n);
component_cnt = 0;
for (auto cp: cut_points) {
components[cp] = component_cnt++;
}
for (auto &ec: edge_components) {
for (auto [u, v]: ec) {
if (!is_cut_point[u])
components[u] = component_cnt;
if (!is_cut_point[v])
components[v] = component_cnt;
}
// if (was)
component_cnt++;
}
comp_vertices.resize(component_cnt);
for (int i = 0; i < n; ++i) {
comp_vertices[components[i]]++;
}
}
graph<int> bc_tree;
set<pair<int, int>> good_edge;
void build_tree() {
bc_tree = graph<int>(component_cnt);
set<pair<int, int>> bc_tree_edges;
int id = len(cut_points) - 1;
for (const auto &eg: edge_components) {
id++;
for (auto [u, v]: eg) {
if (is_cut_point[u]) {
// bc_tree_edges[components[u]].insert(id);
// bc_tree_edges[id].insert(components[u]);
int v_u = components[u];
int v_v = id;
if (v_u > v_v) {
swap(v_u, v_v);
}
if (bc_tree_edges.count({v_u, v_v})) {
good_edge.insert({v_u, v_v});
}
bc_tree_edges.emplace(v_u, v_v);
}
if (is_cut_point[v]) {
int v_u = components[v];
int v_v = id;
if (v_u > v_v) {
swap(v_u, v_v);
}
if (bc_tree_edges.count({v_u, v_v})) {
good_edge.insert({v_u, v_v});
}
bc_tree_edges.emplace(v_u, v_v);
}
}
}
// for (int i = 0; i < component_cnt; ++i) {
// for (auto to: bc_tree_edges[i]) {
// bc_tree[i].push_back(to);
// }
// }
for (auto [u, v]: bc_tree_edges) {
bc_tree[u].push_back(v);
bc_tree[v].push_back(u);
}
}
BlockCutTree(graph<int> &g) : g(g) {
n = len(g);
timer = 0;
fup = tin = vec<int>(n);
used = vec<bool>(n);
is_cut_point = vec<bool>(n);
}
void print() {
set<pII> edges;
for (int i = 0; i < component_cnt; ++i) {
for (auto to: bc_tree[i]) {
if (edges.count({i, to}) or edges.count({to, i})) {
continue;
}
edges.emplace(i, to);
}
}
cout << len(edges) << endl;
for (auto [u, v]: edges) {
cout << u + 1 << " " << v + 1 << endl;
}
}
};
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
i64 n, m;
cin >> n >> m;
graph<int> g(n);
for (int i = 0; i < m; ++i) {
int u, v;
cin >> u >> v, --u, --v;
g[u].push_back(v);
g[v].push_back(u);
}
// int all = 0;
// vec<int> sizes(n, 0);
// vec<bool> was(n, false);
/*
function<void(int, int)> dfs = [&](int v, int p) {
if (was[v]) return;
was[v] = true;
sizes[v] = 1;
for (auto u: g[v]) {
if (u == p) continue;
dfs(u, v);
sizes[v] += sizes[u];
}
int top = ttn - sizes[v];
all += top * (sizes[v] - 1) * 2;
for (auto u: g[v]) {
if (u == p) continue;
int tn = sizes[v] - 1 - sizes[u];
all += tn * sizes[u];
}
};
*/
BlockCutTree bct(g);
bct.build_components();
bct.build_tree();
// bct.print();
// cout << endl;
i64 all = 0;
int dn = len(bct.bc_tree);
vec<int> sizes(dn, 0);
vec<int> dec(dn, 0);
vec<bool> was(dn, false);
function<int(int, int)> calc_cur_size = [&](int v, int p) {
int sum = bct.comp_vertices[v];
for (auto u: bct.bc_tree[v]) {
if (u != p)
sum += calc_cur_size(u, v);
}
return sum;
};
int ttn = n;
function<void(int, int)> dfs = [&](int v, int p) {
if (was[v]) return;
was[v] = true;
sizes[v] = bct.comp_vertices[v];
for (auto u: bct.bc_tree[v]) {
if (u == p)
continue;
dfs(u, v);
sizes[v] += sizes[u];
}
if (bct.comp_vertices[v] >= 3) {
int tc = bct.comp_vertices[v];
all += tc * (tc - 1) * (tc - 2);
}
if (bct.comp_vertices[v] >= 2) {
int tc = bct.comp_vertices[v];
int top = ttn - sizes[v];
all += tc * (tc - 1) * top * 2;
}
int top = ttn - sizes[v];
int tc = bct.comp_vertices[v];
dec[v] = 0;
for (auto u: bct.bc_tree[v]) {
if (u == p)
continue;
all += top * tc * sizes[u] * 2;
all += tc * (tc - 1) * sizes[u] * 2;
all += (sizes[u] * (sizes[u] - 1) - dec[u]) * tc;
int dc = sizes[v] - sizes[u] - tc;
all += tc * dc * sizes[u];
// if (bct.is_cut_point[u])
dec[v] += sizes[u] * (sizes[u] - 1)*tc;
}
};
for (int i = 0; i < dn; i++) {
if (!was[i]) {
ttn = calc_cur_size(i, -1);
dfs(i, -1);
}
}
cout << all << endl;
}
Compilation message
count_triplets.cpp: In member function 'void BlockCutTree::dfs(long long int, long long int)':
count_triplets.cpp:174:30: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
174 | auto [a, b] = buffer.top();
| ^
count_triplets.cpp: In member function 'void BlockCutTree::build_components()':
count_triplets.cpp:216:23: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
216 | for (auto [u, v]: ec) {
| ^
count_triplets.cpp: In member function 'void BlockCutTree::build_tree()':
count_triplets.cpp:241:23: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
241 | for (auto [u, v]: eg) {
| ^
count_triplets.cpp:274:19: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
274 | for (auto [u, v]: bc_tree_edges) {
| ^
count_triplets.cpp: In member function 'void BlockCutTree::print()':
count_triplets.cpp:299:19: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
299 | for (auto [u, v]: edges) {
| ^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
1 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
348 KB |
Output is correct |
| 4 |
Correct |
1 ms |
344 KB |
Output is correct |
| 5 |
Correct |
1 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| 7 |
Correct |
0 ms |
344 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
0 ms |
348 KB |
Output is correct |
| 10 |
Correct |
0 ms |
348 KB |
Output is correct |
| 11 |
Incorrect |
0 ms |
348 KB |
Output isn't correct |
| 12 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
1 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
348 KB |
Output is correct |
| 4 |
Correct |
1 ms |
344 KB |
Output is correct |
| 5 |
Correct |
1 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| 7 |
Correct |
0 ms |
344 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
0 ms |
348 KB |
Output is correct |
| 10 |
Correct |
0 ms |
348 KB |
Output is correct |
| 11 |
Incorrect |
0 ms |
348 KB |
Output isn't correct |
| 12 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
58 ms |
32152 KB |
Output is correct |
| 2 |
Correct |
55 ms |
32332 KB |
Output is correct |
| 3 |
Incorrect |
104 ms |
43976 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
856 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
102 ms |
40964 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
860 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
102 ms |
41132 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
1 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
348 KB |
Output is correct |
| 4 |
Correct |
1 ms |
344 KB |
Output is correct |
| 5 |
Correct |
1 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| 7 |
Correct |
0 ms |
344 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
0 ms |
348 KB |
Output is correct |
| 10 |
Correct |
0 ms |
348 KB |
Output is correct |
| 11 |
Incorrect |
0 ms |
348 KB |
Output isn't correct |
| 12 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
1 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
348 KB |
Output is correct |
| 4 |
Correct |
1 ms |
344 KB |
Output is correct |
| 5 |
Correct |
1 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| 7 |
Correct |
0 ms |
344 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
0 ms |
348 KB |
Output is correct |
| 10 |
Correct |
0 ms |
348 KB |
Output is correct |
| 11 |
Incorrect |
0 ms |
348 KB |
Output isn't correct |
| 12 |
Halted |
0 ms |
0 KB |
- |
