#line 1 "verify/graph/flow/min_cost_b_flow.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/min_cost_b_flow"
#line 1 "graph/flow/bounded_min_cost_flow.hpp"
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cmath>
#include <functional>
#include <limits>
#include <optional>
#include <queue>
#include <utility>
#include <vector>
namespace m1une {
namespace flow {
template <
class Cap,
class Cost,
class TotalCost = Cost,
std::size_t PivotLimitFactor = 8
>
struct BoundedMinCostFlow {
static_assert(std::numeric_limits<Cap>::is_integer);
static_assert(std::numeric_limits<Cap>::is_signed);
static_assert(std::numeric_limits<Cost>::is_specialized);
static_assert(std::numeric_limits<Cost>::is_signed);
struct Edge {
int from;
int to;
Cap lower;
Cap upper;
Cost cost;
};
struct ResultEdge {
int from;
int to;
Cap lower;
Cap upper;
Cap flow;
Cost cost;
};
struct Result {
std::vector<ResultEdge> edges;
std::vector<Cap> balance;
std::vector<Cost> potential;
TotalCost cost;
ResultEdge get_edge(int i) const {
assert(0 <= i && i < int(edges.size()));
return edges[i];
}
Cap flow(int i) const {
assert(0 <= i && i < int(edges.size()));
return edges[i].flow;
}
};
private:
struct NetworkEdge {
int to;
Cap cap;
Cost cost;
};
struct NetworkSimplexSolver {
enum class Status {
optimal,
infeasible,
pivot_limit_reached,
};
struct Parent {
int vertex;
int edge;
Cap up;
Cap down;
};
int n;
std::vector<NetworkEdge> edges;
std::vector<Cap> excess;
std::vector<Cost> potential;
std::size_t pivot_count = 0;
NetworkSimplexSolver(int vertex_count, const std::vector<Cap>& balance)
: n(vertex_count), excess(balance) {}
void reserve_edges(int edge_count) {
edges.reserve(2 * (edge_count + n));
}
int add_edge(int from, int to, Cap lower, Cap upper, Cost cost) {
int id = int(edges.size()) / 2;
edges.push_back(NetworkEdge{to, upper - lower, cost});
edges.push_back(NetworkEdge{from, Cap(0), -cost});
excess[from] -= lower;
excess[to] += lower;
return id;
}
Status solve(std::size_t pivot_limit) {
pivot_count = 0;
const int original_edge_count = int(edges.size());
potential.assign(n + 1, Cost(0));
Cost artificial_cost = Cost(1);
for (int edge = 0; edge < original_edge_count; edge += 2) {
artificial_cost += edges[edge].cost < Cost(0)
? -edges[edge].cost : edges[edge].cost;
}
std::vector<Parent> parent(n);
edges.reserve(original_edge_count + 2 * n);
for (int vertex = 0; vertex < n; vertex++) {
if (excess[vertex] >= Cap(0)) {
edges.push_back(NetworkEdge{n, Cap(0), artificial_cost});
edges.push_back(NetworkEdge{vertex, excess[vertex], -artificial_cost});
potential[vertex] = -artificial_cost;
} else {
edges.push_back(NetworkEdge{n, -excess[vertex], -artificial_cost});
edges.push_back(NetworkEdge{vertex, Cap(0), artificial_cost});
potential[vertex] = artificial_cost;
}
int edge = int(edges.size()) - 2;
parent[vertex] = Parent{
n, edge, edges[edge].cap, edges[edge ^ 1].cap
};
}
std::vector<int> depth(n + 1, 1);
depth[n] = 0;
std::vector<int> next(2 * (n + 1));
std::vector<int> previous(2 * (n + 1));
auto connect = [&](int first, int second) {
next[first] = second;
previous[second] = first;
};
for (int vertex = 0; vertex <= n; vertex++) {
connect(2 * vertex, 2 * vertex + 1);
}
for (int vertex = 0; vertex < n; vertex++) {
connect(2 * vertex + 1, next[2 * n]);
connect(2 * n, 2 * vertex);
}
auto push_flow = [&](int entering_edge) {
const int first = edges[entering_edge ^ 1].to;
const int second = edges[entering_edge].to;
const Cost cycle_cost =
edges[entering_edge].cost
+ potential[first] - potential[second];
Cap amount = edges[entering_edge].cap;
bool leave_first_side = true;
int leaving_vertex = second;
int first_ancestor = first;
int second_ancestor = second;
auto move_first_up = [&] {
if (parent[first_ancestor].down < amount) {
amount = parent[first_ancestor].down;
leaving_vertex = first_ancestor;
leave_first_side = true;
}
first_ancestor = parent[first_ancestor].vertex;
};
auto move_second_up = [&] {
if (parent[second_ancestor].up <= amount) {
amount = parent[second_ancestor].up;
leaving_vertex = second_ancestor;
leave_first_side = false;
}
second_ancestor = parent[second_ancestor].vertex;
};
if (depth[first_ancestor] >= depth[second_ancestor]) {
int difference = depth[first_ancestor] - depth[second_ancestor];
for (int i = 0; i < difference; i++) move_first_up();
} else {
int difference = depth[second_ancestor] - depth[first_ancestor];
for (int i = 0; i < difference; i++) move_second_up();
}
while (first_ancestor != second_ancestor) {
move_first_up();
move_second_up();
}
const int ancestor = first_ancestor;
if (amount != Cap(0)) {
int vertex = first;
while (vertex != ancestor) {
parent[vertex].up += amount;
parent[vertex].down -= amount;
vertex = parent[vertex].vertex;
}
vertex = second;
while (vertex != ancestor) {
parent[vertex].up -= amount;
parent[vertex].down += amount;
vertex = parent[vertex].vertex;
}
}
int vertex = first;
int new_parent = second;
std::pair<Cap, Cap> parent_capacities{
edges[entering_edge].cap - amount,
edges[entering_edge ^ 1].cap + amount
};
Cost potential_difference = -cycle_cost;
if (!leave_first_side) {
std::swap(vertex, new_parent);
std::swap(parent_capacities.first, parent_capacities.second);
potential_difference = -potential_difference;
}
int parent_edge = entering_edge ^ (leave_first_side ? 0 : 1);
while (new_parent != leaving_vertex) {
int new_depth = depth[new_parent];
int tour_index = 2 * vertex;
while (tour_index != 2 * vertex + 1) {
if ((tour_index & 1) == 0) {
new_depth++;
potential[tour_index / 2] += potential_difference;
depth[tour_index / 2] = new_depth;
} else {
new_depth--;
}
tour_index = next[tour_index];
}
connect(previous[2 * vertex], next[2 * vertex + 1]);
connect(2 * vertex + 1, next[2 * new_parent]);
connect(2 * new_parent, 2 * vertex);
std::swap(parent[vertex].edge, parent_edge);
parent_edge ^= 1;
std::swap(parent[vertex].up, parent_capacities.first);
std::swap(parent[vertex].down, parent_capacities.second);
std::swap(parent_capacities.first, parent_capacities.second);
int old_parent = parent[vertex].vertex;
parent[vertex].vertex = new_parent;
new_parent = vertex;
vertex = old_parent;
}
edges[parent_edge].cap = parent_capacities.first;
edges[parent_edge ^ 1].cap = parent_capacities.second;
};
bool pivot_limit_reached = false;
auto pivot = [&](int entering_edge) {
if (pivot_count == pivot_limit) {
pivot_limit_reached = true;
return false;
}
push_flow(entering_edge);
pivot_count++;
return true;
};
const int candidate_limit = std::max(
int(0.2 * std::sqrt(double(original_edge_count))), 10
);
const int minor_limit = std::max(candidate_limit / 10, 3);
std::vector<int> candidates;
candidates.reserve(candidate_limit);
auto minor_pivot = [&] {
Cost best_cost = Cost(0);
int best_edge = -1;
int index = 0;
while (index < int(candidates.size())) {
int edge = candidates[index];
if (edges[edge].cap == Cap(0)) {
candidates[index] = candidates.back();
candidates.pop_back();
continue;
}
Cost reduced_cost =
edges[edge].cost
+ potential[edges[edge ^ 1].to]
- potential[edges[edge].to];
if (reduced_cost >= Cost(0)) {
candidates[index] = candidates.back();
candidates.pop_back();
continue;
}
if (reduced_cost < best_cost) {
best_cost = reduced_cost;
best_edge = edge;
}
index++;
}
if (best_edge == -1) return false;
return pivot(best_edge);
};
int edge = 0;
while (true) {
for (int iteration = 0; iteration < minor_limit; iteration++) {
if (!minor_pivot()) break;
}
if (pivot_limit_reached) return Status::pivot_limit_reached;
Cost best_cost = Cost(0);
int best_edge = -1;
candidates.clear();
for (int scanned = 0; scanned < int(edges.size()); scanned++) {
if (edges[edge].cap != Cap(0)) {
Cost reduced_cost =
edges[edge].cost
+ potential[edges[edge ^ 1].to]
- potential[edges[edge].to];
if (reduced_cost < Cost(0)) {
if (reduced_cost < best_cost) {
best_cost = reduced_cost;
best_edge = edge;
}
candidates.push_back(edge);
if (int(candidates.size()) == candidate_limit) break;
}
}
edge++;
if (edge == int(edges.size())) edge = 0;
}
if (candidates.empty()) break;
if (!pivot(best_edge)) return Status::pivot_limit_reached;
}
for (int vertex = 0; vertex < n; vertex++) {
edges[parent[vertex].edge].cap = parent[vertex].up;
edges[parent[vertex].edge ^ 1].cap = parent[vertex].down;
}
bool feasible = true;
for (int vertex = 0; vertex < n; vertex++) {
int artificial_edge = original_edge_count + 2 * vertex;
if (
(excess[vertex] >= Cap(0)
&& edges[artificial_edge ^ 1].cap != Cap(0))
|| (excess[vertex] < Cap(0)
&& edges[artificial_edge].cap != Cap(0))
) {
feasible = false;
break;
}
}
potential.pop_back();
return feasible ? Status::optimal : Status::infeasible;
}
Cap edge_flow(int edge_id, Cap lower) const {
return lower + edges[2 * edge_id + 1].cap;
}
};
struct ScalingEdge {
int to;
int reverse;
Cap cap;
Cap flow;
Cost cost;
};
struct ScalingSolver {
int n;
std::vector<std::vector<ScalingEdge>> graph;
std::vector<std::pair<int, int>> positions;
std::vector<Cap> excess;
std::vector<Cost> potential;
std::vector<Cost> distance;
std::vector<int> parent_vertex;
std::vector<int> parent_edge;
std::vector<int> excess_vertices;
std::vector<int> deficit_vertices;
Cost farthest = Cost(0);
ScalingSolver(int vertex_count, const std::vector<Cap>& balance)
: n(vertex_count), graph(vertex_count), excess(balance),
potential(vertex_count, Cost(0)) {}
void reserve_edges(int edge_count) {
positions.reserve(edge_count);
}
int add_edge(int from, int to, Cap lower, Cap upper, Cost cost) {
int id = int(positions.size());
int from_edge = int(graph[from].size());
int to_edge = int(graph[to].size());
if (from == to) to_edge++;
positions.emplace_back(from, from_edge);
graph[from].push_back(ScalingEdge{
to, to_edge, upper, Cap(0), cost
});
graph[to].push_back(ScalingEdge{
from, from_edge, -lower, Cap(0), -cost
});
return id;
}
Cap residual_capacity(int from, int edge_id) const {
const auto& edge = graph[from][edge_id];
return edge.cap - edge.flow;
}
Cost residual_cost(int from, const ScalingEdge& edge) const {
return edge.cost + potential[from] - potential[edge.to];
}
void push(int from, int edge_id, Cap amount) {
auto& edge = graph[from][edge_id];
edge.flow += amount;
graph[edge.to][edge.reverse].flow -= amount;
}
void saturate_negative(Cap delta) {
excess_vertices.clear();
deficit_vertices.clear();
for (int from = 0; from < n; from++) {
for (
int edge_id = 0;
edge_id < int(graph[from].size());
edge_id++
) {
const auto& edge = graph[from][edge_id];
Cap residual = edge.cap - edge.flow;
residual -= residual % delta;
if (
residual_cost(from, edge) < Cost(0)
|| residual < Cap(0)
) {
int to = edge.to;
push(from, edge_id, residual);
excess[from] -= residual;
excess[to] += residual;
}
}
}
for (int vertex = 0; vertex < n; vertex++) {
if (excess[vertex] > Cap(0)) {
excess_vertices.push_back(vertex);
} else if (excess[vertex] < Cap(0)) {
deficit_vertices.push_back(vertex);
}
}
}
bool dual(Cap delta) {
excess_vertices.erase(
std::remove_if(
excess_vertices.begin(), excess_vertices.end(),
[&](int vertex) { return excess[vertex] < delta; }
),
excess_vertices.end()
);
deficit_vertices.erase(
std::remove_if(
deficit_vertices.begin(), deficit_vertices.end(),
[&](int vertex) { return excess[vertex] > -delta; }
),
deficit_vertices.end()
);
const Cost unreachable = std::numeric_limits<Cost>::max();
distance.assign(n, unreachable);
parent_vertex.assign(n, -1);
parent_edge.assign(n, -1);
using QueueEntry = std::pair<Cost, int>;
std::priority_queue<
QueueEntry,
std::vector<QueueEntry>,
std::greater<QueueEntry>
> queue;
for (int vertex : excess_vertices) {
distance[vertex] = Cost(0);
queue.emplace(Cost(0), vertex);
}
farthest = Cost(0);
int reached_deficits = 0;
while (!queue.empty()) {
auto [current_distance, from] = queue.top();
queue.pop();
if (distance[from] != current_distance) continue;
farthest = current_distance;
if (excess[from] <= -delta) reached_deficits++;
if (reached_deficits >= int(deficit_vertices.size())) break;
for (
int edge_id = 0;
edge_id < int(graph[from].size());
edge_id++
) {
const auto& edge = graph[from][edge_id];
if (edge.cap - edge.flow < delta) continue;
Cost next_distance =
current_distance + residual_cost(from, edge);
if (next_distance >= distance[edge.to]) continue;
distance[edge.to] = next_distance;
parent_vertex[edge.to] = from;
parent_edge[edge.to] = edge_id;
queue.emplace(next_distance, edge.to);
}
}
for (int vertex = 0; vertex < n; vertex++) {
potential[vertex] += std::min(distance[vertex], farthest);
}
return reached_deficits > 0;
}
void primal(Cap delta) {
for (int sink : deficit_vertices) {
if (distance[sink] > farthest) continue;
Cap amount = -excess[sink];
int root = sink;
while (parent_edge[root] != -1) {
int from = parent_vertex[root];
amount = std::min(
amount,
residual_capacity(from, parent_edge[root])
);
root = from;
}
amount = std::min(amount, excess[root]);
amount -= amount % delta;
if (amount <= Cap(0)) continue;
int vertex = sink;
while (parent_edge[vertex] != -1) {
int from = parent_vertex[vertex];
int edge_id = parent_edge[vertex];
push(from, edge_id, amount);
if (residual_capacity(from, edge_id) == Cap(0)) {
parent_edge[vertex] = -1;
}
vertex = from;
}
excess[sink] += amount;
excess[root] -= amount;
}
}
bool solve() {
Cap scale_bound = Cap(1);
for (Cap value : excess) {
scale_bound = std::max(scale_bound, value);
scale_bound = std::max(scale_bound, -value);
}
for (const auto& edges : graph) {
for (const auto& edge : edges) {
Cap residual = edge.cap - edge.flow;
scale_bound = std::max(scale_bound, residual);
scale_bound = std::max(scale_bound, -residual);
}
}
Cap delta = Cap(1);
while (delta <= scale_bound / Cap(2)) delta *= Cap(2);
while (true) {
saturate_negative(delta);
while (dual(delta)) primal(delta);
if (delta == Cap(1)) break;
delta /= Cap(2);
}
return excess_vertices.empty() && deficit_vertices.empty();
}
Cap edge_flow(int edge_id, Cap) const {
auto [from, index] = positions[edge_id];
return graph[from][index].flow;
}
};
int _n;
std::vector<Edge> _edges;
std::vector<Cap> _balance;
template <class Solver>
Result make_result(
const std::vector<Cap>& balance,
const Solver& solver,
std::vector<Cost> potential
) const {
Result result;
result.balance = balance;
result.cost = TotalCost(0);
result.edges.reserve(_edges.size());
for (int i = 0; i < int(_edges.size()); i++) {
const auto& edge = _edges[i];
Cap flow = solver.edge_flow(i, edge.lower);
result.cost += TotalCost(flow) * TotalCost(edge.cost);
result.edges.push_back(ResultEdge{
edge.from,
edge.to,
edge.lower,
edge.upper,
flow,
edge.cost
});
}
result.potential = std::move(potential);
return result;
}
std::vector<Cost> residual_potential(
const std::vector<ResultEdge>& edges
) const {
std::vector<Cost> potential(_n, Cost(0));
bool updated = false;
for (int iteration = 0; iteration < _n; iteration++) {
updated = false;
for (const ResultEdge& edge : edges) {
if (
edge.flow < edge.upper
&& potential[edge.to] > potential[edge.from] + edge.cost
) {
potential[edge.to] = potential[edge.from] + edge.cost;
updated = true;
}
if (
edge.lower < edge.flow
&& potential[edge.from] > potential[edge.to] - edge.cost
) {
potential[edge.from] = potential[edge.to] - edge.cost;
updated = true;
}
}
if (!updated) break;
}
assert(!updated);
return potential;
}
std::optional<Result> polynomial_min_cost_flow_impl(
const std::vector<Cap>& balance
) const {
ScalingSolver solver(_n, balance);
solver.reserve_edges(int(_edges.size()));
for (const auto& edge : _edges) {
solver.add_edge(
edge.from,
edge.to,
edge.lower,
edge.upper,
edge.cost
);
}
if (!solver.solve()) return std::nullopt;
Result result = make_result(balance, solver, {});
result.potential = residual_potential(result.edges);
return result;
}
public:
BoundedMinCostFlow() : BoundedMinCostFlow(0) {}
explicit BoundedMinCostFlow(int n) : _n(n), _balance(n, Cap(0)) {
assert(0 <= n);
}
int size() const {
return _n;
}
int edge_count() const {
return int(_edges.size());
}
void reserve_edges(int edge_count) {
assert(0 <= edge_count);
_edges.reserve(edge_count);
}
int add_edge(int from, int to, Cap lower, Cap upper, Cost cost) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
assert(lower <= upper);
int id = int(_edges.size());
_edges.push_back(Edge{from, to, lower, upper, cost});
return id;
}
Edge get_edge(int i) const {
assert(0 <= i && i < int(_edges.size()));
return _edges[i];
}
std::vector<Edge> edges() const {
return _edges;
}
void set_balance(int v, Cap b) {
assert(0 <= v && v < _n);
_balance[v] = b;
}
void add_balance(int v, Cap b) {
assert(0 <= v && v < _n);
_balance[v] += b;
}
void add_supply(int v, Cap supply) {
assert(Cap(0) <= supply);
add_balance(v, supply);
}
void add_demand(int v, Cap demand) {
assert(Cap(0) <= demand);
add_balance(v, -demand);
}
Cap balance(int v) const {
assert(0 <= v && v < _n);
return _balance[v];
}
const std::vector<Cap>& balances() const {
return _balance;
}
std::optional<Result> min_cost_flow() const {
return min_cost_flow(_balance);
}
std::optional<Result> min_cost_flow(const std::vector<Cap>& balance) const {
assert(int(balance.size()) == _n);
Cap balance_sum = Cap(0);
for (Cap value : balance) balance_sum += value;
if (balance_sum != Cap(0)) return std::nullopt;
NetworkSimplexSolver solver(_n, balance);
solver.reserve_edges(int(_edges.size()));
for (const auto& edge : _edges) {
solver.add_edge(edge.from, edge.to, edge.lower, edge.upper, edge.cost);
}
const std::size_t graph_size =
std::size_t(_n) + _edges.size() + 1;
std::size_t pivot_limit = 0;
if constexpr (PivotLimitFactor != 0) {
const std::size_t maximum =
std::numeric_limits<std::size_t>::max();
pivot_limit = graph_size > maximum / PivotLimitFactor
? maximum : PivotLimitFactor * graph_size;
}
auto status = solver.solve(pivot_limit);
if (status == NetworkSimplexSolver::Status::infeasible) {
return std::nullopt;
}
if (status == NetworkSimplexSolver::Status::pivot_limit_reached) {
return polynomial_min_cost_flow_impl(balance);
}
return make_result(balance, solver, std::move(solver.potential));
}
std::optional<Result> min_cost_flow_polynomial() const {
return min_cost_flow_polynomial(_balance);
}
std::optional<Result> min_cost_flow_polynomial(
const std::vector<Cap>& balance
) const {
assert(int(balance.size()) == _n);
Cap balance_sum = Cap(0);
for (Cap value : balance) balance_sum += value;
if (balance_sum != Cap(0)) return std::nullopt;
return polynomial_min_cost_flow_impl(balance);
}
std::optional<Result> min_cost_st_flow(int s, int t, Cap flow_value) const {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
assert(s != t);
std::vector<Cap> balance = _balance;
balance[s] += flow_value;
balance[t] -= flow_value;
return min_cost_flow(balance);
}
std::optional<Result> min_cost_st_flow_polynomial(
int s,
int t,
Cap flow_value
) const {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
assert(s != t);
std::vector<Cap> balance = _balance;
balance[s] += flow_value;
balance[t] -= flow_value;
return min_cost_flow_polynomial(balance);
}
};
template <
class Cap,
class Cost,
class TotalCost = Cost,
std::size_t PivotLimitFactor = 8
>
using BMinCostFlow = BoundedMinCostFlow<
Cap,
Cost,
TotalCost,
PivotLimitFactor
>;
} // namespace flow
} // namespace m1une
#line 1 "utilities/int128.hpp"
#line 5 "utilities/int128.hpp"
#include <cctype>
#include <istream>
#include <ostream>
#include <stdexcept>
#include <string>
namespace m1une {
namespace utilities {
using i128 = __int128_t;
using u128 = __uint128_t;
inline std::string to_string(u128 x) {
if (x == 0) {
return "0";
}
std::string s;
while (x > 0) {
s.push_back(static_cast<char>('0' + x % 10));
x /= 10;
}
std::reverse(s.begin(), s.end());
return s;
}
inline std::string to_string(i128 x) {
if (x < 0) {
u128 magnitude = static_cast<u128>(-(x + 1)) + 1;
return "-" + to_string(magnitude);
}
return to_string(static_cast<u128>(x));
}
inline u128 parse_uint128(const std::string& s) {
if (s.empty()) {
throw std::invalid_argument("empty string");
}
u128 value = 0;
for (char c : s) {
if (!std::isdigit(static_cast<unsigned char>(c))) {
throw std::invalid_argument("invalid unsigned __int128 literal");
}
value = value * 10 + static_cast<unsigned>(c - '0');
}
return value;
}
inline i128 parse_int128(const std::string& s) {
if (s.empty()) {
throw std::invalid_argument("empty string");
}
bool negative = s[0] == '-';
std::size_t pos = (s[0] == '-' || s[0] == '+') ? 1 : 0;
if (pos == s.size()) {
throw std::invalid_argument("invalid __int128 literal");
}
i128 value = 0;
for (; pos < s.size(); ++pos) {
char c = s[pos];
if (!std::isdigit(static_cast<unsigned char>(c))) {
throw std::invalid_argument("invalid __int128 literal");
}
int digit = c - '0';
value = value * 10 + (negative ? -digit : digit);
}
return value;
}
} // namespace utilities
} // namespace m1une
inline std::ostream& operator<<(std::ostream& os, __uint128_t x) {
return os << m1une::utilities::to_string(x);
}
inline std::ostream& operator<<(std::ostream& os, __int128_t x) {
return os << m1une::utilities::to_string(x);
}
inline std::istream& operator>>(std::istream& is, __uint128_t& x) {
std::string s;
is >> s;
if (is) {
x = m1une::utilities::parse_uint128(s);
}
return is;
}
inline std::istream& operator>>(std::istream& is, __int128_t& x) {
std::string s;
is >> s;
if (is) {
x = m1une::utilities::parse_int128(s);
}
return is;
}
#line 5 "verify/graph/flow/min_cost_b_flow.test.cpp"
#line 1 "utilities/fast_io.hpp"
#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#line 15 "utilities/fast_io.hpp"
#include <sys/stat.h>
#include <type_traits>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"
namespace m1une {
namespace utilities {
struct FastOutput;
namespace internal {
// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;
// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};
template <class T>
struct is_range<T, std::void_t<
decltype(std::begin(std::declval<T&>())),
decltype(std::end(std::declval<T&>()))
>> : std::true_type {};
template <class T>
inline constexpr bool is_range_v = is_range<T>::value;
template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));
template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;
template <class T, class = void>
struct range_stored_value {
using type = range_value_t<T>;
};
template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};
template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;
// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};
template <class T, std::size_t N>
struct is_char_array<T[N]>
: std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};
template <class T>
struct is_string_like
: std::bool_constant<
std::is_same_v<std::decay_t<T>, std::string>
|| std::is_same_v<std::decay_t<T>, const char*>
|| std::is_same_v<std::decay_t<T>, char*>
|| is_char_array<std::remove_reference_t<T>>::value
> {};
template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;
// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};
template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
: std::true_type {};
template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;
template <class T, class = void>
struct has_static_mod_raw : std::false_type {};
template <class T>
struct has_static_mod_raw<
T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
: std::true_type {};
template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;
// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
std::is_integral_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>
|| std::is_same_v<std::remove_cv_t<T>, __uint128_t>;
template <class T>
inline constexpr bool is_signed_v =
std::is_signed_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>;
template <class T>
struct make_unsigned {
using type = std::make_unsigned_t<T>;
};
template <>
struct make_unsigned<__int128_t> {
using type = __uint128_t;
};
template <>
struct make_unsigned<__uint128_t> {
using type = __uint128_t;
};
template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;
} // namespace internal
struct FastInput {
static constexpr int buffer_size = 1 << 20;
private:
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _length;
int _file_descriptor;
bool _streaming;
bool refill() {
_position = 0;
if (_streaming) {
ssize_t length;
do {
length = ::read(_file_descriptor, _buffer, buffer_size);
} while (length < 0 && errno == EINTR);
if (length <= 0) {
_length = 0;
return false;
}
_length = int(length);
} else {
_length = int(std::fread(_buffer, 1, buffer_size, _stream));
}
return _length != 0;
}
template <class T>
bool read_integer_from_stream(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-') {
negative = true;
c = read_char_raw();
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
result = negative ? result * 10 - (c - '0')
: result * 10 + (c - '0');
c = read_char_raw();
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + T(c - '0');
c = read_char_raw();
}
value = negative ? T(0) - result : result;
}
return true;
}
bool prepare_number() {
if (_length - _position >= 64) return true;
const int remaining = _length - _position;
if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
_position = 0;
_length = remaining + added;
if (_length < buffer_size) _buffer[_length] = '\0';
return _length != 0;
}
public:
explicit FastInput(std::FILE* stream = stdin)
: _stream(stream),
_position(0),
_length(0),
_file_descriptor(::fileno(stream)),
_streaming([&] {
struct stat status;
return _file_descriptor >= 0
&& ::fstat(_file_descriptor, &status) == 0
&& !S_ISREG(status.st_mode);
}()) {}
FastInput(const FastInput&) = delete;
FastInput& operator=(const FastInput&) = delete;
int read_char_raw() {
if (_position == _length && !refill()) return EOF;
return _buffer[_position++];
}
bool skip_spaces() {
int c = read_char_raw();
while (c != EOF && c <= ' ') c = read_char_raw();
if (c == EOF) return false;
--_position;
return true;
}
bool read(char& value) {
if (!skip_spaces()) return false;
value = char(read_char_raw());
return true;
}
bool read(std::string& value) {
if (!skip_spaces()) return false;
value.clear();
while (true) {
const int begin = _position;
while (_position < _length &&
static_cast<unsigned char>(_buffer[_position]) > ' ') {
++_position;
}
value.append(_buffer + begin, _position - begin);
if (_position < _length) {
++_position;
return true;
}
if (!refill()) return true;
}
}
bool read(bool& value) {
int x;
if (!read(x)) return false;
value = x != 0;
return true;
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>,
bool
>
read(T& value) {
if (_streaming) return read_integer_from_stream(value);
if (!prepare_number()) return false;
int c = static_cast<unsigned char>(_buffer[_position++]);
while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);
bool negative = false;
if (c == '-') {
negative = true;
c = static_cast<unsigned char>(_buffer[_position++]);
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
const int first = c - '0';
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = negative ? result * 100 - (first * 10 + second)
: result * 100 + (first * 10 + second);
++_position;
} else {
result = negative ? result * 10 - first : result * 10 + first;
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
const unsigned first = unsigned(c - '0');
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = result * 100 + T(first * 10 + unsigned(second));
++_position;
} else {
result = result * 10 + T(first);
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = negative ? T(0) - result : result;
}
if (_position > _length) _position = _length;
return true;
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>, bool>
read(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-' || c == '+') {
negative = c == '-';
c = read_char_raw();
}
long double result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + (c - '0');
c = read_char_raw();
}
if (c == '.') {
long double place = 0.1L;
c = read_char_raw();
while ('0' <= c && c <= '9') {
result += (c - '0') * place;
place *= 0.1L;
c = read_char_raw();
}
}
if (c == 'e' || c == 'E') {
c = read_char_raw();
bool exponent_negative = false;
if (c == '-' || c == '+') {
exponent_negative = c == '-';
c = read_char_raw();
}
int exponent = 0;
while ('0' <= c && c <= '9') {
exponent = exponent * 10 + (c - '0');
c = read_char_raw();
}
long double scale = 1;
long double power = 10;
while (exponent > 0) {
if (exponent & 1) scale *= power;
power *= power;
exponent >>= 1;
}
result = exponent_negative ? result / scale : result * scale;
}
value = static_cast<T>(negative ? -result : result);
return true;
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>,
bool
>
read(T& value) {
long long x;
if (!read(x)) return false;
if constexpr (internal::has_static_mod_raw_v<T>) {
if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
value = T::raw(uint32_t(x));
} else {
value = T(x);
}
} else {
value = T(x);
}
return true;
}
template <class First, class Second>
bool read(std::pair<First, Second>& value) {
if (!read(value.first)) return false;
return read(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>,
bool
>
read(Range& range) {
using StoredValue = internal::range_stored_value_t<Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
for (auto&& value : range) {
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
bool x;
if (!read(x)) return false;
value = x;
} else {
if (!read(value)) return false;
}
}
return true;
}
template <class First, class Second, class... Rest>
bool read(First& first, Second& second, Rest&... rest) {
if (!read(first)) return false;
return read(second, rest...);
}
template <class T>
FastInput& operator>>(T& value) {
if (!read(value)) std::abort();
return *this;
}
};
struct FastOutput {
static constexpr int buffer_size = 1 << 20;
private:
inline static const auto digit_quads = [] {
std::array<char, 40000> result{};
for (int i = 0; i < 10000; i++) {
int value = i;
for (int j = 3; j >= 0; j--) {
result[4 * i + j] = char('0' + value % 10);
value /= 10;
}
}
return result;
}();
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _precision;
std::chars_format _float_format;
char _range_separator;
std::string* _capture = nullptr;
template <class T>
std::string format_cell(const T& value) {
std::string result;
struct CaptureGuard {
std::string*& target;
std::string* previous;
~CaptureGuard() { target = previous; }
} guard{_capture, _capture};
_capture = &result;
write(value);
return result;
}
template <class Matrix>
void write_aligned_matrix(const Matrix& matrix) {
std::vector<std::vector<std::string>> rows;
std::vector<std::size_t> widths;
for (const auto& row : matrix) {
auto& cells = rows.emplace_back();
std::size_t column = 0;
for (const auto& value : row) {
cells.push_back(format_cell(value));
if (column == widths.size()) widths.push_back(0);
widths[column] = std::max(widths[column], cells.back().size());
++column;
}
}
bool first = true;
for (const auto& row : rows) {
if (!first) write_char('\n');
first = false;
for (std::size_t column = 0; column < row.size(); ++column) {
if (column != 0) write_char(_range_separator);
for (std::size_t padding = row[column].size();
padding < widths[column]; ++padding) {
write_char(' ');
}
write(row[column]);
}
}
}
public:
explicit FastOutput(std::FILE* stream = stdout)
: _stream(stream),
_position(0),
_precision(6),
_float_format(std::chars_format::general),
_range_separator(' ') {
if (_stream == stdout
&& internal::standard_output_instance == nullptr) {
internal::standard_output_instance = this;
}
}
FastOutput(const FastOutput&) = delete;
FastOutput& operator=(const FastOutput&) = delete;
~FastOutput() {
flush();
if (internal::standard_output_instance == this) {
internal::standard_output_instance = nullptr;
}
}
void flush() {
if (_position != 0) {
std::fwrite(_buffer, 1, _position, _stream);
_position = 0;
}
std::fflush(_stream);
}
void write_char(char c) {
if (_capture != nullptr) {
_capture->push_back(c);
return;
}
if (_position == buffer_size) flush();
_buffer[_position++] = c;
}
void write(const char* s) {
while (*s != '\0') write_char(*s++);
}
void write(const std::string& s) {
if (_capture != nullptr) {
_capture->append(s);
return;
}
std::size_t position = 0;
while (position < s.size()) {
if (_position == buffer_size) flush();
const std::size_t copied =
std::min<std::size_t>(buffer_size - _position, s.size() - position);
std::memcpy(_buffer + _position, s.data() + position, copied);
_position += int(copied);
position += copied;
}
}
void write(char c) {
write_char(c);
}
void write(bool value) {
write_char(value ? '1' : '0');
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>>
write(T value) {
char digits[128];
auto [end, error] = std::to_chars(
digits,
digits + sizeof(digits),
value,
_float_format,
_precision
);
if (error != std::errc()) std::abort();
for (const char* pointer = digits; pointer != end; pointer++) {
write_char(*pointer);
}
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>
>
write(T value) {
using Raw = std::remove_cv_t<T>;
using Unsigned = internal::make_unsigned_t<Raw>;
Unsigned magnitude;
if constexpr (internal::is_signed_v<Raw>) {
if (value < 0) {
write_char('-');
magnitude = Unsigned(0) - Unsigned(value);
} else {
magnitude = Unsigned(value);
}
} else {
magnitude = value;
}
if (magnitude == 0) {
write_char('0');
return;
}
unsigned chunks[16];
int count = 0;
while (magnitude >= 10000) {
const Unsigned quotient = magnitude / 10000;
chunks[count++] = unsigned(magnitude - quotient * 10000);
magnitude = quotient;
}
if (_capture == nullptr && _position > buffer_size - 64) flush();
char captured[64];
char* const begin = _capture != nullptr ? captured : _buffer + _position;
char* destination = begin;
const unsigned leading = unsigned(magnitude);
const char* first = digit_quads.data() + 4 * leading;
int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
for (; skip < 4; skip++) *destination++ = first[skip];
while (count--) {
const char* digits = digit_quads.data() + 4 * chunks[count];
std::memcpy(destination, digits, 4);
destination += 4;
}
if (_capture != nullptr) {
_capture->append(begin, destination - begin);
} else {
_position += int(destination - begin);
}
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>
>
write(const T& value) {
write(value.val());
}
template <class First, class Second>
void write(const std::pair<First, Second>& value) {
write(value.first);
write_char(' ');
write(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>
>
write(const Range& range) {
using StoredValue = internal::range_stored_value_t<const Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
bool first = true;
for (const auto& value : range) {
if (!first) write_char(nested ? '\n' : _range_separator);
first = false;
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
write(static_cast<bool>(value));
} else {
write(value);
}
}
}
template <class First, class... Rest>
void print(const First& first, const Rest&... rest) {
write(first);
((write_char(' '), write(rest)), ...);
}
void println() {
write_char('\n');
}
void set_precision(int precision) {
_precision = precision;
}
void set_fixed(int precision = 6) {
_float_format = std::chars_format::fixed;
_precision = precision;
}
void set_general(int precision = 6) {
_float_format = std::chars_format::general;
_precision = precision;
}
void set_range_separator(char separator) {
_range_separator = separator;
}
template <class Matrix>
void write_aligned(const Matrix& matrix) {
using Row = internal::range_stored_value_t<const Matrix>;
using Cell = internal::range_stored_value_t<const Row>;
static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
"write_aligned requires a two-dimensional range");
static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
"write_aligned requires scalar cells");
write_aligned_matrix(matrix);
}
template <class Matrix>
void println_aligned(const Matrix& matrix) {
write_aligned(matrix);
write_char('\n');
}
template <class... Args>
void println(const Args&... args) {
print(args...);
write_char('\n');
}
template <class T>
FastOutput& operator<<(const T& value) {
write(value);
return *this;
}
};
} // namespace utilities
} // namespace m1une
#line 8 "verify/graph/flow/min_cost_b_flow.test.cpp"
int main() {
m1une::utilities::FastInput fast_input;
m1une::utilities::FastOutput fast_output;
using Flow = long long;
using Cost = long long;
using TotalCost = __int128_t;
using Solver = m1une::flow::BoundedMinCostFlow<Flow, Cost, TotalCost>;
int vertex_count, edge_count;
fast_input >> vertex_count >> edge_count;
Solver solver(vertex_count);
solver.reserve_edges(edge_count);
for (int vertex = 0; vertex < vertex_count; vertex++) {
Flow balance;
fast_input >> balance;
solver.set_balance(vertex, balance);
}
for (int edge = 0; edge < edge_count; edge++) {
int from, to;
Flow lower, upper;
long long cost;
fast_input >> from >> to >> lower >> upper >> cost;
solver.add_edge(from, to, lower, upper, cost);
}
auto result = solver.min_cost_flow();
if (!result.has_value()) {
fast_output << "infeasible\n";
return 0;
}
assert(int(result->potential.size()) == vertex_count);
for (const auto& edge : result->edges) {
Cost reduced_cost =
edge.cost + result->potential[edge.from] - result->potential[edge.to];
if (edge.flow < edge.upper) assert(Cost(0) <= reduced_cost);
if (edge.lower < edge.flow) assert(reduced_cost <= Cost(0));
}
fast_output << result->cost << '\n';
for (Cost potential : result->potential) fast_output << potential << '\n';
for (const auto& edge : result->edges) fast_output << edge.flow << '\n';
}
verify/graph/flow/min_cost_b_flow.test.cpp