CSES-solutions/CSES Problem Set/Police Chase.cpp

/* Problem URL: https://cses.fi/problemset/task/1695 */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

const int INF = INT32_MAX >> 1;

struct dinitz {
	const bool scaling = false; // com scaling -> O(nm log(MAXCAP)),
	int lim;                    // com constante alta
	struct edge {
		int to, cap, rev, flow;
		bool res;
		edge(int to_, int cap_, int rev_, bool res_)
			: to(to_), cap(cap_), rev(rev_), flow(0), res(res_) {}
	};

	vector<vector<edge>> g;
	vector<int> lev, beg;
	ll F;
	dinitz(int n) : g(n), F(0) {}

	void add(int a, int b, int c) {
		g[a].emplace_back(b, c, g[b].size(), false);
		g[b].emplace_back(a, 0, g[a].size()-1, true);
	}
	bool bfs(int s, int t) {
		lev = vector<int>(g.size(), -1); lev[s] = 0;
		beg = vector<int>(g.size(), 0);
		queue<int> q; q.push(s);
		while (q.size()) {
			int u = q.front(); q.pop();
			for (auto& i : g[u]) {
				if (lev[i.to] != -1 or (i.flow == i.cap)) continue;
				if (scaling and i.cap - i.flow < lim) continue;
				lev[i.to] = lev[u] + 1;
				q.push(i.to);
			}
		}
		return lev[t] != -1;
	}
	int dfs(int v, int s, int f = INF) {
		if (!f or v == s) return f;
		for (int& i = beg[v]; i < g[v].size(); i++) {
			auto& e = g[v][i];
			if (lev[e.to] != lev[v] + 1) continue;
			int foi = dfs(e.to, s, min(f, e.cap - e.flow));
			if (!foi) continue;
			e.flow += foi, g[e.to][e.rev].flow -= foi;
			return foi;
		}
		return 0;
	}
	ll max_flow(int s, int t) {
		for (lim = scaling ? (1<<30) : 1; lim; lim /= 2)
			while (bfs(s, t)) while (int ff = dfs(s, t)) F += ff;
		return F;
	}
};

// Recupera as arestas do corte s-t
vector<pair<int, int>> get_cut(dinitz& g, int s, int t) {
	g.max_flow(s, t);
	vector<pair<int, int>> cut;
	vector<int> vis(g.g.size(), 0), st = {s};
	vis[s] = 1;
	while (st.size()) {
		int u = st.back(); st.pop_back();
		for (auto e : g.g[u]) if (!vis[e.to] and e.flow < e.cap)
			vis[e.to] = 1, st.push_back(e.to);
	}
	for (int i = 0; i < g.g.size(); i++) for (auto e : g.g[i])
		if (vis[i] and !vis[e.to] and !e.res) cut.emplace_back(i, e.to);
	return cut;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m;
    cin >> n >> m;

    dinitz din(n);

    while (m--) {
        int a, b;
        cin >> a >> b;
        a--, b--;

        din.add(a, b, 1);
        din.add(b, a, 1);
    }

    V<pair<int, int>> ans = get_cut(din, 0, n - 1);

    cout << ans.size() << '\n';
    for (auto [a, b] : ans) {
        cout << a + 1 << ' ' << b + 1 << '\n';
    }
}