/*
PROG: source
LANG: C++11
_____
.' '.
/ 0 0 \
| ^ |
| \ / |
\ '---' /
'._____.'
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
struct chash
{
int operator()(int x) const
{
x ^= (x >> 20) ^ (x >> 12);
return x ^ (x >> 7) ^ (x >> 4);
}
int operator()(long long x) const
{
return x ^ (x >> 32);
}
};
template<typename T> using orderedset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using hashtable = gp_hash_table<T, T, chash>;
template<class T>
void readi(T &x)
{
T input = 0;
bool negative = false;
char c = ' ';
while (c < '-')
{
c = getchar();
}
if (c == '-')
{
negative = true;
c = getchar();
}
while (c >= '0')
{
input = input * 10 + (c - '0');
c = getchar();
}
if (negative)
{
input = -input;
}
x = input;
}
template<class T>
void printi(T output)
{
if (output == 0)
{
putchar('0');
return;
}
if (output < 0)
{
putchar('-');
output = -output;
}
int aout[20];
int ilen = 0;
while(output)
{
aout[ilen] = ((output % 10));
output /= 10;
ilen++;
}
for (int i = ilen - 1; i >= 0; i--)
{
putchar(aout[i] + '0');
}
return;
}
template<class T>
void ckmin(T &a, T b)
{
a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
a = max(a, b);
}
template<class T>
T normalize(T x, T mod = 1000000007)
{
return (((x % mod) + mod) % mod);
}
long long randomizell(long long mod)
{
return ((1ll << 45) * rand() + (1ll << 30) * rand() + (1ll << 15) * rand() + rand()) % mod;
}
int randomize(int mod)
{
return ((1ll << 15) * rand() + rand()) % mod;
}
#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define debug(x) cerr << #x << " = " << x << endl;
const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-10;
#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 200013
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
int N, M, T, K;
vector<int> edge[MAXN], edge1[MAXN];
int sz[MAXN];
vector<pii> bridge;
vector<pii> edges;
bool ap[MAXN];
vector<int> bcc[MAXN];
int id[MAXN], aid[MAXN];
int parent[MAXN];
int subtree[MAXN];
int disc[MAXN], low[MAXN];
int dsu[MAXN], dsz[MAXN];
vector<int> nodes[MAXN];
bool seen[MAXN];
ll ans = 0, tot = 0;
int find_parent(int u)
{
return (u == dsu[u] ? u : dsu[u] = find_parent(dsu[u]));
}
void merge(int u, int v)
{
u = find_parent(u);
v = find_parent(v);
if (u == v) return;
if (dsz[u] > dsz[v])
{
swap(u, v);
}
dsz[v] += dsz[u];
dsz[u] = 0;
dsu[u] = v;
return;
}
void dfs(int u, bool head = false)
{
disc[u] = T;
low[u] = T;
seen[u] = true;
T++;
int children = 0;
for (int v : edge[u])
{
if (v == parent[u])
{
continue;
}
if (seen[v])
{
ckmin(low[u], low[v]);
continue;
}
children++;
parent[v] = u;
edges.PB({u, v});
dfs(v);
ckmin(low[u], low[v]);
if (low[v] >= disc[u])
{
if (low[v] != disc[u])
{
bridge.PB({u, v});
}
if (!head)
{
ap[u] = true;
while(edges.back() != MP(u, v))
{
bcc[K].PB(edges.back().fi);
bcc[K].PB(edges.back().se);
edges.pop_back();
}
bcc[K].PB(edges.back().fi);
bcc[K].PB(edges.back().se);
edges.pop_back();
K++;
}
}
if (head)
{
if (children > 1)
{
ap[u] = true;
}
while(edges.back() != MP(u, v))
{
bcc[K].PB(edges.back().fi);
bcc[K].PB(edges.back().se);
edges.pop_back();
}
bcc[K].PB(edges.back().fi);
bcc[K].PB(edges.back().se);
edges.pop_back();
K++;
}
}
}
void dfs1(int u)
{
subtree[u] = sz[u];
for (int v : edge1[u])
{
if (v == parent[u])
{
continue;
}
parent[v] = u;
dfs1(v);
subtree[u] += subtree[v];
}
return;
}
int32_t main()
{
ios_base::sync_with_stdio(0);
srand(time(0));
// cout << fixed << setprecision(10);
// cerr << fixed << setprecision(10);
if (fopen("input.in", "r"))
{
freopen ("input.in", "r", stdin);
freopen ("output.out", "w", stdout);
}
cin >> N >> M;
for (int i = 0; i < N; i++)
{
dsu[i] = i;
dsz[i] = i;
}
for (int i = 0; i < M; i++)
{
int u, v;
cin >> u >> v;
u--; v--;
edge[u].PB(v);
edge[v].PB(u);
merge(u, v);
}
for (int i = 0; i < N; i++)
{
parent[i] = N;
}
for (int i = 0; i < N; i++)
{
nodes[find_parent(i)].PB(i);
}
for (int cc = 0; cc < N; cc++)
{
if (find_parent(cc) != cc)
{
continue;
}
int n = nodes[cc].size();
dfs(cc, 1);
for (int i = 0; i < K; i++)
{
sort(bcc[i].begin(), bcc[i].end());
bcc[i].erase(unique(bcc[i].begin(), bcc[i].end()), bcc[i].end());
// cerr << "bcc # " << i << ":";
for (int u : bcc[i])
{
// cerr << ' ' << u;
id[u] = i;
if (!ap[u])
{
sz[i]++;
}
}
// cerr << endl;
}
for (int i = 0; i < n; i++)
{
int u = nodes[cc][i];
if (ap[u])
{
aid[u] = K;
sz[K] = 1;
K++;
// cerr << "ap " << i << " id " << K - 1 << endl;
}
}
for (int i = 0; i < K; i++)
{
// cerr << "bcc " << i << ":";
for (int u : bcc[i])
{
// cerr << ' ' << u;
if (ap[u])
{
edge1[i].PB(aid[u]);
edge1[aid[u]].PB(i);
// cerr << "edge1 " << aid[u] << ' ' << i << endl;
}
}
// cerr << endl;
}
// for (int i = 0; i < K; i++)
// {
// for (int u : edge1[i])
// {
// if (i <= u) cerr << i << " -> " << u << endl;
// }
// }
for (int i = 0; i < K; i++)
{
parent[i] = K;
}
dfs1(0);
//all 3 distinct blocks
//case 1: it's a path
for (int i = 0; i < K; i++)
{
tot += 2ll * sz[i] * (subtree[i] - sz[i]) * (n - subtree[i]);
}
//case 2: side, go to a ap, then back to a cc it's in OR backward
for (int i = 0; i < K; i++)
{
if (bcc[i].empty()) continue;
for (int v : edge1[i])
{
if (v == parent[i]) continue;
ans += 2ll * (n - subtree[v] - sz[i]) * sz[i];
}
if (i) tot += 2ll * (subtree[i] - sz[i]) * sz[i];
}
//three equal guys
for (int i = 0; i < K; i++)
{
tot += 1ll * sz[i] * (sz[i] - 1) * (sz[i] - 2);
}
//a=b or b=c
for (int i = 0; i < K; i++)
{
tot += 2ll * sz[i] * (sz[i] - 1) * (n - sz[i]);
}
//a=c
for (int i = 0; i < K; i++)
{
if (bcc[i].empty()) continue;
tot += 1ll * sz[i] * (sz[i] - 1) * (edge1[i].size());
}
for (int i = 0; i < K; i++)
{
bcc[i].clear();
sz[i] = 0;
edge1[i].clear();
subtree[i] = 0;
}
ans += tot;
K = 0; T = 0; tot = 0;
}
// for (int i = 0; i < K; i++)
// {
// for (int v : edge1[i])
// {
// cerr << i << "->" << v << endl;
// }
// cerr << "size " << i << " = " << sz[i] << endl;
// }
// for (int i = 0; i < K; i++)
// {
// cerr << "subtree " << i << "=" << subtree[i] << endl;
// }
//if a -> b must pass through c, then: a -> b -> c is bad; c -> b -> a is bad, c -> a -> b is bad, b -> a -> c
//three separate components
cout << ans << '\n';
// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
return 0;
}
Compilation message
count_triplets.cpp: In function 'int32_t main()':
count_triplets.cpp:264:25: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
freopen ("input.in", "r", stdin);
~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
count_triplets.cpp:265:25: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
freopen ("output.out", "w", stdout);
~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
21 ms |
19192 KB |
Output is correct |
| 2 |
Correct |
23 ms |
19304 KB |
Output is correct |
| 3 |
Correct |
22 ms |
19304 KB |
Output is correct |
| 4 |
Correct |
22 ms |
19400 KB |
Output is correct |
| 5 |
Correct |
23 ms |
19444 KB |
Output is correct |
| 6 |
Correct |
25 ms |
19444 KB |
Output is correct |
| 7 |
Incorrect |
20 ms |
19444 KB |
Output isn't correct |
| 8 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
21 ms |
19192 KB |
Output is correct |
| 2 |
Correct |
23 ms |
19304 KB |
Output is correct |
| 3 |
Correct |
22 ms |
19304 KB |
Output is correct |
| 4 |
Correct |
22 ms |
19400 KB |
Output is correct |
| 5 |
Correct |
23 ms |
19444 KB |
Output is correct |
| 6 |
Correct |
25 ms |
19444 KB |
Output is correct |
| 7 |
Incorrect |
20 ms |
19444 KB |
Output isn't correct |
| 8 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
174 ms |
37960 KB |
Output is correct |
| 2 |
Correct |
185 ms |
39432 KB |
Output is correct |
| 3 |
Correct |
238 ms |
41564 KB |
Output is correct |
| 4 |
Correct |
227 ms |
43128 KB |
Output is correct |
| 5 |
Correct |
209 ms |
43128 KB |
Output is correct |
| 6 |
Correct |
278 ms |
45968 KB |
Output is correct |
| 7 |
Correct |
244 ms |
45968 KB |
Output is correct |
| 8 |
Correct |
224 ms |
45968 KB |
Output is correct |
| 9 |
Correct |
228 ms |
45968 KB |
Output is correct |
| 10 |
Correct |
208 ms |
45968 KB |
Output is correct |
| 11 |
Correct |
220 ms |
45968 KB |
Output is correct |
| 12 |
Correct |
163 ms |
45968 KB |
Output is correct |
| 13 |
Correct |
154 ms |
45968 KB |
Output is correct |
| 14 |
Correct |
138 ms |
45968 KB |
Output is correct |
| 15 |
Correct |
156 ms |
45968 KB |
Output is correct |
| 16 |
Correct |
160 ms |
45968 KB |
Output is correct |
| 17 |
Correct |
39 ms |
45968 KB |
Output is correct |
| 18 |
Correct |
34 ms |
45968 KB |
Output is correct |
| 19 |
Correct |
35 ms |
45968 KB |
Output is correct |
| 20 |
Correct |
35 ms |
45968 KB |
Output is correct |
| 21 |
Correct |
41 ms |
45968 KB |
Output is correct |
| 22 |
Correct |
36 ms |
45968 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
20 ms |
45968 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
238 ms |
55476 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
22 ms |
55476 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
233 ms |
56656 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
21 ms |
19192 KB |
Output is correct |
| 2 |
Correct |
23 ms |
19304 KB |
Output is correct |
| 3 |
Correct |
22 ms |
19304 KB |
Output is correct |
| 4 |
Correct |
22 ms |
19400 KB |
Output is correct |
| 5 |
Correct |
23 ms |
19444 KB |
Output is correct |
| 6 |
Correct |
25 ms |
19444 KB |
Output is correct |
| 7 |
Incorrect |
20 ms |
19444 KB |
Output isn't correct |
| 8 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
21 ms |
19192 KB |
Output is correct |
| 2 |
Correct |
23 ms |
19304 KB |
Output is correct |
| 3 |
Correct |
22 ms |
19304 KB |
Output is correct |
| 4 |
Correct |
22 ms |
19400 KB |
Output is correct |
| 5 |
Correct |
23 ms |
19444 KB |
Output is correct |
| 6 |
Correct |
25 ms |
19444 KB |
Output is correct |
| 7 |
Incorrect |
20 ms |
19444 KB |
Output isn't correct |
| 8 |
Halted |
0 ms |
0 KB |
- |
