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Add graph/ebcc.cc 

Signed-off-by: subcrip <contact@subc.rip>
This commit is contained in:
subcrip 2024-11-20 14:47:57 +00:00
parent cb03157987
commit d7f3dafa12
1 changed files with 98 additions and 0 deletions
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// WARN: Input should be a simple graph
//
// Returns: (BCC count, indices of BCC of each vertex)
//
// BCC index starts from 1
pair<int, vector<int>> ebcc(const vector<vector<int>>& ch) {
int n = ch.size() - 1;
vector<int> c(n + 1);
vector<int> low(n + 1), dfn(n + 1);
vector<bool> vis(n + 1);
vector<int> stack;
int time = 0;
int cnt = 0;
auto dfs = [&] (auto dfs, int v, int pa) -> void {
low[v] = dfn[v] = ++time;
stack.emplace_back(v);
vis[v] = 1;
for (auto&& u : ch[v]) {
if (u == pa) continue;
if (not dfn[u]) {
dfs(dfs, u, v);
chmin(low[v], low[u]);
} else if (vis[u]) {
chmin(low[v], dfn[u]);
}
}
if (dfn[v] == low[v]) {
cnt += 1;
c[v] = cnt;
while (stack.back() != v) {
c[stack.back()] = cnt;
vis[stack.back()] = 0;
stack.pop_back();
}
stack.pop_back();
}
};
for (int i = 1; i <= n; ++i) {
if (not dfn[i]) {
dfs(dfs, i, 0);
}
}
return { cnt, c };
}
// INFO: This function treats vertex pairs that have multiple edges as eBCCs.
//
// Returns: (BCC count, indices of BCC of each vertex)
//
// BCC index starts from 1
pair<int, vector<int>> ebcc_with_mult(const vector<vector<pii>>& ch) {
int n = ch.size() - 1;
vector<int> c(n + 1);
vector<int> low(n + 1), dfn(n + 1);
vector<bool> vis(n + 1);
vector<int> stack;
int time = 0;
int cnt = 0;
auto dfs = [&] (auto dfs, int v, int prev_idx) -> void {
low[v] = dfn[v] = ++time;
stack.emplace_back(v);
vis[v] = 1;
for (auto&& [u, i] : ch[v]) {
if (i == prev_idx) continue;
if (not dfn[u]) {
dfs(dfs, u, i);
chmin(low[v], low[u]);
} else if (vis[u]) {
chmin(low[v], dfn[u]);
}
}
if (dfn[v] == low[v]) {
cnt += 1;
c[v] = cnt;
while (stack.back() != v) {
c[stack.back()] = cnt;
vis[stack.back()] = 0;
stack.pop_back();
}
stack.pop_back();
}
};
for (int i = 1; i <= n; ++i) {
if (not dfn[i]) {
dfs(dfs, i, -1);
}
}
return { cnt, c };
}