cp-library-cpp
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test/src/optimization/project_selection_problem/arc085_c.test.cpp
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- Last update: 2024-01-31 03:27:19+09:00
- Problem: https://atcoder.jp/contests/arc085/tasks/arc085_e
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Depends on
Project Selection Problem
(library/optimization/project_selection_problem.hpp)
Code
#define PROBLEM "https://atcoder.jp/contests/arc085/tasks/arc085_e"
#include "library/optimization/project_selection_problem.hpp"
#include <iostream>
int main() {
int n;
std::cin >> n;
using Cost = long long;
Cost inf = std::numeric_limits<Cost>::max() / 2;
std::vector<Cost> a(n + 1);
for (int i = 1; i <= n; ++i) {
std::cin >> a[i];
}
suisen::ProjectSelection<Cost> psp(n + 1);
for (int x = 1; x <= n; ++x) {
psp.add_profit_0(x, a[x]);
for (int y = 2 * x; y <= n; y += x) {
psp.add_cost_01(y, x, inf);
}
}
std::cout << psp.max_profit().first << std::endl;
}#line 1 "test/src/optimization/project_selection_problem/arc085_c.test.cpp"
#define PROBLEM "https://atcoder.jp/contests/arc085/tasks/arc085_e"
#line 1 "library/optimization/project_selection_problem.hpp"
#include <array>
#include <cassert>
#include <utility>
#include <tuple>
#include <vector>
#include <atcoder/maxflow>
namespace suisen {
template <typename Cost>
struct ProjectSelection {
using Item = std::size_t;
private:
template <typename T>
using CostFunc = std::array<T, 2>;
public:
using CostFunc0 = Cost;
using CostFunc1 = CostFunc<CostFunc0>;
using CostFunc2 = CostFunc<CostFunc1>;
using CostFunc3 = CostFunc<CostFunc2>;
ProjectSelection() = default;
explicit ProjectSelection(std::size_t n) : _num(n), _cost1(n) {}
void add_cost(CostFunc0 cost) { _cost0 += cost; }
void add_profit(CostFunc0 profit) { add_cost(-profit); }
void add_cost_0(Item i, Cost cost) { add_cost(i, CostFunc1{ cost, 0 }); }
void add_cost_1(Item i, Cost cost) { add_cost(i, CostFunc1{ 0, cost }); }
void add_profit_0(Item i, Cost profit) { add_cost(i, CostFunc1{ -profit, 0 }); }
void add_profit_1(Item i, Cost profit) { add_cost(i, CostFunc1{ 0, -profit }); }
void add_cost(Item i, CostFunc1 cost) {
assert(i < _num);
_cost1[i][0] += cost[0];
_cost1[i][1] += cost[1];
}
void add_profit(Item i, CostFunc1 profit) { add_cost(i, neg(profit)); }
void add_cost_01(Item i, Item j, Cost cost) {
assert(i < _num);
assert(j < _num);
assert(i != j);
add_edge(i, j, cost);
}
void add_cost_10(Item i, Item j, Cost cost) { add_cost_01(j, i, cost); }
void add_cost_not_same(Item i, Item j, Cost cost) { add_cost(i, j, CostFunc2{ 0, cost, cost, 0 }); }
void add_profit_00(Item i, Item j, Cost profit) { add_cost(i, j, CostFunc2{ -profit, 0, 0, 0 }); }
void add_profit_11(Item i, Item j, Cost profit) { add_cost(i, j, CostFunc2{ 0, 0, 0, -profit }); }
void add_profit_same(Item i, Item j, Cost profit) { add_cost(i, j, CostFunc2{ -profit, 0, 0, -profit }); }
// cost: submodular (i.e., cost[0][1] + cost[1][0] >= cost[0][0] + cost[1][1])
void add_cost(Item i, Item j, CostFunc2 cost) {
assert(i < _num);
assert(j < _num);
assert(i != j);
add_cost(cost[0][0]);
add_cost(i, CostFunc1{ 0, cost[1][0] - cost[0][0] });
add_cost(j, CostFunc1{ 0, cost[1][1] - cost[1][0] });
add_cost_01(i, j, (cost[0][1] + cost[1][0]) - (cost[0][0] + cost[1][1]));
}
void add_profit(Item i, Item j, const CostFunc2 &profit) { add_cost(i, j, neg(profit)); }
// cost: submodular (i.e., cost(X) + cost(Y) >= cost(X | Y) + cost(X & Y))
void add_cost(Item i, Item j, Item k, CostFunc3 cost) {
assert(i < _num);
assert(j < _num);
assert(k < _num);
assert(i != j);
assert(j != k);
assert(k != i);
const Cost A = cost[0][0][0], B = cost[0][0][1];
const Cost C = cost[0][1][0], D = cost[0][1][1];
const Cost E = cost[1][0][0], F = cost[1][0][1];
const Cost G = cost[1][1][0], H = cost[1][1][1];
const Cost P = (A + D + F + G) - (B + C + E + H);
if (P >= 0) {
const Cost P1 = F - B, P2 = G - E, P3 = D - C;
const Cost P12 = (C + E) - (A + G), P23 = (B + C) - (A + D), P31 = (B + E) - (A + F);
add_cost(A);
add_cost(i, CostFunc1{ 0, P1 });
add_cost(j, CostFunc1{ 0, P2 });
add_cost(k, CostFunc1{ 0, P3 });
add_cost_01(i, j, P12);
add_cost_01(j, k, P23);
add_cost_01(k, i, P31);
add_profit_all_1(std::array<Item, 3>{ i, j, k }, P);
} else {
const Cost P1 = C - G, P2 = B - D, P3 = E - F;
const Cost P21 = (D + F) - (B + H), P32 = (F + G) - (E + H), P13 = (D + G) - (C + H);
add_cost(H);
add_cost(i, CostFunc1{ P1, 0 });
add_cost(j, CostFunc1{ P2, 0 });
add_cost(k, CostFunc1{ P3, 0 });
add_cost_01(j, i, P21);
add_cost_01(k, j, P32);
add_cost_01(i, k, P13);
add_profit_all_0(std::array<Item, 3>{ i, j, k }, -P);
}
}
template <typename Container>
auto add_profit_all_0(const Container& is, Cost profit) -> decltype(static_cast<Item>(*is.begin()), is.end(), void()) {
assert(profit >= 0);
if (is.size() == 0) {
return add_profit(profit);
} else if (is.size() == 1) {
return add_profit(is[0], CostFunc1{ profit, 0 });
} else if (is.size() == 2) {
return add_profit_00(is[0], is[1], profit);
}
add_profit(profit);
const Item aux = _num + _num_aux++;
add_edge(S, aux, profit);
for (Item i : is) {
add_edge(aux, i, profit);
}
}
template <typename Container>
auto add_profit_all_1(const Container& is, Cost profit) -> decltype(static_cast<Item>(*is.begin()), is.end(), void()) {
assert(profit >= 0);
if (is.size() == 0) {
return add_profit(profit);
} else if (is.size() == 1) {
return add_profit(is[0], CostFunc1{ 0, profit });
} else if (is.size() == 2) {
return add_profit_11(is[0], is[1], profit);
}
add_profit(profit);
const Item aux = _num + _num_aux++;
for (Item i : is) {
add_edge(i, aux, profit);
}
add_edge(aux, T, profit);
}
auto min_cost() {
atcoder::mf_graph<Cost> g(_num + _num_aux + 2);
const std::size_t s = _num + _num_aux, t = s + 1;
make_edges_for_cost1();
for (const auto &[i, j, cost] : _edges) {
std::size_t u = (i == S) ? s : (i == T) ? t : i;
std::size_t v = (j == S) ? s : (j == T) ? t : j;
g.add_edge(u, v, cost);
}
Cost ans = _cost0 + g.flow(s, t);
auto x = g.min_cut(s);
x.resize(_num);
for (std::size_t i = 0; i < _num; ++i) {
x[i] = not x[i];
}
return std::make_pair(ans, x);
}
auto max_profit() {
auto res = min_cost();
res.first = -res.first;
return res;
}
private:
static constexpr std::size_t S = ~0;
static constexpr std::size_t T = ~1;
std::size_t _num;
std::size_t _num_aux = 0;
Cost _cost0 = 0;
std::vector<CostFunc1> _cost1;
std::vector<std::tuple<Item, Item, Cost>> _edges{};
void make_edges_for_cost1() {
for (std::size_t i = 0; i < _num; ++i) {
CostFunc1& cost = _cost1[i];
if (cost[0] <= cost[1]) {
add_cost(cost[0]);
add_edge(S, i, cost[1] - cost[0]);
} else {
add_cost(cost[1]);
add_edge(i, T, cost[0] - cost[1]);
}
cost = { 0, 0 };
}
}
void add_edge(std::size_t i, std::size_t j, Cost cost) {
assert(cost >= 0);
assert(i == S or i == T or i < _num + _num_aux);
assert(j == S or j == T or j < _num + _num_aux);
assert(i != j);
if (cost == 0) return;
_edges.emplace_back(i, j, cost);
}
static constexpr Cost neg(Cost cost) { return -cost; }
template <typename T>
static constexpr CostFunc<T> neg(const CostFunc<T> &cost) { return { neg(cost[0]), neg(cost[1]) }; }
};
} // namespace suisen
#line 4 "test/src/optimization/project_selection_problem/arc085_c.test.cpp"
#include <iostream>
int main() {
int n;
std::cin >> n;
using Cost = long long;
Cost inf = std::numeric_limits<Cost>::max() / 2;
std::vector<Cost> a(n + 1);
for (int i = 1; i <= n; ++i) {
std::cin >> a[i];
}
suisen::ProjectSelection<Cost> psp(n + 1);
for (int x = 1; x <= n; ++x) {
psp.add_profit_0(x, a[x]);
for (int y = 2 * x; y <= n; y += x) {
psp.add_cost_01(y, x, inf);
}
}
std::cout << psp.max_profit().first << std::endl;
}