Linear system incidence
(Mylib/Graph/lsi.cpp)

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• Last update: 2021-04-23 23:44:44+09:00

Operations

Requirements

Notes

Problems

References

• https://opt-cp.com/cp/linear-system-incidence/

Depends on

• Basic graph (Mylib/Graph/Template/graph.cpp)

Code

#pragma once
#include <algorithm>
#include <cassert>
#include <optional>
#include <vector>
#include "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T, typename U>
  std::optional<std::vector<U>> lsi(const graph<T> &g, const std::vector<U> &c) {
    const int N = g.size();
    assert((int) c.size() == N);

    graph<T> h(N);

    int M = 0;
    for (auto &v : g) {
      for (auto &e : v) {
        h[e.from].push_back(e);
        h[e.to].push_back(e);
        M = std::max(M, e.index + 1);
      }
    }

    std::vector<U> ret(M);
    std::vector<bool> check(N);

    auto dfs =
        [&](auto &dfs, int cur) -> U {
      check[cur] = true;

      U t = c[cur];

      for (auto &e : h[cur]) {
        auto v = e.from == cur ? e.to : e.from;
        if (check[v]) continue;

        auto y = dfs(dfs, v);

        if (e.from == cur)
          ret[e.index] = y;
        else
          ret[e.index] = -y;

        t += y;
      }

      return t;
    };

    for (int i = 0; i < N; ++i) {
      if (check[i]) continue;
      auto y = dfs(dfs, i);
      if (y != 0) return std::nullopt;
    }

    return ret;
  }
}  // namespace haar_lib

#line 2 "Mylib/Graph/lsi.cpp"
#include <algorithm>
#include <cassert>
#include <optional>
#include <vector>
#line 2 "Mylib/Graph/Template/graph.cpp"
#include <iostream>
#line 4 "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  struct edge {
    int from, to;
    T cost;
    int index = -1;
    edge() {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
  };

  template <typename T>
  struct graph {
    using weight_type = T;
    using edge_type   = edge<T>;

    std::vector<std::vector<edge<T>>> data;

    auto& operator[](size_t i) { return data[i]; }
    const auto& operator[](size_t i) const { return data[i]; }

    auto begin() const { return data.begin(); }
    auto end() const { return data.end(); }

    graph() {}
    graph(int N) : data(N) {}

    bool empty() const { return data.empty(); }
    int size() const { return data.size(); }

    void add_edge(int i, int j, T w, int index = -1) {
      data[i].emplace_back(i, j, w, index);
    }

    void add_undirected(int i, int j, T w, int index = -1) {
      add_edge(i, j, w, index);
      add_edge(j, i, w, index);
    }

    template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
    void read(int M) {
      for (int i = 0; i < M; ++i) {
        int u, v;
        std::cin >> u >> v;
        u -= I;
        v -= I;
        T w = 1;
        if (WEIGHTED) std::cin >> w;
        if (DIRECTED)
          add_edge(u, v, w, i);
        else
          add_undirected(u, v, w, i);
      }
    }
  };

  template <typename T>
  using tree = graph<T>;
}  // namespace haar_lib
#line 7 "Mylib/Graph/lsi.cpp"

namespace haar_lib {
  template <typename T, typename U>
  std::optional<std::vector<U>> lsi(const graph<T> &g, const std::vector<U> &c) {
    const int N = g.size();
    assert((int) c.size() == N);

    graph<T> h(N);

    int M = 0;
    for (auto &v : g) {
      for (auto &e : v) {
        h[e.from].push_back(e);
        h[e.to].push_back(e);
        M = std::max(M, e.index + 1);
      }
    }

    std::vector<U> ret(M);
    std::vector<bool> check(N);

    auto dfs =
        [&](auto &dfs, int cur) -> U {
      check[cur] = true;

      U t = c[cur];

      for (auto &e : h[cur]) {
        auto v = e.from == cur ? e.to : e.from;
        if (check[v]) continue;

        auto y = dfs(dfs, v);

        if (e.from == cur)
          ret[e.index] = y;
        else
          ret[e.index] = -y;

        t += y;
      }

      return t;
    };

    for (int i = 0; i < N; ++i) {
      if (check[i]) continue;
      auto y = dfs(dfs, i);
      if (y != 0) return std::nullopt;
    }

    return ret;
  }
}  // namespace haar_lib

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