cplib-cpp
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flow/test/mincostflow.yuki1324.test.cpp
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- Last update: 2023-02-09 02:29:06+08:00
- Problem: https://yukicoder.me/problems/no/1324
Depends on
Code
#define PROBLEM "https://yukicoder.me/problems/no/1324"
#include "../mincostflow_nonegativeloop.hpp"
#include <iostream>
#include <vector>
using namespace std;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
int N, K;
cin >> N >> K;
vector<int> A(N), B(N);
vector<vector<int>> P(N, vector<int>(N));
for (auto &x : A) cin >> x;
for (auto &x : B) cin >> x;
for (auto &v : P) {
for (auto &x : v) cin >> x;
}
const int gs = N * 2, gt = gs + 1;
MinCostFlow<int, long long> graph(gt + 1);
long long ret = 0;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
ret += P[i][j] * P[i][j];
for (int a = 0; a < A[i]; a++) graph.add_edge(i, j + N, 1, 2 * (a - P[i][j]) + 1);
}
graph.add_edge(gs, i, A[i], 0);
graph.add_edge(i + N, gt, B[i], 0);
}
cout << ret + graph.flow(gs, gt, K).second << '\n';
}#line 1 "flow/test/mincostflow.yuki1324.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1324"
#line 2 "flow/mincostflow_nonegativeloop.hpp"
#include <cassert>
#include <limits>
#include <queue>
#include <vector>
// CUT begin
// Minimum cost flow WITH NO NEGATIVE CYCLE (just negative cost edge is allowed)
// Verified:
// - SRM 770 Div1 Medium https://community.topcoder.com/stat?c=problem_statement&pm=15702
// - CodeChef LTIME98 Ancient Magic https://www.codechef.com/problems/ANCT
template <class Cap, class Cost, Cost INF_COST = std::numeric_limits<Cost>::max() / 2>
struct MinCostFlow {
template <class E> struct csr {
std::vector<int> start;
std::vector<E> elist;
explicit csr(int n, const std::vector<std::pair<int, E>> &edges)
: start(n + 1), elist(edges.size()) {
for (auto e : edges) { start[e.first + 1]++; }
for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; }
auto counter = start;
for (auto e : edges) { elist[counter[e.first]++] = e.second; }
}
};
public:
MinCostFlow() {}
explicit MinCostFlow(int n) : is_dual_infeasible(false), _n(n) {
static_assert(std::numeric_limits<Cap>::max() > 0, "max() must be greater than 0");
}
int add_edge(int from, int to, Cap cap, Cost cost) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
assert(0 <= cap);
if (cost < 0) is_dual_infeasible = true;
int m = int(_edges.size());
_edges.push_back({from, to, cap, 0, cost});
return m;
}
struct edge {
int from, to;
Cap cap, flow;
Cost cost;
};
edge get_edge(int i) {
int m = int(_edges.size());
assert(0 <= i && i < m);
return _edges[i];
}
std::vector<edge> edges() { return _edges; }
std::pair<Cap, Cost> flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
return slope(s, t, flow_limit).back();
}
std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
return slope(s, t, std::numeric_limits<Cap>::max());
}
std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
assert(s != t);
int m = int(_edges.size());
std::vector<int> edge_idx(m);
auto g = [&]() {
std::vector<int> degree(_n), redge_idx(m);
std::vector<std::pair<int, _edge>> elist;
elist.reserve(2 * m);
for (int i = 0; i < m; i++) {
auto e = _edges[i];
edge_idx[i] = degree[e.from]++;
redge_idx[i] = degree[e.to]++;
elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}});
elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}});
}
auto _g = csr<_edge>(_n, elist);
for (int i = 0; i < m; i++) {
auto e = _edges[i];
edge_idx[i] += _g.start[e.from];
redge_idx[i] += _g.start[e.to];
_g.elist[edge_idx[i]].rev = redge_idx[i];
_g.elist[redge_idx[i]].rev = edge_idx[i];
}
return _g;
}();
auto result = slope(g, s, t, flow_limit);
for (int i = 0; i < m; i++) {
auto e = g.elist[edge_idx[i]];
_edges[i].flow = _edges[i].cap - e.cap;
}
return result;
}
private:
bool is_dual_infeasible;
int _n;
std::vector<edge> _edges;
// inside edge
struct _edge {
int to, rev;
Cap cap;
Cost cost;
};
std::vector<std::pair<Cap, Cost>> slope(csr<_edge> &g, int s, int t, Cap flow_limit) {
// variants (C = maxcost):
// -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
// reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge
// dual_dist[i] = (dual[i], dist[i])
std::vector<std::pair<Cost, Cost>> dual_dist(_n);
if (is_dual_infeasible) {
auto check_dag = [&]() {
std::vector<int> deg_in(_n);
for (int v = 0; v < _n; v++) {
for (int i = g.start[v]; i < g.start[v + 1]; i++) {
deg_in[g.elist[i].to] += g.elist[i].cap > 0;
}
}
std::vector<int> st;
st.reserve(_n);
for (int i = 0; i < _n; i++) {
if (!deg_in[i]) st.push_back(i);
}
for (int n = 0; n < _n; n++) {
if (int(st.size()) == n) return false; // Not DAG
int now = st[n];
for (int i = g.start[now]; i < g.start[now + 1]; i++) {
const auto &e = g.elist[i];
if (!e.cap) continue;
deg_in[e.to]--;
if (deg_in[e.to] == 0) st.push_back(e.to);
if (dual_dist[e.to].first >= dual_dist[now].first + e.cost)
dual_dist[e.to].first = dual_dist[now].first + e.cost;
}
}
return true;
}();
if (!check_dag) throw;
auto dt = dual_dist[t].first;
for (int v = 0; v < _n; v++) dual_dist[v].first -= dt;
is_dual_infeasible = false;
}
std::vector<int> prev_e(_n);
std::vector<bool> vis(_n);
struct Q {
Cost key;
int to;
bool operator<(Q r) const { return key > r.key; }
};
std::vector<int> que_min;
std::vector<Q> que;
auto dual_ref = [&]() {
for (int i = 0; i < _n; i++) {
dual_dist[i].second = std::numeric_limits<Cost>::max();
}
std::fill(vis.begin(), vis.end(), false);
que_min.clear();
que.clear();
// que[0..heap_r) was heapified
unsigned heap_r = 0;
dual_dist[s].second = 0;
que_min.push_back(s);
while (!que_min.empty() || !que.empty()) {
int v;
if (!que_min.empty()) {
v = que_min.back();
que_min.pop_back();
} else {
while (heap_r < que.size()) {
heap_r++;
std::push_heap(que.begin(), que.begin() + heap_r);
}
v = que.front().to;
std::pop_heap(que.begin(), que.end());
que.pop_back();
heap_r--;
}
if (vis[v]) continue;
vis[v] = true;
if (v == t) break;
// dist[v] = shortest(s, v) + dual[s] - dual[v]
// dist[v] >= 0 (all reduced cost are positive)
// dist[v] <= (n-1)C
Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
for (int i = g.start[v]; i < g.start[v + 1]; i++) {
auto e = g.elist[i];
if (!e.cap) continue;
// |-dual[e.to] + dual[v]| <= (n-1)C
// cost <= C - -(n-1)C + 0 = nC
Cost cost = e.cost - dual_dist[e.to].first + dual_v;
if (dual_dist[e.to].second - dist_v > cost) {
Cost dist_to = dist_v + cost;
dual_dist[e.to].second = dist_to;
prev_e[e.to] = e.rev;
if (dist_to == dist_v) {
que_min.push_back(e.to);
} else {
que.push_back(Q{dist_to, e.to});
}
}
}
}
if (!vis[t]) { return false; }
for (int v = 0; v < _n; v++) {
if (!vis[v]) continue;
// dual[v] = dual[v] - dist[t] + dist[v]
// = dual[v] - (shortest(s, t) + dual[s] - dual[t]) +
// (shortest(s, v) + dual[s] - dual[v]) = - shortest(s,
// t) + dual[t] + shortest(s, v) = shortest(s, v) -
// shortest(s, t) >= 0 - (n-1)C
dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second;
}
return true;
};
Cap flow = 0;
Cost cost = 0, prev_cost_per_flow = -1;
bool first_aug = true;
std::vector<std::pair<Cap, Cost>> result = {{Cap(0), Cost(0)}};
while (flow < flow_limit) {
if (!dual_ref()) break;
Cap c = flow_limit - flow;
for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap);
}
for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
auto &e = g.elist[prev_e[v]];
e.cap += c;
g.elist[e.rev].cap -= c;
}
Cost d = -dual_dist[s].first;
flow += c;
cost += c * d;
if (!first_aug && prev_cost_per_flow == d) { result.pop_back(); }
result.push_back({flow, cost});
prev_cost_per_flow = d;
first_aug = false;
}
return result;
}
};
#line 3 "flow/test/mincostflow.yuki1324.test.cpp"
#include <iostream>
#line 5 "flow/test/mincostflow.yuki1324.test.cpp"
using namespace std;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
int N, K;
cin >> N >> K;
vector<int> A(N), B(N);
vector<vector<int>> P(N, vector<int>(N));
for (auto &x : A) cin >> x;
for (auto &x : B) cin >> x;
for (auto &v : P) {
for (auto &x : v) cin >> x;
}
const int gs = N * 2, gt = gs + 1;
MinCostFlow<int, long long> graph(gt + 1);
long long ret = 0;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
ret += P[i][j] * P[i][j];
for (int a = 0; a < A[i]; a++) graph.add_edge(i, j + N, 1, 2 * (a - P[i][j]) + 1);
}
graph.add_edge(gs, i, A[i], 0);
graph.add_edge(i + N, gt, B[i], 0);
}
cout << ret + graph.flow(gs, gt, K).second << '\n';
}