結果

問題 No.1615 Double Down
コンテスト
ユーザー shobonvip
提出日時 2025-11-17 14:50:17
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,534 ms / 10,000 ms
コード長 10,471 bytes
コンパイル時間 2,950 ms
コンパイル使用メモリ 236,104 KB
実行使用メモリ 19,784 KB
最終ジャッジ日時 2025-11-17 14:51:00
合計ジャッジ時間 36,942 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 54
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ソースコード

diff # 

/**
	author:  shobonvip
	created: 2025.11.17 14:16:14
**/

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

template <typename T> bool chmin(T &a, const T &b) {
	if (a <= b) return false;
	a = b;
	return true;
}

template <typename T> bool chmax(T &a, const T &b) {
	if (a >= b) return false;
	a = b;
	return true;
}

template <typename T> T max(vector<T> &a){
	assert(!a.empty());
	T ret = a[0];
	for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]);
	return ret;
}

template <typename T> T min(vector<T> &a){
	assert(!a.empty());
	T ret = a[0];
	for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]);
	return ret;
}

template <typename T> T sum(vector<T> &a){
	T ret = 0;
	for (int i=0; i<(int)a.size(); i++) ret += a[i];
	return ret;
}

struct scc_graph {
   int n, k;
   vector<vector<int>> g, rg;
   vector<int> vs, cmp, seen;
   void dfs(int v) {
      seen[v] = 1;
      for(int u : g[v]) {
         if(seen[u] < 0) dfs(u);
      }
      vs.emplace_back(v);
   }
   void rdfs(int v) {
      cmp[v] = k;
      for(int u : rg[v]) {
         if(cmp[u] < 0) rdfs(u);
      }
   }
   scc_graph(int _n) : n(_n), g(_n), rg(_n) {}
   void add_edge(int f, int t) {
      g[f].emplace_back(t);
      rg[t].emplace_back(f);
   }
   vector<vector<int>> scc() {
      seen.assign(n, -1);
      rep(i, 0, n) {
         if(seen[i] < 0) dfs(i);
      }
      reverse(all(vs));
      cmp.assign(n, -1);
      k = 0;
      for(int v : vs) {
         if(cmp[v] < 0) {
            rdfs(v);
            k++;
         }
      }
      vector<vector<int>> ret(k);
      rep(i, 0, n) { ret[cmp[i]].emplace_back(i); }
      return ret;
   }
};

// all hash: cb5cee
template<class Cap> struct mf_graph {
   struct nedge {
      int to, rev;
      Cap cap;
   };

   int nn;
   vector<pair<int, int>> pos;
   vector<vector<nedge>> g;
   mf_graph() : nn(0) {}
   explicit mf_graph(int n) : nn(n), g(n) {}

   int add_edge(int from, int to, Cap cap) {
      int m = pos.size();
      pos.push_back({from, int(g[from].size())});
      int frid = int(g[from].size());
      int toid = int(g[to].size());
      if(from == to) toid++;
      g[from].push_back(nedge{to, toid, cap});
      g[to].push_back(nedge{from, frid, 0});
      return m;
   }

   Cap flow(int s, int t) { return flow(s, t, numeric_limits<Cap>::max()); }

   Cap flow(int s, int t, Cap flow_limit) {
      vector<int> lv(nn), iter(nn);
      queue<int> q;
      auto bfs = [&]() {
         fill(all(lv), -1);
         lv[s] = 0;
         queue<int>().swap(q);
         q.push(s);
         while(!q.empty()) {
            int v = q.front();
            q.pop();
            for(auto e : g[v]) {
               if(e.cap == 0 || lv[e.to] >= 0) continue;
               lv[e.to] = lv[v] + 1;
               if(e.to == t) return;
               q.push(e.to);
            }
         }
      };

      auto dfs = [&](auto self, int v, Cap up) {
         if(v == s) return up;
         Cap res = 0;
         int lvvv = lv[v];
         for(int& i = iter[v]; i < int(g[v].size()); i++) {
            nedge& e = g[v][i];
            if(lvvv <= lv[e.to] || g[e.to][e.rev].cap == 0) continue;
            Cap d = self(self, e.to, min(up - res, g[e.to][e.rev].cap));
            if(d <= 0) continue;
            g[v][i].cap += d;
            g[e.to][e.rev].cap -= d;
            res += d;
            if(res == up) return res;
         }
         lv[v] = nn;
         return res;
      };

      Cap flow = 0;
      while(flow < flow_limit) {
         bfs();
         if(lv[t] == -1) break;
         fill(all(iter), 0);
         Cap f = dfs(dfs, t, flow_limit - flow);
         if(!f) break;
         flow += f;
      }
      return flow;
   }

   /*
   struct edge {
      int from, to;
      Cap cap, flow;
   };

   edge get_edge(int i) {
      int m = int(pos.size());
      auto _e = g[pos[i].first][pos[i].second];
      auto _re = g[_e.to][_e.rev];
      return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
   }

   vector<bool> min_cut(int s) {
      vector<bool> visited(nn);
      queue<int> q;
      q.push(s);
      while(!q.empty()) {
         int p = q.front();
         q.pop();
         visited[p] = true;
         for(auto e : g[p]) {
            if(e.cap && !visited[e.to]) {
               visited[e.to] = true;
               q.push(e.to);
            }
         }
      }
      return visited;
   }

   vector<edge> edges() {
      int m = int(pos.size());
      vector<edge> result;
      for(int i = 0; i < m; i++) { result.push_back(get_edge(i)); }
      return result;
   }
          */
};

vector<pair<vector<int>,vector<int>>>
dm_decomposition(int L, int R, vector<pair<int,int>> edges) {
	for (auto [x, y]: edges) {
		assert(0 <= x && x < L);
		assert(0 <= y && y < R);
	}

	mf_graph<int> mf(L+R+2);
	for (auto [x, y]: edges) {
		mf.add_edge(x, y+L, 1);
	}
	rep(i,0,L) mf.add_edge(L+R, i, 1);
	rep(i,0,R) mf.add_edge(i+L, L+R+1, 1);
	mf.flow(L+R, L+R+1);
	vector<int> match(L+R, -1);
	rep(x,0,L) {
		for (auto &e: mf.g[x]) {
			if (L <= e.to && e.to < L+R && e.cap == 0) {
				match[x] = e.to;
				match[e.to] = x;
			}
		}
	}

	scc_graph scc(L+R);
	for (auto [x,y]: edges) {
		scc.add_edge(x, y+L);
	}
	rep(i,0,L) {
		if (match[i] >= L) scc.add_edge(match[i], i);
	}

	auto ns = scc.scc();
	vector<int> cmp_map(ns.size(), -2);
	vector<int> vis(L+R);
	vector<int> st;
	rep(c,0,2) {
		vector<vector<int>> to(L+R);
		auto color = [&L](int x) {
			return x >= L;
		};
		for (auto [u, v]: edges) {
			v += L;
			if (color(u) != c) swap(u, v);
			to[u].push_back(v);
			if(match[u] == v) to[v].push_back(u);
		}
		rep(i,0,L+R) {
			if (match[i]>=0 || color(i) != c || vis[i]) continue;
			vis[i] = 1; st = {i};
			while(!st.empty()) {
				int now = st.back();
				cmp_map[scc.cmp[now]] = c-1;
				st.pop_back();
				for (int nxt: to[now]) {
					if (!vis[nxt]) {
						vis[nxt] = 1;
						st.push_back(nxt);
					}
				}
			}
		}
	}

	int nset = 1;
	rep(n,0,(int)ns.size()) {
		if (cmp_map[n] == -2) cmp_map[n] = nset++;
	}
	for (auto &x: cmp_map) {
		if (x==-1) x = nset;
	}
	nset++;
	vector<pair<vector<int>,vector<int>>> groups(nset);
	rep(i,0,L){
		if (match[i]<0) continue;
		int c = cmp_map[scc.cmp[i]];
		groups[c].first.push_back(i);
		groups[c].second.push_back(match[i]-L);
	}
	rep(i,0,L) {
		if (match[i]>=0) continue;
		int c = cmp_map[scc.cmp[i]];
		groups[c].first.push_back(i);
	}
	rep(i,0,R) {
		if (match[L+i]>=0) continue;
		int c = cmp_map[scc.cmp[L+i]];
		groups[c].second.push_back(i);
	}
	return groups;
}

// https://hitonanode.github.io/cplib-cpp/graph/test/dulmage_mendelsohn.yuki1615.test.cpp

std::vector<std::pair<std::vector<int>, std::vector<int>>>
verify_dulmage_mendelsohn(int L, int R, const std::vector<std::pair<int, int>> &edges) {
    auto ret = dm_decomposition(L, R, edges);
    assert(ret.size() >= 2);
    vector<int> lord(L, -1), rord(R, -1);
    set<pair<int, int>> edges_set(edges.begin(), edges.end());

    for (int igrp = 0; igrp < int(ret.size()); ++igrp) {
        for (int vl : ret[igrp].first) {
            assert(lord[vl] < 0);
            lord[vl] = igrp;
        }
        for (int vr : ret[igrp].second) {
            assert(rord[vr] < 0);
            rord[vr] = igrp;
        }
        if (igrp == 0) {
            assert(ret[igrp].first.size() < ret[igrp].second.size() or ret[igrp].first.empty());
        } else if (igrp + 1 == int(ret.size())) {
            assert(ret[igrp].first.size() > ret[igrp].second.size() or ret[igrp].second.empty());
        } else {
            assert(ret[igrp].first.size() == ret[igrp].second.size());
            assert(ret[igrp].first.size());
        }
        for (int j = 0; j < min<int>(ret[igrp].first.size(), ret[igrp].second.size()); ++j) {
            auto u = ret[igrp].first[j], v = ret[igrp].second[j];
            assert(edges_set.count(make_pair(u, v)));
        }
    }
    assert(count(lord.begin(), lord.end(), -1) == 0);
    assert(count(rord.begin(), rord.end(), -1) == 0);

    for (auto e : edges) {
        assert(0 <= e.first and e.first < L);
        assert(0 <= e.second and e.second < R);
        assert(lord.at(e.first) <= rord.at(e.second)); // Check topological order
    }
    return ret;
}


int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	
    int N, M, K, L;
    cin >> N >> M >> K >> L;
    vector<vector<pair<int, int>>> z2xy(K + 1);

    while (L--) {
        int x, y, z;
        cin >> x >> y >> z;
        x--, y--;
        z2xy[K - z].emplace_back(x, y);
    }
    vector<int> vtp(N + M, 3);

    vector<pair<int, int>> alive_edges;

    long long ret = 0;
    int nmatch = 0;

    vector<int> experience12(N + M);
    vector<int> fixed_pair(N, -1);

    for (const auto &xys : z2xy) {
        for (auto p : xys) {
            int u = p.first, v = p.second;
            if (experience12[u] or experience12[N + v]) continue;
            alive_edges.emplace_back(u, v);
        }

        auto dm_ret = verify_dulmage_mendelsohn(N, M, alive_edges);

        int nmatchnxt = 0;
        for (const auto &p : dm_ret) nmatchnxt += min(p.first.size(), p.second.size());

        ret = ret * 2 + nmatchnxt - nmatch;

        for (auto l : dm_ret.front().first) vtp[l] = 2, experience12[l] = 1;
        for (auto r : dm_ret.front().second) vtp[r + N] = 3;
        for (auto l : dm_ret.back().first) vtp[l] = 3;
        for (auto r : dm_ret.back().second) vtp[r + N] = 2, experience12[r + N] = 1;

        for (int i = 1; i + 1 < int(dm_ret.size()); ++i) {
            for (int j = 0; j < int(dm_ret[i].first.size()); ++j) {
                int l = dm_ret[i].first[j], r = dm_ret[i].second[j];
                if (fixed_pair[l] < 0) {
                    vtp[l] = vtp[r + N] = 1, fixed_pair[l] = r;
                    experience12[l] = experience12[r + N] = 1;
                    alive_edges.emplace_back(l, r);
                }
            }
        }

        for (int cur = 0; cur < int(alive_edges.size());) {
            int u = alive_edges[cur].first, v = alive_edges[cur].second;
            if (vtp[u] + vtp[v + N] == 5 or fixed_pair[u] == v) {
                cur++;
            } else {
                alive_edges[cur].swap(alive_edges.back());
                alive_edges.pop_back();
            }
        }
        nmatch = nmatchnxt;
    }
    cout << ret << endl;
}
0