templates
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graph/tarjan_undirected.hpp
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- Last update: 2021-09-12 23:20:08-04:00
- Include:
#include "graph/tarjan_undirected.hpp"
Depends on
template.hpp
Verified with
- tests/graph/articulation_points.test.cpp
- tests/graph/biconnected_components.test.cpp
- tests/graph/bridges.test.cpp
Code
#pragma once
#include "../template.hpp"
const int BICONNECTED_COMPONENTS = 1 << 0, ARTICULATION_POINTS = 1 << 1, BRIDGES = 1 << 2;
template <typename GraphType, typename EdgeType, int MODE> struct Tarjan {
EdgeType E;
int cord = 0;
vector<int> ord, low;
vector<pii> stk;
vector<int> articulation_points;
vector<int> bridges;
vector<vector<pii>> components;
void solve(int N, GraphType &g) {
cord = 0;
ord.assign(N+1, 0); low.assign(N+1, 0);
stk.clear();
if (MODE & BICONNECTED_COMPONENTS) components.clear();
if (MODE & ARTICULATION_POINTS) articulation_points.clear();
if (MODE & BRIDGES) bridges.clear();
function<void(int, int)> tarjan = [&] (int c, int pi) {
bool artic = false;
int cc = 0;
ord[c] = low[c] = ++cord;
for (auto _to : g[c]) {
int to = E.v(_to), toi = E.i(_to);
if (toi != pi) {
if (!ord[to]) {
if (MODE & BICONNECTED_COMPONENTS) stk.emplace_back(c, to);
if (MODE & ARTICULATION_POINTS) cc++;
tarjan(to, toi);
low[c] = min(low[c], low[to]);
// we got an articulation point bois :sunglasses:
if (low[to] >= ord[c]) {
if (MODE & ARTICULATION_POINTS) artic = true;
if (MODE & BICONNECTED_COMPONENTS) {
components.push_back(vector<pii>());
int u, v;
do {
auto _e = stk.back();
stk.pop_back();
tie(u, v) = _e;
components.back().emplace_back(u, v);
} while (u != c || v != to);
}
}
if (MODE & BRIDGES) {
if (low[to] > ord[c])
bridges.push_back(toi);
}
} else if (ord[to] < ord[c]) {
if (MODE & BICONNECTED_COMPONENTS) stk.emplace_back(c, to);
low[c] = min(low[c], ord[to]);
}
}
}
if (MODE & ARTICULATION_POINTS)
if ((pi != -1 && artic) || (pi == -1 && cc > 1))
articulation_points.push_back(c);
};
for (int i = 1; i <= N; i++)
if (!ord[i])
tarjan(i, -1);
}
#if __cplusplus == 201703L // CPP17 only things
void bind(opt_ref<vector<int>> ord0, opt_ref<vector<int>> low0) {
if (ord0) ord.swap(*ord0);
if (low0) low.swap(*low0);
}
#endif
};#line 2 "template.hpp"
#include <bits/stdc++.h>
#define DEBUG 1
using namespace std;
// Defines
#define fs first
#define sn second
#define pb push_back
#define eb emplace_back
#define mpr make_pair
#define mtp make_tuple
#define all(x) (x).begin(), (x).end()
// Basic type definitions
#if __cplusplus == 201703L // CPP17 only things
template <typename T> using opt_ref = optional<reference_wrapper<T>>; // for some templates
#endif
using ll = long long; using ull = unsigned long long; using ld = long double;
using pii = pair<int, int>; using pll = pair<long long, long long>;
#ifdef __GNUG__
// PBDS order statistic tree
#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template <typename T, class comp = less<T>> using os_tree = tree<T, null_type, comp, rb_tree_tag, tree_order_statistics_node_update>;
template <typename K, typename V, class comp = less<K>> using treemap = tree<K, V, comp, rb_tree_tag, tree_order_statistics_node_update>;
// HashSet
#include <ext/pb_ds/assoc_container.hpp>
template <typename T, class Hash> using hashset = gp_hash_table<T, null_type, Hash>;
template <typename K, typename V, class Hash> using hashmap = gp_hash_table<K, V, Hash>;
const ll RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash { ll operator()(ll x) const { return x ^ RANDOM; } };
#endif
// More utilities
int SZ(string &v) { return v.length(); }
template <typename C> int SZ(C &v) { return v.size(); }
template <typename C> void UNIQUE(vector<C> &v) { sort(v.begin(), v.end()); v.resize(unique(v.begin(), v.end()) - v.begin()); }
template <typename T, typename U> void maxa(T &a, U b) { a = max(a, b); }
template <typename T, typename U> void mina(T &a, U b) { a = min(a, b); }
const ll INF = 0x3f3f3f3f, LLINF = 0x3f3f3f3f3f3f3f3f;
#line 3 "graph/tarjan_undirected.hpp"
const int BICONNECTED_COMPONENTS = 1 << 0, ARTICULATION_POINTS = 1 << 1, BRIDGES = 1 << 2;
template <typename GraphType, typename EdgeType, int MODE> struct Tarjan {
EdgeType E;
int cord = 0;
vector<int> ord, low;
vector<pii> stk;
vector<int> articulation_points;
vector<int> bridges;
vector<vector<pii>> components;
void solve(int N, GraphType &g) {
cord = 0;
ord.assign(N+1, 0); low.assign(N+1, 0);
stk.clear();
if (MODE & BICONNECTED_COMPONENTS) components.clear();
if (MODE & ARTICULATION_POINTS) articulation_points.clear();
if (MODE & BRIDGES) bridges.clear();
function<void(int, int)> tarjan = [&] (int c, int pi) {
bool artic = false;
int cc = 0;
ord[c] = low[c] = ++cord;
for (auto _to : g[c]) {
int to = E.v(_to), toi = E.i(_to);
if (toi != pi) {
if (!ord[to]) {
if (MODE & BICONNECTED_COMPONENTS) stk.emplace_back(c, to);
if (MODE & ARTICULATION_POINTS) cc++;
tarjan(to, toi);
low[c] = min(low[c], low[to]);
// we got an articulation point bois :sunglasses:
if (low[to] >= ord[c]) {
if (MODE & ARTICULATION_POINTS) artic = true;
if (MODE & BICONNECTED_COMPONENTS) {
components.push_back(vector<pii>());
int u, v;
do {
auto _e = stk.back();
stk.pop_back();
tie(u, v) = _e;
components.back().emplace_back(u, v);
} while (u != c || v != to);
}
}
if (MODE & BRIDGES) {
if (low[to] > ord[c])
bridges.push_back(toi);
}
} else if (ord[to] < ord[c]) {
if (MODE & BICONNECTED_COMPONENTS) stk.emplace_back(c, to);
low[c] = min(low[c], ord[to]);
}
}
}
if (MODE & ARTICULATION_POINTS)
if ((pi != -1 && artic) || (pi == -1 && cc > 1))
articulation_points.push_back(c);
};
for (int i = 1; i <= N; i++)
if (!ord[i])
tarjan(i, -1);
}
#if __cplusplus == 201703L // CPP17 only things
void bind(opt_ref<vector<int>> ord0, opt_ref<vector<int>> low0) {
if (ord0) ord.swap(*ord0);
if (low0) low.swap(*low0);
}
#endif
};