test/verify/aoj-3022.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3022

Depends on

• Bi Connected Components(二重頂点連結成分分解) (graph/connected-components/bi-connected-components.hpp)
• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Block Cut Tree (graph/others/block-cut-tree.hpp)
• Low Link(橋/関節点) (graph/others/low-link.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3022

#include "../../template/template.hpp"

#include "../../graph/others/block-cut-tree.hpp"

int main() {
  int N, M;
  cin >> N >> M;
  vector< int > A(N);
  cin >> A;
  BlockCutTree<> bct(N);
  bct.read(M);
  bct.build();
  vector< int64 > weight(bct.tree.size());
  int64 all = 0;
  for(int i = 0; i < N; i++) {
    weight[bct[i]] += A[i];
    all += A[i];
  }
  vector< int64 > ans(N, all);
  for(int i = 0; i < N; i++) {
    ans[i] -= A[i];
  }
  MFP([&](auto rec, int idx, int par) -> int64 {
    int64 mx = 0, sum = 0;
    for(auto &to : bct.tree.g[idx]) {
      if(to == par) continue;
      auto res = rec(to, idx);
      sum += res;
      chmax(mx, res);
    }
    if(idx >= (int)bct.bc.size()) {
      ans[bct.group[idx][0]] = max(all - sum - weight[idx], mx);
    }
    return sum + weight[idx];
  })(0, -1);
  for(auto &p : ans) cout << p << "\n";
}

#line 1 "test/verify/aoj-3022.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3022

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/aoj-3022.test.cpp"

#line 2 "graph/others/block-cut-tree.hpp"

#line 2 "graph/graph-template.hpp"

/**
 * @brief Graph Template(グラフテンプレート)
 */
template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 2 "graph/others/low-link.hpp"

#line 4 "graph/others/low-link.hpp"

/**
 * @brief Low Link(橋/関節点)
 * @see http://kagamiz.hatenablog.com/entry/2013/10/05/005213
 *
 */
template <typename T = int>
struct LowLink : Graph<T> {
 public:
  using Graph<T>::Graph;
  vector<int> ord, low, articulation;
  vector<Edge<T> > bridge;
  using Graph<T>::g;

  virtual void build() {
    used.assign(g.size(), 0);
    ord.assign(g.size(), 0);
    low.assign(g.size(), 0);
    int k = 0;
    for (int i = 0; i < (int)g.size(); i++) {
      if (!used[i]) k = dfs(i, k, -1);
    }
  }

  explicit LowLink(const Graph<T> &g) : Graph<T>(g) {}

 private:
  vector<int> used;

  int dfs(int idx, int k, int par) {
    used[idx] = true;
    ord[idx] = k++;
    low[idx] = ord[idx];
    bool is_articulation = false, beet = false;
    int cnt = 0;
    for (auto &to : g[idx]) {
      if (to == par && !exchange(beet, true)) {
        continue;
      }
      if (!used[to]) {
        ++cnt;
        k = dfs(to, k, idx);
        low[idx] = min(low[idx], low[to]);
        is_articulation |= par >= 0 && low[to] >= ord[idx];
        if (ord[idx] < low[to]) bridge.emplace_back(to);
      } else {
        low[idx] = min(low[idx], ord[to]);
      }
    }
    is_articulation |= par == -1 && cnt > 1;
    if (is_articulation) articulation.push_back(idx);
    return k;
  }
};
#line 3 "graph/connected-components/bi-connected-components.hpp"

template <typename T = int>
struct BiConnectedComponents : LowLink<T> {
 public:
  using LowLink<T>::LowLink;
  using LowLink<T>::g;
  using LowLink<T>::ord;
  using LowLink<T>::low;

  vector<vector<Edge<T> > > bc;

  void build() override {
    LowLink<T>::build();
    used.assign(g.size(), 0);
    for (int i = 0; i < (int)used.size(); i++) {
      if (!used[i]) dfs(i, -1);
    }
  }

  explicit BiConnectedComponents(const Graph<T> &g) : Graph<T>(g) {}

 private:
  vector<int> used;
  vector<Edge<T> > tmp;

  void dfs(int idx, int par) {
    used[idx] = true;
    bool beet = false;
    for (auto &to : g[idx]) {
      if (to == par && !exchange(beet, true)) continue;
      if (!used[to] || ord[to] < ord[idx]) {
        tmp.emplace_back(to);
      }
      if (!used[to]) {
        dfs(to, idx);
        if (low[to] >= ord[idx]) {
          bc.emplace_back();
          for (;;) {
            auto e = tmp.back();
            bc.back().emplace_back(e);
            tmp.pop_back();
            if (e.idx == to.idx) break;
          }
        }
      }
    }
  }
};
#line 5 "graph/others/block-cut-tree.hpp"

/**
 * @brief Block Cut Tree
 * @see https://ei1333.hateblo.jp/entry/2020/03/25/010057
 */
template <typename T = int>
struct BlockCutTree : BiConnectedComponents<T> {
 public:
  using BiConnectedComponents<T>::BiConnectedComponents;
  using BiConnectedComponents<T>::g;
  using BiConnectedComponents<T>::articulation;
  using BiConnectedComponents<T>::bc;

  vector<int> rev;
  vector<vector<int> > group;
  Graph<T> tree;

  explicit BlockCutTree(const Graph<T> &g) : Graph<T>(g) {}

  int operator[](const int &k) const { return rev[k]; }

  void build() override {
    BiConnectedComponents<T>::build();
    rev.assign(g.size(), -1);
    int ptr = (int)bc.size();
    for (auto &idx : articulation) {
      rev[idx] = ptr++;
    }
    vector<int> last(ptr, -1);
    tree = Graph<T>(ptr);
    for (int i = 0; i < (int)bc.size(); i++) {
      for (auto &e : bc[i]) {
        for (auto &ver : {e.from, e.to}) {
          if (rev[ver] >= (int)bc.size()) {
            if (exchange(last[rev[ver]], i) != i) {
              tree.add_edge(rev[ver], i, e.cost);
            }
          } else {
            rev[ver] = i;
          }
        }
      }
    }
    group.resize(ptr);
    for (int i = 0; i < (int)g.size(); i++) {
      group[rev[i]].emplace_back(i);
    }
  }
};
#line 6 "test/verify/aoj-3022.test.cpp"

int main() {
  int N, M;
  cin >> N >> M;
  vector< int > A(N);
  cin >> A;
  BlockCutTree<> bct(N);
  bct.read(M);
  bct.build();
  vector< int64 > weight(bct.tree.size());
  int64 all = 0;
  for(int i = 0; i < N; i++) {
    weight[bct[i]] += A[i];
    all += A[i];
  }
  vector< int64 > ans(N, all);
  for(int i = 0; i < N; i++) {
    ans[i] -= A[i];
  }
  MFP([&](auto rec, int idx, int par) -> int64 {
    int64 mx = 0, sum = 0;
    for(auto &to : bct.tree.g[idx]) {
      if(to == par) continue;
      auto res = rec(to, idx);
      sum += res;
      chmax(mx, res);
    }
    if(idx >= (int)bct.bc.size()) {
      ans[bct.group[idx][0]] = max(all - sum - weight[idx], mx);
    }
    return sum + weight[idx];
  })(0, -1);
  for(auto &p : ans) cout << p << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	testcase_00	AC	8 ms	4 MB
g++	testcase_01	AC	8 ms	4 MB
g++	testcase_02	AC	8 ms	4 MB
g++	testcase_03	AC	8 ms	4 MB
g++	testcase_04	AC	7 ms	4 MB
g++	testcase_05	AC	7 ms	4 MB
g++	testcase_06	AC	8 ms	4 MB
g++	testcase_07	AC	8 ms	4 MB
g++	testcase_08	AC	7 ms	4 MB
g++	testcase_09	AC	8 ms	4 MB
g++	testcase_10	AC	8 ms	4 MB
g++	testcase_11	AC	57 ms	21 MB
g++	testcase_12	AC	74 ms	29 MB
g++	testcase_13	AC	38 ms	14 MB
g++	testcase_14	AC	43 ms	17 MB
g++	testcase_15	AC	48 ms	17 MB
g++	testcase_16	AC	46 ms	17 MB
g++	testcase_17	AC	25 ms	12 MB
g++	testcase_18	AC	68 ms	25 MB
g++	testcase_19	AC	35 ms	14 MB
g++	testcase_20	AC	65 ms	25 MB
g++	testcase_21	AC	93 ms	41 MB
g++	testcase_22	AC	91 ms	41 MB
g++	testcase_23	AC	94 ms	41 MB
g++	testcase_24	AC	92 ms	41 MB
g++	testcase_25	AC	93 ms	41 MB
g++	testcase_26	AC	92 ms	41 MB
g++	testcase_27	AC	94 ms	41 MB
g++	testcase_28	AC	94 ms	41 MB
g++	testcase_29	AC	94 ms	41 MB
g++	testcase_30	AC	101 ms	41 MB
g++	testcase_31	AC	55 ms	19 MB
g++	testcase_32	AC	9 ms	4 MB
g++	testcase_33	AC	72 ms	34 MB
g++	testcase_34	AC	73 ms	34 MB
g++	testcase_35	AC	74 ms	34 MB
clang++	testcase_00	AC	8 ms	4 MB
clang++	testcase_01	AC	8 ms	4 MB
clang++	testcase_02	AC	8 ms	4 MB
clang++	testcase_03	AC	7 ms	4 MB
clang++	testcase_04	AC	8 ms	4 MB
clang++	testcase_05	AC	8 ms	4 MB
clang++	testcase_06	AC	8 ms	4 MB
clang++	testcase_07	AC	8 ms	4 MB
clang++	testcase_08	AC	8 ms	4 MB
clang++	testcase_09	AC	8 ms	4 MB
clang++	testcase_10	AC	8 ms	4 MB
clang++	testcase_11	AC	59 ms	20 MB
clang++	testcase_12	AC	75 ms	29 MB
clang++	testcase_13	AC	40 ms	14 MB
clang++	testcase_14	AC	45 ms	17 MB
clang++	testcase_15	AC	48 ms	17 MB
clang++	testcase_16	AC	46 ms	17 MB
clang++	testcase_17	AC	25 ms	12 MB
clang++	testcase_18	AC	68 ms	25 MB
clang++	testcase_19	AC	34 ms	15 MB
clang++	testcase_20	AC	67 ms	25 MB
clang++	testcase_21	AC	98 ms	41 MB
clang++	testcase_22	AC	97 ms	41 MB
clang++	testcase_23	AC	98 ms	41 MB
clang++	testcase_24	AC	96 ms	41 MB
clang++	testcase_25	AC	97 ms	41 MB
clang++	testcase_26	AC	98 ms	41 MB
clang++	testcase_27	AC	96 ms	41 MB
clang++	testcase_28	AC	96 ms	41 MB
clang++	testcase_29	AC	94 ms	41 MB
clang++	testcase_30	AC	94 ms	41 MB
clang++	testcase_31	AC	58 ms	18 MB
clang++	testcase_32	AC	9 ms	4 MB
clang++	testcase_33	AC	70 ms	34 MB
clang++	testcase_34	AC	98 ms	35 MB
clang++	testcase_35	AC	76 ms	34 MB

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