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Dinic's Algorithm
(src/graph/directed/flow/Dinic.hpp)
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- Last update: 2021-11-25 21:45:58+09:00
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#include "src/graph/directed/flow/Dinic.hpp"
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#pragma once
/**
* @file Dinic.hpp
* @brief Dinic's Algorithm
*/
#include <limits>
#include "base.hpp"
namespace workspace {
/**
* @brief Compute the maximum flow.
* @tparam _Cap Capacity type
*/
template <class _Cap> class Dinic : public flow_graph<_Cap> {
using _Base = flow_graph<_Cap>;
public:
using _Base::_Base;
using typename _Base::size_type;
protected:
constexpr static size_type nil = -1;
std::vector<size_type> __level;
std::vector<typename _Base::container_type::value_type::iterator> __iter;
_Cap dfs(size_type __src, size_type __dst, _Cap __limit) noexcept {
if (__src == __dst) return __limit;
_Cap __flow(0);
for (auto &__e{__iter[__dst]}; __e != _Base::graph[__dst].end(); ++__e)
if (static_cast<_Cap>(0) < __e->flow &&
__level[__e->head] < __level[__dst])
if (_Cap achv = dfs(__src, __e->head, std::min(__limit, __e->flow));
static_cast<_Cap>(0) < achv) {
__e->push(-achv);
__flow += achv, __limit -= achv;
if (__limit == static_cast<_Cap>(0)) break;
}
return __flow;
}
public:
/**
* @brief Run Dinic's algorithm.
* @param __src Source
* @param __dst Destination
* @return Maximum flow.
*/
_Cap run(size_type __src, size_type __dst) noexcept {
return run(__src, __dst, std::numeric_limits<_Cap>::max());
}
/**
* @brief Run Dinic's algorithm.
* @param __src Source
* @param __dst Destination
* @param __limit Flow limit
* @return Maximum flow.
*/
_Cap run(size_type __src, size_type __dst, _Cap __limit) noexcept {
assert(__src < _Base::size()), assert(__dst < _Base::size()),
assert(__src != __dst);
__level.resize(_Base::size(), nil);
__iter.resize(_Base::size());
if (!(static_cast<_Cap>(0) < __limit)) return 0;
_Cap __flow = 0;
for (std::vector<size_type> __q(_Base::size());;
std::fill(__level.begin(), __level.end(), nil)) {
__level[__q.front() = __src] = 0;
for (auto __ql{__q.begin()}, __qr{std::next(__ql)};
__level[__dst] == nil && __ql != __qr; ++__ql)
for (const auto &__e : _Base::graph[*__ql])
if (static_cast<_Cap>(0) < __e.capacity && __level[__e.head] == nil)
__level[ *__qr++ = __e.head] = __level[*__ql] + 1;
if (__level[__dst] == nil) break;
for (size_type __x{}; __x != _Base::size(); ++__x)
__iter[__x] = _Base::graph[__x].begin();
__flow += dfs(__src, __dst, __limit);
}
return __flow;
}
// Minimum Cut.
// Call it after `run`.
auto min_cut() const noexcept {
std::vector<typename _Base::edge> __cut;
for (size_type __x{}; __x != _Base::size(); ++__x)
if (~__level[__x])
for (const auto &__e : _Base::operator[](__x))
if (!~__level[__e.head]) __cut.emplace_back(__e);
return __cut;
}
};
} // namespace workspace#line 2 "src/graph/directed/flow/Dinic.hpp"
/**
* @file Dinic.hpp
* @brief Dinic's Algorithm
*/
#include <limits>
#line 2 "src/graph/directed/flow/base.hpp"
/**
* @file base.hpp
* @brief Flow Graph
*/
#include <cassert>
#include <numeric>
#include <tuple>
#include <vector>
namespace workspace {
template <class _Cap, class _Cost = void> class flow_graph {
protected:
class adjacency_impl;
public:
using container_type = std::vector<adjacency_impl>;
using size_type = typename container_type::size_type;
class unweighted_edge {
public:
size_type tail; // Source
size_type head; // Destination
_Cap capacity; // Capacity
_Cap flow; // Flow
unweighted_edge(size_type __s, size_type __d, const _Cap &__u = 1)
: tail(__s), head(__d), capacity(__u), flow(0) {
assert(!(capacity < static_cast<_Cap>(0))),
assert(!(flow < static_cast<_Cap>(0)));
}
// tail, head, capacity, flow
template <class _Os>
friend _Os &operator<<(_Os &__os, const unweighted_edge &__e) {
return __os << __e.tail << ' ' << __e.head << ' ' << __e.capacity << ' '
<< __e.flow;
}
protected:
unweighted_edge() = default;
unweighted_edge(size_type __s, size_type __d, const _Cap &__u,
const _Cap &__f)
: tail(__s), head(__d), capacity(__u), flow(__f) {}
unweighted_edge make_rev() const { return {head, tail, flow, capacity}; }
};
class weighted_edge : public unweighted_edge {
public:
_Cost cost; // _Cost
weighted_edge(const unweighted_edge &__e, const _Cost &__c = 0)
: unweighted_edge(__e), cost(__c) {}
weighted_edge(size_type __s, size_type __d, const _Cap &__u = 1,
const _Cost &__c = 0)
: unweighted_edge(__s, __d, __u), cost(__c) {}
// tail, head, capacity, flow, cost
template <class _Os>
friend _Os &operator<<(_Os &__os, const weighted_edge &__e) {
return __os << static_cast<unweighted_edge>(__e) << ' ' << __e.cost;
}
protected:
weighted_edge() = default;
weighted_edge make_rev() const {
return {unweighted_edge::make_rev(), -cost};
}
};
using edge = std::conditional_t<std::is_void<_Cost>::value, unweighted_edge,
weighted_edge>;
protected:
struct edge_impl : edge {
bool aux = false;
edge_impl *rev = nullptr;
edge_impl() = default;
edge_impl(const edge &__e) : edge(__e) {}
edge_impl(edge &&__e) : edge(__e) {}
void push(_Cap __f) {
edge::capacity -= __f;
edge::flow += __f;
if (rev) {
rev->capacity += __f;
rev->flow -= __f;
}
}
edge_impl make_rev() {
edge_impl __e = edge::make_rev();
__e.aux = true;
__e.rev = this;
return __e;
}
};
public:
class adjacency {
public:
using value_type = edge;
using reference = edge &;
using const_reference = edge const &;
using pointer = edge *;
using const_pointer = const edge *;
class iterator {
edge_impl *__p;
public:
iterator(edge_impl *__p = nullptr) : __p(__p) {}
bool operator!=(const iterator &__x) const { return __p != __x.__p; }
bool operator==(const iterator &__x) const { return __p == __x.__p; }
iterator &operator++() {
do ++__p;
while (__p->rev && __p->aux);
return *this;
}
iterator operator++(int) {
auto __cp = *this;
do ++__p;
while (__p->rev && __p->aux);
return __cp;
}
iterator &operator--() {
do --__p;
while (__p->aux);
return *this;
}
iterator operator--(int) {
auto __cp = *this;
do --__p;
while (__p->aux);
return __cp;
}
pointer operator->() const { return __p; }
reference operator*() const { return *__p; }
};
class const_iterator {
const edge_impl *__p;
public:
const_iterator(const edge_impl *__p = nullptr) : __p(__p) {}
bool operator!=(const const_iterator &__x) const {
return __p != __x.__p;
}
bool operator==(const const_iterator &__x) const {
return __p == __x.__p;
}
const_iterator &operator++() {
do ++__p;
while (__p->rev && __p->aux);
return *this;
}
const_iterator operator++(int) {
auto __cp = *this;
do ++__p;
while (__p->rev && __p->aux);
return __cp;
}
const_iterator &operator--() {
do --__p;
while (__p->aux);
return *this;
}
const_iterator operator--(int) {
auto __cp = *this;
do --__p;
while (__p->aux);
return __cp;
}
const_pointer operator->() const { return __p; }
const_reference operator*() const { return *__p; }
};
adjacency()
: first(new edge_impl[2]), last(first + 1), __s(first), __t(first) {}
~adjacency() { delete[] first; }
const_reference operator[](size_type __i) const {
assert(__i < size());
return *(first + __i);
}
size_type size() const { return __t - first; }
auto begin() { return iterator{__s}; }
auto begin() const { return const_iterator{__s}; }
auto end() { return iterator{__t}; }
auto end() const { return const_iterator{__t}; }
/**
* @brief Construct a new adjacency object
*
* @param __x Rvalue reference to another object
*/
adjacency(adjacency &&__x) : first(nullptr) { operator=(std::move(__x)); }
/**
* @brief Assignment operator.
*
* @param __x Rvalue reference to another object
* @return Reference to this object.
*/
adjacency &operator=(adjacency &&__x) {
delete[] first;
first = __x.first, __x.first = nullptr;
last = __x.last, __s = __x.__s, __t = __x.__t;
return *this;
}
protected:
edge_impl *first, *last, *__s, *__t;
};
using value_type = adjacency;
using reference = adjacency &;
using const_reference = adjacency const &;
protected:
class adjacency_impl : public adjacency {
public:
using _Base = adjacency;
using _Base::__s;
using _Base::__t;
using _Base::first;
using _Base::last;
using iterator = edge_impl *;
iterator push(const edge_impl &__e) {
realloc();
*__t = __e;
if (__s->aux) ++__s;
return __t++;
}
iterator push(edge_impl &&__e) {
realloc();
*__t = std::move(__e);
if (__s->aux) ++__s;
return __t++;
}
iterator begin() const { return first; }
iterator end() const { return __t; }
void realloc() {
if (__t == last) {
size_type __n(last - first);
iterator loc = new edge_impl[__n << 1 | 1];
__s += loc - first;
__t = loc;
for (iterator __p{first}; __p != last; ++__p, ++__t) {
*__t = *__p;
if (__p->rev) __p->rev->rev = __t;
}
delete[] first;
first = loc;
last = __t + __n;
}
}
};
// Only member variable.
container_type graph;
public:
/**
* @brief Construct a new flow graph object
*
* @param __n Number of vertices
*/
flow_graph(size_type __n = 0) : graph(__n) {}
/**
* @brief Construct a new flow graph object
*
* @param __x Const reference to another object
*/
flow_graph(const flow_graph &__x) : graph(__x.size()) {
for (auto &&__adj : __x)
for (auto &&__e : __adj) add_edge(__e);
}
/**
* @brief Construct a new flow graph object
*
* @param __x Rvalue reference to another object
*/
flow_graph(flow_graph &&__x) : graph(std::move(__x.graph)) {}
/**
* @brief Assignment operator.
*
* @param __x Const reference to another object
* @return Reference to this object.
*/
flow_graph &operator=(const flow_graph &__x) {
return operator=(std::move(flow_graph{__x}));
}
/**
* @brief Assignment operator.
*
* @param __x Rvalue reference to another object
* @return Reference to this object.
*/
flow_graph &operator=(flow_graph &&__x) {
graph = std::move(__x.graph);
return *this;
}
/**
* @return Whether the graph is empty.
*/
bool empty() const { return graph.empty(); }
/**
* @return Number of nodes.
*/
size_type size() const { return graph.size(); }
/**
* @param node Node
* @return Referece to the adjacency list of the node.
*/
reference operator[](size_type node) {
assert(node < size());
return graph[node];
}
/**
* @param node Node
* @return Const referece to the adjacency list of the node.
*/
const_reference operator[](size_type node) const {
assert(node < size());
return graph[node];
}
class iterator : public container_type::iterator {
using _Base = typename container_type::iterator;
public:
using reference = adjacency &;
using pointer = adjacency *;
iterator(const _Base &__i) : _Base(__i) {}
pointer operator->() const { return _Base::operator->(); }
reference operator*() const { return _Base::operator*(); }
};
class const_iterator : public container_type::const_iterator {
using _Base = typename container_type::const_iterator;
public:
using const_reference = const adjacency &;
using const_pointer = const adjacency *;
const_iterator(const _Base &__i) : _Base(__i) {}
const_pointer operator->() const { return _Base::operator->(); }
const_reference operator*() const { return _Base::operator*(); }
};
auto begin() { return iterator{graph.begin()}; }
auto begin() const { return const_iterator{graph.begin()}; }
auto end() { return iterator{graph.end()}; }
auto end() const { return const_iterator{graph.end()}; }
/**
* @brief Add a node to the graph.
*
* @return Index of the node.
*/
size_type add_node() { return add_nodes(1).front(); }
/**
* @brief Add some nodes to the graph.
*
* @param __n Number of nodes added
* @return List of indices of the nodes.
*/
std::vector<size_type> add_nodes(size_type __n) noexcept {
std::vector<size_type> __nodes(__n);
std::iota(__nodes.begin(), __nodes.end(), graph.size());
graph.resize(graph.size() + __n);
return __nodes;
}
/**
* @brief Add a directed edge to the graph.
*
* @return Reference to the edge.
*/
template <class... _Args>
typename std::enable_if<std::is_constructible<edge, _Args...>::value,
edge &>::type
add_edge(_Args &&...__args) {
edge_impl __e = edge(std::forward<_Args>(__args)...);
assert(__e.tail < size()), assert(__e.head < size());
edge_impl *__p = graph[__e.tail].push(std::move(__e));
// Careful with a self loop.
if (__p->tail != __p->head)
__p->rev = graph[__p->head].push(__p->make_rev());
return *__p;
}
/**
* @brief Add an undirected edge to the graph. Its cost must be non-negative.
*
* @return Reference to the edge.
*/
template <class... _Args> edge &add_undirected_edge(_Args &&...__args) {
edge_impl __e = edge(std::forward<_Args>(__args)...);
assert(__e.tail < size()), assert(__e.head < size());
__e.flow += __e.capacity;
edge_impl *__p = graph[__e.tail].push(std::move(__e));
// Careful with a self loop.
if (__p->tail != __p->head) {
edge_impl __r = __p->make_rev();
__r.aux = false;
__p->rev = graph[__p->head].push(std::move(__r));
}
return *__p;
}
template <class _Os>
friend _Os &operator<<(_Os &__os, flow_graph const &__g) {
for (const auto &__adj : __g)
for (const auto &__e : __adj) __os << __e << "\n";
return __os;
}
};
} // namespace workspace
#line 11 "src/graph/directed/flow/Dinic.hpp"
namespace workspace {
/**
* @brief Compute the maximum flow.
* @tparam _Cap Capacity type
*/
template <class _Cap> class Dinic : public flow_graph<_Cap> {
using _Base = flow_graph<_Cap>;
public:
using _Base::_Base;
using typename _Base::size_type;
protected:
constexpr static size_type nil = -1;
std::vector<size_type> __level;
std::vector<typename _Base::container_type::value_type::iterator> __iter;
_Cap dfs(size_type __src, size_type __dst, _Cap __limit) noexcept {
if (__src == __dst) return __limit;
_Cap __flow(0);
for (auto &__e{__iter[__dst]}; __e != _Base::graph[__dst].end(); ++__e)
if (static_cast<_Cap>(0) < __e->flow &&
__level[__e->head] < __level[__dst])
if (_Cap achv = dfs(__src, __e->head, std::min(__limit, __e->flow));
static_cast<_Cap>(0) < achv) {
__e->push(-achv);
__flow += achv, __limit -= achv;
if (__limit == static_cast<_Cap>(0)) break;
}
return __flow;
}
public:
/**
* @brief Run Dinic's algorithm.
* @param __src Source
* @param __dst Destination
* @return Maximum flow.
*/
_Cap run(size_type __src, size_type __dst) noexcept {
return run(__src, __dst, std::numeric_limits<_Cap>::max());
}
/**
* @brief Run Dinic's algorithm.
* @param __src Source
* @param __dst Destination
* @param __limit Flow limit
* @return Maximum flow.
*/
_Cap run(size_type __src, size_type __dst, _Cap __limit) noexcept {
assert(__src < _Base::size()), assert(__dst < _Base::size()),
assert(__src != __dst);
__level.resize(_Base::size(), nil);
__iter.resize(_Base::size());
if (!(static_cast<_Cap>(0) < __limit)) return 0;
_Cap __flow = 0;
for (std::vector<size_type> __q(_Base::size());;
std::fill(__level.begin(), __level.end(), nil)) {
__level[__q.front() = __src] = 0;
for (auto __ql{__q.begin()}, __qr{std::next(__ql)};
__level[__dst] == nil && __ql != __qr; ++__ql)
for (const auto &__e : _Base::graph[*__ql])
if (static_cast<_Cap>(0) < __e.capacity && __level[__e.head] == nil)
__level[ *__qr++ = __e.head] = __level[*__ql] + 1;
if (__level[__dst] == nil) break;
for (size_type __x{}; __x != _Base::size(); ++__x)
__iter[__x] = _Base::graph[__x].begin();
__flow += dfs(__src, __dst, __limit);
}
return __flow;
}
// Minimum Cut.
// Call it after `run`.
auto min_cut() const noexcept {
std::vector<typename _Base::edge> __cut;
for (size_type __x{}; __x != _Base::size(); ++__x)
if (~__level[__x])
for (const auto &__e : _Base::operator[](__x))
if (!~__level[__e.head]) __cut.emplace_back(__e);
return __cut;
}
};
} // namespace workspace