#include <bits/stdc++.h>
using namespace std;
int n, m;
typedef vector<int> vi;
typedef pair<int,int> ii;
struct node{
int depth = -1;
int low;
int parent;
bool vis = false;
bool isArti = false;
vi adj;
};
vector<unordered_set<int> > biconnected;
stack<int> s; ///this is only needed for biconnected components
///note: this will ignore single nodes with no edges
static node g[200005];
int rootChildren = 0;
void dfs(int u){
if(g[u].depth == -1) g[u].depth = g[g[u].parent].depth + 1;
g[u].low = g[u].depth;
g[u].vis = true;
s.push(u);
for(int i = 0;i < g[u].adj.size();i++){
int v = g[u].adj[i];
if(!g[v].vis){
g[v].parent = u;
if(g[u].depth == 0) rootChildren++;
dfs(v);
g[u].low = min(g[u].low,g[v].low);
if(g[v].low >= g[u].depth){
g[u].isArti = true;
g[u].low = min(g[u].low,g[v].low);
unordered_set<int> newSet;
int nn;
biconnected.push_back(newSet); ///create new biconnected component
do{
assert(!s.empty());
nn = s.top();
s.pop();
biconnected.back().insert(nn);
}while(nn != u);
}
}
else if(v != g[u].parent){
g[u].low = min(g[u].low,g[v].depth); ///g[v].depth not num!!!!!!
}
}
}
struct node2{
long long sz;
long long dp = 0;
bool isArti = false;
bool vis = false;
int r;
int p = -1;
vi adj;
};
vector<node2> bct; ///block-cut tree
long long root = -1;
void dp(int u){
if(bct[u].vis) return;
bct[u].vis = true;
bct[u].dp = bct[u].sz;
bct[u].r = root;
for(int i = 0;i < bct[u].adj.size();i++){
int v = bct[u].adj[i];
if(bct[v].vis) continue;
bct[v].p = u;
dp(v);
bct[u].dp += bct[v].dp;
}
}
int main()
{
cin >> n >> m;
ii edges[m];
for(int i = 0;i < m;i++){
int a, b;
cin >> a >> b;
a--;
b--;
g[a].adj.push_back(b);
g[b].adj.push_back(a);
edges[i] = ii(a,b);
}
for(int i = 0;i < n;i++){
if(!g[i].vis){
rootChildren = 0;
g[i].depth = 0;
dfs(i);
if(rootChildren > 1) g[i].isArti = true;
else g[i].isArti = false; ///this line is needed
}
}
unordered_map<int,int> artis;
for(int i = 0;i < n;i++){
if(g[i].isArti){
artis[i] = bct.size();
node2 nn;
nn.sz = 1;
nn.isArti = true;
bct.push_back(nn);
}
}
for(int i = 0;i < biconnected.size();i++){
node2 nn;
nn.sz = biconnected[i].size();
nn.isArti = false;
for(unordered_set<int>::iterator it = biconnected[i].begin();it != biconnected[i].end();it++){
if(artis.find(*it) != artis.end()){
nn.adj.push_back(artis[*it]);
bct[artis[*it]].adj.push_back(bct.size());
nn.sz--;
}
}
bct.push_back(nn);
}
for(int i = 0;i < bct.size();i++){
root = i;
dp(i);
}
long long ans = 0ll;
for(int i = 0;i < bct.size();i++){
vector<long long> branches;
vector<long long> branchStart;
long long total = 0ll;
for(int j = 0;j < bct[i].adj.size();j++){
if(bct[i].adj[j] != bct[i].p){
branches.push_back(bct[bct[i].adj[j]].dp);
branchStart.push_back(bct[bct[i].adj[j]].sz);
}
}
if(bct[i].p >= 0){
branches.push_back(bct[bct[i].r].dp - bct[i].dp);
branchStart.push_back(bct[bct[i].p].sz);
}
for(int j = 0;j < branches.size();j++) total += branches[j];
long long extra = 0ll;
if(!bct[i].isArti) extra = max(0ll,(long long)(bct[i].adj.size())-2);
for(int j = 0;j < branches.size();j++){
///branch1 to self or neighbor articulation point to branch2
ans += branches[j] * (total - branches[j]) * (bct[i].sz + extra);
///branch to self to self or self to self to branch
ans += 2 * (bct[i].sz) * (bct[i].sz - 1) * branches[j];
if(bct[i].isArti){
///direct branch to self to same branch(not reverse) or its reverse
ans += 2ll * bct[i].sz * branchStart[j] * (branches[j] - branchStart[j]);
///direct branch to self to direct or its reverse
ans += bct[i].sz * (branchStart[j]) * (branchStart[j] - 1);
}
}
///self to self to self
ans += (bct[i].sz) * (bct[i].sz - 1) * (bct[i].sz - 2);
}
cout << ans;
}
Compilation message
count_triplets.cpp: In function 'void dfs(int)':
count_triplets.cpp:25:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
25 | for(int i = 0;i < g[u].adj.size();i++){
| ~~^~~~~~~~~~~~~~~~~
count_triplets.cpp: In function 'void dp(int)':
count_triplets.cpp:70:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
70 | for(int i = 0;i < bct[u].adj.size();i++){
| ~~^~~~~~~~~~~~~~~~~~~
count_triplets.cpp: In function 'int main()':
count_triplets.cpp:113:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::unordered_set<int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
113 | for(int i = 0;i < biconnected.size();i++){
| ~~^~~~~~~~~~~~~~~~~~~~
count_triplets.cpp:126:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<node2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
126 | for(int i = 0;i < bct.size();i++){
| ~~^~~~~~~~~~~~
count_triplets.cpp:132:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<node2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
132 | for(int i = 0;i < bct.size();i++){
| ~~^~~~~~~~~~~~
count_triplets.cpp:136:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
136 | for(int j = 0;j < bct[i].adj.size();j++){
| ~~^~~~~~~~~~~~~~~~~~~
count_triplets.cpp:146:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
146 | for(int j = 0;j < branches.size();j++) total += branches[j];
| ~~^~~~~~~~~~~~~~~~~
count_triplets.cpp:149:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
149 | for(int j = 0;j < branches.size();j++){
| ~~^~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 2 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 3 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 4 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 5 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 6 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 7 |
Runtime error |
16 ms |
16364 KB |
Execution killed with signal 6 |
| 8 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 2 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 3 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 4 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 5 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 6 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 7 |
Runtime error |
16 ms |
16364 KB |
Execution killed with signal 6 |
| 8 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
156 ms |
34788 KB |
Output is correct |
| 2 |
Correct |
159 ms |
34724 KB |
Output is correct |
| 3 |
Runtime error |
196 ms |
59048 KB |
Execution killed with signal 6 |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
18 ms |
16540 KB |
Execution killed with signal 6 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
138 ms |
25836 KB |
Execution killed with signal 6 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
17 ms |
16364 KB |
Execution killed with signal 6 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
124 ms |
25836 KB |
Execution killed with signal 6 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 2 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 3 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 4 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 5 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 6 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 7 |
Runtime error |
16 ms |
16364 KB |
Execution killed with signal 6 |
| 8 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 2 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 3 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 4 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 5 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 6 |
Correct |
6 ms |
8172 KB |
Output is correct |
| 7 |
Runtime error |
16 ms |
16364 KB |
Execution killed with signal 6 |
| 8 |
Halted |
0 ms |
0 KB |
- |
