# competitive-programming-library

This documentation is automatically generated by online-judge-verify-helper

View the Project on GitHub kmyk/competitive-programming-library

# graph/strongly_connected_components.yosupo.test.cpp

## Code

#define PROBLEM "https://judge.yosupo.jp/problem/scc"
#include "graph/strongly_connected_components.hpp"
#include "graph/quotient_graph.hpp"
#include "graph/topological_sort.hpp"
#include "utils/macros.hpp"
#include <cassert>
#include <cstdio>
#include <vector>
using namespace std;

int main() {
// input
int n, m; scanf("%d%d", &n, &m);
vector<vector<int> > g(n);
REP (i, m) {
int a, b; scanf("%d%d", &a, &b);
g[a].push_back(b);
}

// solve
int size; vector<int> component_of; tie(size, component_of) = decompose_to_strongly_connected_components(g);
vector<vector<int> > component(size);
REP (i, n) {
component[component_of[i]].push_back(i);
}
vector<vector<int> > h = make_quotient_graph(g, size, component_of);
vector<int> order = topological_sort(h);
assert (order.size() == size);

// output
printf("%d\n", size);
for (int a : order) {
printf("%d", (int)component[a].size());
for (int i : component[a]) {
printf(" %d", i);
}
printf("\n");
}
return 0;
}



#line 1 "graph/strongly_connected_components.yosupo.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/scc"
#line 2 "graph/strongly_connected_components.hpp"
#include <functional>
#include <utility>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 4 "graph/transpose_graph.hpp"

/**
* @param g is an adjacent list of a digraph
* @note $O(V + E)$
* @see https://en.wikipedia.org/wiki/Transpose_graph
*/
std::vector<std::vector<int> > make_transpose_graph(std::vector<std::vector<int> > const & g) {
int n = g.size();
std::vector<std::vector<int> > h(n);
REP (i, n) {
for (int j : g[i]) {
h[j].push_back(i);
}
}
return h;
}
#line 7 "graph/strongly_connected_components.hpp"

/**
* @brief strongly connected components decomposition, Kosaraju's algorithm / 強連結成分分解
* @return the pair (the number k of components, the function from vertices of g to components)
* @param g is an adjacent list of a digraph
* @param g_rev is the transpose graph of g
* @note $O(V + E)$
*/
std::pair<int, std::vector<int> > decompose_to_strongly_connected_components(const std::vector<std::vector<int> > & g, const std::vector<std::vector<int> > & g_rev) {
int n = g.size();
std::vector<int> acc(n); {
std::vector<bool> used(n);
std::function<void (int)> dfs = [&](int i) {
used[i] = true;
for (int j : g[i]) if (not used[j]) dfs(j);
acc.push_back(i);
};
REP (i,n) if (not used[i]) dfs(i);
reverse(ALL(acc));
}
int size = 0;
std::vector<int> component_of(n); {
std::vector<bool> used(n);
std::function<void (int)> rdfs = [&](int i) {
used[i] = true;
component_of[i] = size;
for (int j : g_rev[i]) if (not used[j]) rdfs(j);
};
for (int i : acc) if (not used[i]) {
rdfs(i);
++ size;
}
}
return { size, move(component_of) };
}

std::pair<int, std::vector<int> > decompose_to_strongly_connected_components(const std::vector<std::vector<int> > & g) {
return decompose_to_strongly_connected_components(g, make_transpose_graph(g));
}
#line 5 "graph/quotient_graph.hpp"

/**
* @param g is an adjacent list of a digraph
* @param size is the size of equivalence classes
* @param component_of is the map from original vertices to equivalence classes
* @note $O(V + E)$
* @see https://en.wikipedia.org/wiki/Quotient_graph
*/
std::vector<std::vector<int> > make_quotient_graph(const std::vector<std::vector<int> > & g, int size, const std::vector<int> & component_of) {
int n = g.size();
std::vector<std::vector<int> > h(size);
REP (i, n) for (int j : g[i]) {
if (component_of[i] != component_of[j]) {
h[component_of[i]].push_back(component_of[j]);
}
}
REP (k, size) {
std::sort(ALL(h[k]));
h[k].erase(std::unique(ALL(h[k])), h[k].end());
}
return h;
}
#line 2 "graph/topological_sort.hpp"
#include <algorithm>
#line 6 "graph/topological_sort.hpp"

/**
* @brief topological sort
* @return a list of vertices which sorted topologically
* @note the empty list is returned if cycles exist
* @note $O(V + E)$
*/
std::vector<int> topological_sort(const std::vector<std::vector<int> > & g) {
int n = g.size();
std::vector<int> order;
std::vector<char> used(n);
std::function<bool (int)> go = [&](int i) {
used[i] = 1;  // in stack
for (int j : g[i]) {
if (used[j] == 1) return true;
if (not used[j]) {
if (go(j)) return true;
}
}
used[i] = 2;  // completely used
order.push_back(i);
return false;
};
REP (i, n) if (not used[i]) {
if (go(i)) return std::vector<int>();
}
std::reverse(ALL(order));
return order;
}
#line 6 "graph/strongly_connected_components.yosupo.test.cpp"
#include <cassert>
#include <cstdio>
#line 9 "graph/strongly_connected_components.yosupo.test.cpp"
using namespace std;

int main() {
// input
int n, m; scanf("%d%d", &n, &m);
vector<vector<int> > g(n);
REP (i, m) {
int a, b; scanf("%d%d", &a, &b);
g[a].push_back(b);
}

// solve
int size; vector<int> component_of; tie(size, component_of) = decompose_to_strongly_connected_components(g);
vector<vector<int> > component(size);
REP (i, n) {
component[component_of[i]].push_back(i);
}
vector<vector<int> > h = make_quotient_graph(g, size, component_of);
vector<int> order = topological_sort(h);
assert (order.size() == size);

// output
printf("%d\n", size);
for (int a : order) {
printf("%d", (int)component[a].size());
for (int i : component[a]) {
printf(" %d", i);
}
printf("\n");
}
return 0;
}