結果
問題 | No.1324 Approximate the Matrix |
ユーザー |
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提出日時 | 2020-12-06 21:30:38 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 47 ms / 2,000 ms |
コード長 | 6,230 bytes |
コンパイル時間 | 2,678 ms |
コンパイル使用メモリ | 210,808 KB |
最終ジャッジ日時 | 2025-01-16 18:34:48 |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 42 |
ソースコード
#include <bits/stdc++.h>using namespace std;#include <algorithm>#include <cassert>#include <limits>#include <queue>#include <vector>namespace atcoder {template <class Cap, class Cost> struct mcf_graph {public:mcf_graph() {}mcf_graph(int n) : _n(n), g(n) {}int add_edge(int from, int to, Cap cap, Cost cost) {assert(0 <= from && from < _n);assert(0 <= to && to < _n);assert(0 <= cap);assert(0 <= cost);int m = int(pos.size());pos.push_back({from, int(g[from].size())});int from_id = int(g[from].size());int to_id = int(g[to].size());if (from == to) to_id++;g[from].push_back(_edge{to, to_id, cap, cost});g[to].push_back(_edge{from, from_id, 0, -cost});return m;}struct edge {int from, to;Cap cap, flow;Cost cost;};edge get_edge(int i) {int m = int(pos.size());assert(0 <= i && i < m);auto _e = g[pos[i].first][pos[i].second];auto _re = g[_e.to][_e.rev];return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,};}std::vector<edge> edges() {int m = int(pos.size());std::vector<edge> result(m);for (int i = 0; i < m; i++) {result[i] = get_edge(i);}return result;}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);// 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 edgestd::vector<Cost> dual(_n, 0), dist(_n);std::vector<int> pv(_n), pe(_n);std::vector<bool> vis(_n);auto dual_ref = [&]() {std::fill(dist.begin(), dist.end(),std::numeric_limits<Cost>::max());std::fill(pv.begin(), pv.end(), -1);std::fill(pe.begin(), pe.end(), -1);std::fill(vis.begin(), vis.end(), false);struct Q {Cost key;int to;bool operator<(Q r) const { return key > r.key; }};std::priority_queue<Q> que;dist[s] = 0;que.push(Q{0, s});while (!que.empty()) {int v = que.top().to;que.pop();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)Cfor (int i = 0; i < int(g[v].size()); i++) {auto e = g[v][i];if (vis[e.to] || !e.cap) continue;// |-dual[e.to] + dual[v]| <= (n-1)C// cost <= C - -(n-1)C + 0 = nCCost cost = e.cost - dual[e.to] + dual[v];if (dist[e.to] - dist[v] > cost) {dist[e.to] = dist[v] + cost;pv[e.to] = v;pe[e.to] = i;que.push(Q{dist[e.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)Cdual[v] -= dist[t] - dist[v];}return true;};Cap flow = 0;Cost cost = 0, prev_cost_per_flow = -1;std::vector<std::pair<Cap, Cost>> result;result.push_back({flow, cost});while (flow < flow_limit) {if (!dual_ref()) break;Cap c = flow_limit - flow;for (int v = t; v != s; v = pv[v]) {c = std::min(c, g[pv[v]][pe[v]].cap);}for (int v = t; v != s; v = pv[v]) {auto& e = g[pv[v]][pe[v]];e.cap -= c;g[v][e.rev].cap += c;}Cost d = -dual[s];flow += c;cost += c * d;if (prev_cost_per_flow == d) {result.pop_back();}result.push_back({flow, cost});prev_cost_per_flow = d;}return result;}private:int _n;struct _edge {int to, rev;Cap cap;Cost cost;};std::vector<std::pair<int, int>> pos;std::vector<std::vector<_edge>> g;};} // namespace atcoderusing namespace atcoder;#define rep2(i, m, n) for (int i = (m); i < (n); ++i)#define rep(i, n) rep2(i, 0, n)template<class T> istream &operator>>(istream &is, vector<T> &v) { for (auto &e : v) is >> e; return is; }struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;int main() {const int BIG = 400;int n, k; cin >> n >> k;int s = 2*n;int t = 2*n + 1;int N = 2*n + 2;mcf_graph<int, int> g(N);vector<int> a(n), b(n); cin >> a >> b;rep(i, n) g.add_edge(s, i, a[i], 0);rep(i, n) g.add_edge(n+i, t, b[i], 0);int ans = 0;rep(i, n) rep(j, n) {int p; cin >> p;ans += p*p;rep(x, a[i]) g.add_edge(i, n+j, 1, 2*(x-p) + 1 + BIG);}auto [cap, cost] = g.flow(s, t, k);ans += cost - k * BIG;cout << ans << '\n';}