competitive-programming-library
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Primal-dual algorithm
(graph/PrimalDual.hpp)
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- Last update: 2023-06-25 16:21:20+09:00
- Include:
#include "graph/PrimalDual.hpp"
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#pragma once
#include "../basic/template.hpp"
class PrimalDualDemandOver {};
class PrimalDual {
class edge {
public:
int to, cap;
lint cost;
int rev, id;
};
int n, idx = 0, s, t;
lint curres = 0;
std::vector<std::vector<edge>> vec;
std::vector<int> prevv, preve;
std::vector<lint> h, dist;
bool negative = false;
lint BellmanFord() {
dist.assign(n, LINF);
dist[s] = 0;
rep(i, n - 1) {
rep(j, n) {
rep(k, vec[j].size()) {
const edge& e = vec[j][k];
if (e.cap > 0 && chmin(dist[e.to], dist[j] + e.cost + h[j] - h[e.to])) {
prevv[e.to] = j;
preve[e.to] = k;
}
}
}
}
if (dist[t] == LINF) throw PrimalDualDemandOver();
rep(i, n) h[i] += dist[i];
for (int i = t; i != s; i = prevv[i]) {
vec[prevv[i]][preve[i]].cap--;
vec[i][vec[prevv[i]][preve[i]].rev].cap++;
}
return h[t];
}
public:
PrimalDual(int n, int s, int t) : n(n), s(s), t(t) {
vec.resize(n);
h.resize(n);
dist.resize(n);
prevv.resize(n);
preve.resize(n);
}
void add_edge(int from, int to, int cap, lint cost) {
if (cost < 0) negative = true;
vec[from].push_back({to, cap, cost, (int)vec[to].size(), -1});
vec[to].push_back({from, 0, -cost, (int)vec[from].size() - 1, idx++});
}
lint add_flow(int f) {
if (negative) {
curres += BellmanFord();
f--;
negative = false;
}
while (f > 0) {
dist.assign(n, LINF);
dist[s] = 0;
prique<std::pair<lint, int>> que;
que.push({0, s});
while (!que.empty()) {
auto p = que.top();
que.pop();
if (dist[p.second] < p.first) continue;
rep(i, vec[p.second].size()) {
edge& e = vec[p.second][i];
if (e.cap > 0 &&
chmin(dist[e.to], dist[p.second] + e.cost + h[p.second] - h[e.to])) {
prevv[e.to] = p.second;
preve[e.to] = i;
que.push({dist[e.to], e.to});
}
}
}
if (dist[t] == LINF) throw PrimalDualDemandOver();
rep(i, n) h[i] += dist[i];
int d = f;
for (int i = t; i != s; i = prevv[i]) {
chmin(d, vec[prevv[i]][preve[i]].cap);
}
f -= d;
curres += (lint)d * h[t];
for (int i = t; i != s; i = prevv[i]) {
vec[prevv[i]][preve[i]].cap -= d;
vec[i][vec[prevv[i]][preve[i]].rev].cap += d;
}
}
return curres;
}
std::vector<lint> restore() {
std::vector<lint> res(idx);
rep(i, n) {
for (const auto& j : vec[i]) {
if (j.id != -1) res[j.id] = j.cap;
}
}
return res;
}
void reset() {
rep(i, n) {
for (auto& j : vec[i]) {
if (j.id != -1) {
vec[j.to][j.rev].cap += j.cap;
j.cap = 0;
}
}
}
}
};
/**
* @title Primal-dual algorithm
*/#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()
using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;
constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
return std::popcount(x);
#else
#ifndef __clang__
return __builtin_popcount(x);
#endif
#endif
x = (x & 0x55555555) + (x >> 1 & 0x55555555);
x = (x & 0x33333333) + (x >> 2 & 0x33333333);
x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
return [f = std::forward<F>(f)](auto&&... args) {
return f(f, std::forward<decltype(args)>(args)...);
};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
return ost << x.first << " " << x.second;
}
template <class Container,
std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
-> decltype(typename Container::iterator(), std::cin)& {
Container tmp;
while (true) {
typename Container::value_type t;
ist >> t;
tmp.emplace_back(t);
if (getchar() == '\n') break;
}
cont = Container(std::move(tmp));
return ist;
}
template <class Container, class Stream,
std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
-> decltype(typename Container::iterator(), ost)& {
for (auto it = cont.begin(); it != cont.end(); it++) {
if (it != cont.begin()) ost << ' ';
ost << *it;
}
return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
lint res = 0;
for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
if (lhs < rhs) {
lhs = rhs;
return true;
}
return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
if (lhs > rhs) {
lhs = rhs;
return true;
}
return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
while (b) {
lint c = a;
a = b;
b = c % b;
}
return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
if (n == 1) return false;
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) return false;
}
return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
T res(1);
while (true) {
if (b & 1) res *= a;
b >>= 1;
if (!b) break;
a *= a;
}
return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
a %= m;
lint res(1);
while (b) {
if (b & 1) res *= a, res %= m;
a *= a, a %= m, b >>= 1;
}
return res;
}
LP extGcd(lint a, lint b) noexcept {
if (b == 0) return {1, 0};
LP s = extGcd(b, a % b);
std::swap(s.first, s.second);
s.second -= a / b * s.first;
return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
auto p = extGcd(m1, m2);
lint g = gcd(m1, m2), l = m1 / g * m2;
lint tmp = (b2 - b1) / g * p.first % (m2 / g);
lint r = (b1 + m1 * tmp + l) % l;
return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
rep(i, a.size()) {
rep(j, b.size()) {
chmax(dp[i + 1][j], dp[i][j]);
chmax(dp[i][j + 1], dp[i][j]);
if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
}
chmax(dp[i + 1][b.size()], dp[i][b.size()]);
}
rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
auto tmp = vec;
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
std::vector<T> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
std::vector<typename InputIter::value_type> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter,
std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
if (lhs.first.first / M < rhs.first.first / M) return true;
if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
return false;
});
int before = -1, cnt = 0;
bool f = false;
for (InputIter i = l; i != r; i++) {
if (before != i->first.first / M) {
if (f) std::reverse(i - cnt, i);
f ^= true, before = i->first.first / M, cnt = 1;
} else
cnt++;
}
if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
std::vector<T> res;
for (T i : vec) {
for (T j : res) {
chmin(i, i ^ j);
}
if (i) res.emplace_back(i);
}
return res;
}
#line 3 "graph/PrimalDual.hpp"
class PrimalDualDemandOver {};
class PrimalDual {
class edge {
public:
int to, cap;
lint cost;
int rev, id;
};
int n, idx = 0, s, t;
lint curres = 0;
std::vector<std::vector<edge>> vec;
std::vector<int> prevv, preve;
std::vector<lint> h, dist;
bool negative = false;
lint BellmanFord() {
dist.assign(n, LINF);
dist[s] = 0;
rep(i, n - 1) {
rep(j, n) {
rep(k, vec[j].size()) {
const edge& e = vec[j][k];
if (e.cap > 0 && chmin(dist[e.to], dist[j] + e.cost + h[j] - h[e.to])) {
prevv[e.to] = j;
preve[e.to] = k;
}
}
}
}
if (dist[t] == LINF) throw PrimalDualDemandOver();
rep(i, n) h[i] += dist[i];
for (int i = t; i != s; i = prevv[i]) {
vec[prevv[i]][preve[i]].cap--;
vec[i][vec[prevv[i]][preve[i]].rev].cap++;
}
return h[t];
}
public:
PrimalDual(int n, int s, int t) : n(n), s(s), t(t) {
vec.resize(n);
h.resize(n);
dist.resize(n);
prevv.resize(n);
preve.resize(n);
}
void add_edge(int from, int to, int cap, lint cost) {
if (cost < 0) negative = true;
vec[from].push_back({to, cap, cost, (int)vec[to].size(), -1});
vec[to].push_back({from, 0, -cost, (int)vec[from].size() - 1, idx++});
}
lint add_flow(int f) {
if (negative) {
curres += BellmanFord();
f--;
negative = false;
}
while (f > 0) {
dist.assign(n, LINF);
dist[s] = 0;
prique<std::pair<lint, int>> que;
que.push({0, s});
while (!que.empty()) {
auto p = que.top();
que.pop();
if (dist[p.second] < p.first) continue;
rep(i, vec[p.second].size()) {
edge& e = vec[p.second][i];
if (e.cap > 0 &&
chmin(dist[e.to], dist[p.second] + e.cost + h[p.second] - h[e.to])) {
prevv[e.to] = p.second;
preve[e.to] = i;
que.push({dist[e.to], e.to});
}
}
}
if (dist[t] == LINF) throw PrimalDualDemandOver();
rep(i, n) h[i] += dist[i];
int d = f;
for (int i = t; i != s; i = prevv[i]) {
chmin(d, vec[prevv[i]][preve[i]].cap);
}
f -= d;
curres += (lint)d * h[t];
for (int i = t; i != s; i = prevv[i]) {
vec[prevv[i]][preve[i]].cap -= d;
vec[i][vec[prevv[i]][preve[i]].rev].cap += d;
}
}
return curres;
}
std::vector<lint> restore() {
std::vector<lint> res(idx);
rep(i, n) {
for (const auto& j : vec[i]) {
if (j.id != -1) res[j.id] = j.cap;
}
}
return res;
}
void reset() {
rep(i, n) {
for (auto& j : vec[i]) {
if (j.id != -1) {
vec[j.to][j.rev].cap += j.cap;
j.cap = 0;
}
}
}
}
};
/**
* @title Primal-dual algorithm
*/