test/aoj/3142.test.cpp

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• Last update: 2024-09-21 21:45:32+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/3142

Depends on

• Union-Find (ポテンシャル) (src/DataStructure/UnionFind_Potentialized.hpp)
• グラフ (src/Graph/Graph.hpp)
• 接続行列の連立方程式 (src/Graph/incidence_matrix_equation.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)

Code

// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/3142
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64

// 接続行列の連立方程式 (long long)
// ポテンシャルUF
#include <iostream>
#include <vector>
#include <algorithm>
#include "src/Graph/incidence_matrix_equation.hpp"
#include "src/DataStructure/UnionFind_Potentialized.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 int N;
 cin >> N;
 Graph g(N, N - 1);
 for (int i= 0; i < N - 1; ++i) cin >> g[i], --g[i];
 vector<long long> c(N);
 for (int i= 0; i < N; ++i) cin >> c[i];
 for (int i= 0, b; i < N; ++i) cin >> b, c[i]-= b;
 auto sol= incidence_matrix_equation(g, c);
 UnionFind_Potentialized<long long> uf(N);
 for (int i= 0; i < N - 1; ++i) {
  auto [u, v]= g[i];
  uf.unite(v, u, sol[i]);
 }
 long long sum= 0, lo= 0;
 for (int i= 0; i < N; ++i) {
  long long p= uf.potential(i);
  sum+= p, lo= min(lo, p);
 }
 cout << sum - lo * N << '\n';
 return 0;
}

#line 1 "test/aoj/3142.test.cpp"
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/3142
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64

// 接続行列の連立方程式 (long long)
// ポテンシャルUF
#include <iostream>
#include <vector>
#include <algorithm>
#line 2 "src/Graph/incidence_matrix_equation.hpp"
#include <cassert>
#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/Graph/incidence_matrix_equation.hpp"
template <class T> std::vector<T> incidence_matrix_equation(const Graph &g, std::vector<T> b) {
 const int n= g.vertex_size();
 assert((int)b.size() == n);
 std::vector<T> x(g.edge_size());
 auto adje= g.adjacency_edge(0);
 std::vector<int> pre(n, -2), ei(adje.p.begin(), adje.p.begin() + n);
 for (int s= 0, p, e; s < n; ++s)
  if (pre[s] == -2)
   for (pre[p= s]= -1;;) {
    if (ei[p] == adje.p[p + 1]) {
     if (e= pre[p]; e < 0) {
      if (b[p] != T()) return {};  // no solution
      break;
     }
     T tmp= b[p];
     p= g[e].to(p);
     if constexpr (std::is_same_v<T, bool>) x[e]= tmp, b[p]= tmp ^ b[p];
     else x[e]= g[e].second == p ? -tmp : tmp, b[p]+= tmp;
    } else if (int q= g[e= adje.dat[ei[p]++]].to(p); pre[q] == -2) pre[p= q]= e;
   }
 return x;
}
#line 5 "src/DataStructure/UnionFind_Potentialized.hpp"
template <class weight_t> class UnionFind_Potentialized {
 std::vector<int> par;
 std::vector<weight_t> val;
public:
 UnionFind_Potentialized(int n): par(n, -1), val(n) {}
 int leader(int u) {
  if (par[u] < 0) return u;
  int r= leader(par[u]);
  if constexpr (std::is_same_v<weight_t, bool>) val[u]= val[u] ^ val[par[u]];
  else val[u]= val[par[u]] + val[u];
  return par[u]= r;
 }
 //  -p(v) + p(u) = w
 bool unite(int u, int v, weight_t w) {
  int a= leader(u), b= leader(v);
  if constexpr (std::is_same_v<weight_t, bool>) w^= val[u] ^ val[v];
  else w= val[v] + w - val[u];
  if (a == b) return w == weight_t();
  if (par[b] > par[a]) std::swap(a, b), w= -w;
  return par[b]+= par[a], par[a]= b, val[a]= w, true;
 }
 bool connected(int u, int v) { return leader(u) == leader(v); }
 int size(int u) { return -par[leader(u)]; }
 weight_t potential(int u) { return leader(u), val[u]; }
 //  -p(v) + p(u)
 weight_t diff(int u, int v) {
  if constexpr (std::is_same_v<weight_t, bool>) return potential(u) ^ potential(v);
  else return -potential(v) + potential(u);
 }
};
#line 12 "test/aoj/3142.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 int N;
 cin >> N;
 Graph g(N, N - 1);
 for (int i= 0; i < N - 1; ++i) cin >> g[i], --g[i];
 vector<long long> c(N);
 for (int i= 0; i < N; ++i) cin >> c[i];
 for (int i= 0, b; i < N; ++i) cin >> b, c[i]-= b;
 auto sol= incidence_matrix_equation(g, c);
 UnionFind_Potentialized<long long> uf(N);
 for (int i= 0; i < N - 1; ++i) {
  auto [u, v]= g[i];
  uf.unite(v, u, sol[i]);
 }
 long long sum= 0, lo= 0;
 for (int i= 0; i < N; ++i) {
  long long p= uf.potential(i);
  sum+= p, lo= min(lo, p);
 }
 cout << sum - lo * N << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	sample_01.in	AC	5 ms	4 MB
g++-13	sample_02.in	AC	4 ms	4 MB
g++-13	testcase_01.in	AC	23 ms	6 MB
g++-13	testcase_02.in	AC	31 ms	8 MB
g++-13	testcase_03.in	AC	11 ms	4 MB
g++-13	testcase_04.in	AC	31 ms	8 MB
g++-13	testcase_05.in	AC	39 ms	9 MB
g++-13	testcase_06.in	AC	39 ms	9 MB
g++-13	testcase_07.in	AC	32 ms	9 MB
g++-13	testcase_08.in	AC	32 ms	9 MB
g++-13	testcase_09.in	AC	36 ms	9 MB
g++-13	testcase_10.in	AC	37 ms	9 MB
g++-13	testcase_11.in	AC	41 ms	9 MB
g++-13	testcase_12.in	AC	37 ms	9 MB
g++-13	testcase_13.in	AC	38 ms	9 MB
g++-13	testcase_14.in	AC	37 ms	9 MB
g++-13	testcase_15.in	AC	33 ms	9 MB
g++-13	testcase_16.in	AC	35 ms	9 MB
g++-13	testcase_17.in	AC	39 ms	9 MB
g++-13	testcase_18.in	AC	35 ms	9 MB
g++-13	testcase_19.in	AC	37 ms	9 MB
g++-13	testcase_20.in	AC	5 ms	4 MB
g++-13	testcase_21.in	AC	4 ms	4 MB
clang++-18	sample_01.in	AC	5 ms	4 MB
clang++-18	sample_02.in	AC	4 ms	4 MB
clang++-18	testcase_01.in	AC	24 ms	7 MB
clang++-18	testcase_02.in	AC	32 ms	8 MB
clang++-18	testcase_03.in	AC	12 ms	4 MB
clang++-18	testcase_04.in	AC	31 ms	8 MB
clang++-18	testcase_05.in	AC	41 ms	9 MB
clang++-18	testcase_06.in	AC	41 ms	9 MB
clang++-18	testcase_07.in	AC	32 ms	9 MB
clang++-18	testcase_08.in	AC	31 ms	9 MB
clang++-18	testcase_09.in	AC	37 ms	9 MB
clang++-18	testcase_10.in	AC	37 ms	9 MB
clang++-18	testcase_11.in	AC	42 ms	9 MB
clang++-18	testcase_12.in	AC	37 ms	9 MB
clang++-18	testcase_13.in	AC	40 ms	9 MB
clang++-18	testcase_14.in	AC	38 ms	9 MB
clang++-18	testcase_15.in	AC	32 ms	9 MB
clang++-18	testcase_16.in	AC	35 ms	9 MB
clang++-18	testcase_17.in	AC	40 ms	9 MB
clang++-18	testcase_18.in	AC	35 ms	9 MB
clang++-18	testcase_19.in	AC	38 ms	9 MB
clang++-18	testcase_20.in	AC	5 ms	4 MB
clang++-18	testcase_21.in	AC	4 ms	4 MB

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