test/aoj/2893.test.cpp

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• Last update: 2024-09-01 10:56:39+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/2893

Depends on

• グラフ (src/Graph/Graph.hpp)
• Incremental-Bridge-Connectivity (二辺連結成分) (src/Graph/IncrementalBridgeConnectivity.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)
• 座標圧縮 (src/Misc/compress.hpp)

Code

// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2893
// competitive-verifier: TLE 1
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <algorithm>
#include "src/Graph/Graph.hpp"
#include "src/Misc/compress.hpp"
#include "src/Graph/IncrementalBridgeConnectivity.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 Graph g(N, M);
 vector<long long> w(M);
 for (int i= 0; i < M; ++i) cin >> g[i] >> w[i], --g[i];
 IncrementalBridgeConnectivity ibc(N);
 for (auto [u, v]: g) ibc.add_edge(u, v);

 vector<int> id(N);
 int n= 0;
 for (int i= 0; i < N; ++i)
  if (ibc.leader(i) == i) id[i]= n++;

 Graph g2(n);
 vector<long long> s(n, 0), w2;
 for (int e= M; e--;) {
  auto [u, v]= g[e];
  u= id[ibc.leader(u)], v= id[ibc.leader(v)];
  if (u == v) s[u]+= w[e];
  else g2.add_edge(u, v), w2.push_back(w[e]);
 }

 auto adje= g2.adjacency_edge(0);

 auto dfs= [&](auto &&dfs, int v, int p) -> void {
  for (int e: adje[v])
   if (int u= g2[e].to(v); u != p) {
    dfs(dfs, u, v);
    s[v]+= s[u] + w2[e];
   }
 };
 dfs(dfs, 0, -1);

 int ans_u= 0, ans_v= 0;
 long long best= 1ll << 60;

 for (int e= 0; e < M; ++e) {
  auto [u, v]= g[e];
  int u2= id[ibc.leader(u)], v2= id[ibc.leader(v)];
  long long cost;
  if (u2 == v2) cost= s[0] - w[e];
  else {
   if (s[u2] > s[v2]) swap(u2, v2);
   long long WA= s[u2], WB= s[0] - s[u2] - w[e];
   cost= abs(WA - WB);
  }
  if (best > cost) best= cost, ans_u= u, ans_v= v;
  else if (best == cost) {
   if (ans_u > u) ans_u= u, ans_v= v;
   else if (ans_u == u && ans_v > v) ans_v= v;
  }
 }

 cout << ans_u + 1 << " " << ans_v + 1 << '\n';
 return 0;
}

#line 1 "test/aoj/2893.test.cpp"
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2893
// competitive-verifier: TLE 1
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <algorithm>
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 4 "src/Misc/compress.hpp"
template <class T> auto compress(std::vector<T> &v) {
 return std::sort(v.begin(), v.end()), v.erase(std::unique(v.begin(), v.end()), v.end()), [&v](T x) { return std::lower_bound(v.begin(), v.end(), x) - v.begin(); };
}
#line 2 "src/Graph/IncrementalBridgeConnectivity.hpp"
#include <utility>
#line 4 "src/Graph/IncrementalBridgeConnectivity.hpp"
class IncrementalBridgeConnectivity {
 std::vector<int> cp, bp, bbf, z;
 int t;
 inline int crt(int v) { return cp[v] < 0 ? v : cp[v]= crt(cp[v]); }
 inline int par(int v) { return bbf[v] < 0 ? -1 : leader(bbf[v]); }
public:
 IncrementalBridgeConnectivity(int n): cp(n, -1), bp(n, -1), bbf(n, -1), z(n), t(0) {}
 inline int leader(int v) { return bp[v] < 0 ? v : bp[v]= leader(bp[v]); }
 int size(int v) { return -bp[leader(v)]; }
 bool two_edge_connected(int u, int v) { return leader(u) == leader(v); }
 bool connected(int u, int v) { return crt(u) == crt(v); }
 void add_edge(int u, int v) {
  int a= crt(u= leader(u)), b= crt(v= leader(v));
  if (a == b)
   for (++t, a= u, b= v;;) {
    if (z[a] == t) {
     for (int w: {u, v})
      for (int p; w= leader(w), w != a; bp[a]+= bp[w], bp[w]= a, w= p)
       if (p= bbf[w], bbf[w]= bbf[a]; bp[a] > bp[w]) std::swap(w, a);
     return;
    }
    if (z[a]= t, a= par(a); b != -1) std::swap(a, b);
   }
  if (cp[a] < cp[b]) std::swap(u, v), cp[a]+= cp[b], cp[b]= a;
  else cp[b]+= cp[a], cp[a]= b;
  for (int p; u != -1; u= p) p= par(u), bbf[u]= v, v= u;
 }
};
#line 10 "test/aoj/2893.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 Graph g(N, M);
 vector<long long> w(M);
 for (int i= 0; i < M; ++i) cin >> g[i] >> w[i], --g[i];
 IncrementalBridgeConnectivity ibc(N);
 for (auto [u, v]: g) ibc.add_edge(u, v);

 vector<int> id(N);
 int n= 0;
 for (int i= 0; i < N; ++i)
  if (ibc.leader(i) == i) id[i]= n++;

 Graph g2(n);
 vector<long long> s(n, 0), w2;
 for (int e= M; e--;) {
  auto [u, v]= g[e];
  u= id[ibc.leader(u)], v= id[ibc.leader(v)];
  if (u == v) s[u]+= w[e];
  else g2.add_edge(u, v), w2.push_back(w[e]);
 }

 auto adje= g2.adjacency_edge(0);

 auto dfs= [&](auto &&dfs, int v, int p) -> void {
  for (int e: adje[v])
   if (int u= g2[e].to(v); u != p) {
    dfs(dfs, u, v);
    s[v]+= s[u] + w2[e];
   }
 };
 dfs(dfs, 0, -1);

 int ans_u= 0, ans_v= 0;
 long long best= 1ll << 60;

 for (int e= 0; e < M; ++e) {
  auto [u, v]= g[e];
  int u2= id[ibc.leader(u)], v2= id[ibc.leader(v)];
  long long cost;
  if (u2 == v2) cost= s[0] - w[e];
  else {
   if (s[u2] > s[v2]) swap(u2, v2);
   long long WA= s[u2], WB= s[0] - s[u2] - w[e];
   cost= abs(WA - WB);
  }
  if (best > cost) best= cost, ans_u= u, ans_v= v;
  else if (best == cost) {
   if (ans_u > u) ans_u= u, ans_v= v;
   else if (ans_u == u && ans_v > v) ans_v= v;
  }
 }

 cout << ans_u + 1 << " " << ans_v + 1 << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	00_sample_00.in	AC	6 ms	4 MB
g++-13	00_sample_01.in	AC	5 ms	4 MB
g++-13	10_random_small_00.in	AC	5 ms	4 MB
g++-13	10_random_small_01.in	AC	5 ms	4 MB
g++-13	10_random_small_02.in	AC	5 ms	3 MB
g++-13	10_random_small_03.in	AC	5 ms	4 MB
g++-13	10_random_small_04.in	AC	5 ms	4 MB
g++-13	11_random_med_00.in	AC	9 ms	4 MB
g++-13	11_random_med_01.in	AC	10 ms	4 MB
g++-13	11_random_med_02.in	AC	22 ms	5 MB
g++-13	11_random_med_03.in	AC	20 ms	5 MB
g++-13	11_random_med_04.in	AC	17 ms	5 MB
g++-13	12_random_large_00.in	AC	13 ms	4 MB
g++-13	12_random_large_01.in	AC	23 ms	7 MB
g++-13	12_random_large_02.in	AC	32 ms	10 MB
g++-13	12_random_large_03.in	AC	33 ms	11 MB
g++-13	12_random_large_04.in	AC	20 ms	5 MB
g++-13	12_random_large_05.in	AC	32 ms	9 MB
g++-13	12_random_large_06.in	AC	22 ms	7 MB
g++-13	12_random_large_07.in	AC	33 ms	11 MB
g++-13	12_random_large_08.in	AC	16 ms	5 MB
g++-13	12_random_large_09.in	AC	24 ms	7 MB
g++-13	19_random_max_00.in	AC	34 ms	11 MB
g++-13	19_random_max_01.in	AC	35 ms	11 MB
g++-13	19_random_max_02.in	AC	35 ms	11 MB
g++-13	19_random_max_03.in	AC	35 ms	11 MB
g++-13	19_random_max_04.in	AC	35 ms	11 MB
g++-13	20_scale_free_00.in	AC	7 ms	4 MB
g++-13	20_scale_free_01.in	AC	26 ms	8 MB
g++-13	20_scale_free_02.in	AC	15 ms	6 MB
g++-13	20_scale_free_03.in	AC	23 ms	7 MB
g++-13	20_scale_free_04.in	AC	25 ms	9 MB
g++-13	90_challenge_00.in	AC	13 ms	5 MB
g++-13	90_challenge_01.in	AC	8 ms	4 MB
g++-13	90_challenge_02.in	AC	15 ms	5 MB
g++-13	90_challenge_03.in	AC	16 ms	5 MB
g++-13	90_challenge_04.in	AC	9 ms	4 MB
clang++-18	00_sample_00.in	AC	6 ms	4 MB
clang++-18	00_sample_01.in	AC	5 ms	4 MB
clang++-18	10_random_small_00.in	AC	5 ms	4 MB
clang++-18	10_random_small_01.in	AC	5 ms	4 MB
clang++-18	10_random_small_02.in	AC	5 ms	4 MB
clang++-18	10_random_small_03.in	AC	5 ms	4 MB
clang++-18	10_random_small_04.in	AC	5 ms	4 MB
clang++-18	11_random_med_00.in	AC	10 ms	4 MB
clang++-18	11_random_med_01.in	AC	12 ms	4 MB
clang++-18	11_random_med_02.in	AC	25 ms	5 MB
clang++-18	11_random_med_03.in	AC	23 ms	5 MB
clang++-18	11_random_med_04.in	AC	20 ms	5 MB
clang++-18	12_random_large_00.in	AC	15 ms	4 MB
clang++-18	12_random_large_01.in	AC	26 ms	7 MB
clang++-18	12_random_large_02.in	AC	36 ms	10 MB
clang++-18	12_random_large_03.in	AC	37 ms	11 MB
clang++-18	12_random_large_04.in	AC	21 ms	5 MB
clang++-18	12_random_large_05.in	AC	33 ms	9 MB
clang++-18	12_random_large_06.in	AC	23 ms	7 MB
clang++-18	12_random_large_07.in	AC	36 ms	11 MB
clang++-18	12_random_large_08.in	AC	17 ms	5 MB
clang++-18	12_random_large_09.in	AC	27 ms	7 MB
clang++-18	19_random_max_00.in	AC	38 ms	11 MB
clang++-18	19_random_max_01.in	AC	38 ms	11 MB
clang++-18	19_random_max_02.in	AC	38 ms	11 MB
clang++-18	19_random_max_03.in	AC	38 ms	11 MB
clang++-18	19_random_max_04.in	AC	38 ms	11 MB
clang++-18	20_scale_free_00.in	AC	7 ms	4 MB
clang++-18	20_scale_free_01.in	AC	28 ms	8 MB
clang++-18	20_scale_free_02.in	AC	15 ms	6 MB
clang++-18	20_scale_free_03.in	AC	24 ms	7 MB
clang++-18	20_scale_free_04.in	AC	26 ms	9 MB
clang++-18	90_challenge_00.in	AC	14 ms	5 MB
clang++-18	90_challenge_01.in	AC	9 ms	4 MB
clang++-18	90_challenge_02.in	AC	17 ms	5 MB
clang++-18	90_challenge_03.in	AC	17 ms	5 MB
clang++-18	90_challenge_04.in	AC	9 ms	4 MB

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