結果
| 問題 | No.1324 Approximate the Matrix |
| ユーザー |
 theory_and_me
|
| 提出日時 | 2020-12-05 17:59:40 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
CE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 8,972 bytes |
| コンパイル時間 | 728 ms |
| コンパイル使用メモリ | 80,116 KB |
| 最終ジャッジ日時 | 2024-11-14 23:56:31 |
| 合計ジャッジ時間 | 1,252 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
main.cpp:17:14: error: 'function' in namespace 'std' does not name a template type
17 | std::function<Cost(Flow)> F; // must be discrete convex
| ^~~~~~~~
main.cpp:9:1: note: 'std::function' is defined in header '<functional>'; did you forget to '#include <functional>'?
8 | #include <iostream>
+++ |+#include <functional>
9 |
main.cpp:41:36: error: 'std::function' has not been declared
41 | int add_edge(int from, int to, std::function<Cost(Flow)> F, Flow cap, Flow flow){
| ^~~
main.cpp:41:49: error: expected ',' or '...' before '<' token
41 | int add_edge(int from, int to, std::function<Cost(Flow)> F, Flow cap, Flow flow){
| ^
main.cpp: In member function 'int mccf_graph<Flow, Cost>::add_edge(int, int, int)':
main.cpp:46:50: error: 'F' was not declared in this scope
46 | E.push_back(edge_with_function{from, to, F, cap, flow});
| ^
main.cpp:46:53: error: 'cap' was not declared in this scope
46 | E.push_back(edge_with_function{from, to, F, cap, flow});
| ^~~
main.cpp:46:58: error: 'flow' was not declared in this scope; did you mean 'Flow'?
46 | E.push_back(edge_with_function{from, to, F, cap, flow});
| ^~~~
| Flow
main.cpp: In function 'int main()':
main.cpp:289:19: error: no matching function for call to 'mccf_graph<long int, long int>::add_edge(int&, int&, main()::<lambda(int64_t)>&, __gnu_cxx::__alloc_traits<std::allocator<int>, int>::value_type&, int)'
289 | G.add_edge(s, i, F, A[i], 0);
| ~~~~~~~~~~^~~~~~~~~~~~~~~~~~
main.cpp:41:9: note: candidate: 'int mccf_graph<Flow, Cost>::add_edge(int, int, int) [with Flow = long int; Cos
ソースコード
// 想定解3 O(N^2)本の辺を張り，流すたびに辺のコストを書き換える
#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <vector>
#include <iostream>
template<class Flow, class Cost> struct mccf_graph{
int n;
// input edges
struct edge_with_function{
int from, to;
std::function<Cost(Flow)> F; // must be discrete convex
Flow cap, flow;
};
// edges on the residual graph
struct edge{
int to, rev, id;
bool available;
Cost cost;
bool is_rev;
// for debug
void print_edge(){ std::cerr << "to: " << to << " cost: " << cost << "\n";}
};
std::vector<std::vector<edge>> g;
std::vector<edge_with_function> E;
std::vector<Cost> dual;
mccf_graph() {}
mccf_graph(int n) : n(n), g(n){
dual.resize(n, 0);
}
int add_edge(int from, int to, std::function<Cost(Flow)> F, Flow cap, Flow flow){
assert(0 <= from and from < n);
assert(0 <= to and to < n);
// assert(cap > 0);
int m = int(E.size());
E.push_back(edge_with_function{from, to, F, cap, flow});
return m;
}
Cost calc_objective(){
Cost obj = 0;
for(auto &e: E){
obj += e.F(e.flow);
}
return obj;
}
/* for debug
void print_g(){
for(int i=0;i<n;i++){
for(edge &e: g[i]){
std::cerr << "to " << e.to;
std::cerr << " rev " << e.rev;
std::cerr << " id " << e.id;
std::cerr << " avail " << (int)e.available;
std::cerr << " cost " << e.cost;
std::cerr << " r_cost " << e.cost - dual[e.to] + dual[i];
std::cerr << " is_rev " << (int)e.is_rev;
std::cerr << "\n";
}
}
std::cerr << "\n";
}
void print_E(){
for(auto &e: E){
std::cerr << "from " << e.from;
std::cerr << " to " << e.to;
std::cerr << " cap " << e.cap;
std::cerr << " flow " << e.flow;
std::cerr << "\n";
}
std::cerr << "\n";
}
for debug */
void solve_SSP(int s, int t){
solve_SSP(s, t, std::numeric_limits<Flow>::max());
}
void solve_SSP(int s, int t, Flow flow_limit){
assert(0 <= s and s < n);
assert(0 <= t and t < n);
assert(s != t);
// construct a residual graph
int m = E.size();
for(int i=0;i<m;i++){
auto &e = E[i];
if(!e.cap) continue;
g[e.from].push_back(edge{e.to, (int)g[e.to].size(), i, true, e.F(1) - e.F(0), false});
g[e.to].push_back(edge{e.from, (int)g[e.from].size()-1, i, false, 0, true});
}
// get flow
std::vector<Cost> dist(n, 0);
std::vector<int> pv(n), pe(n);
std::vector<bool> vis(n);
auto dual_ref_Dijkstra = [&]()->bool{
fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
fill(pv.begin(), pv.end(), -1);
fill(pe.begin(), pe.end(), -1);
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;
for(int i=0;i<(int)g[v].size();i++){
auto &e = g[v][i];
if(vis[e.to] or !e.available) continue;
Cost 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;
}
// assert(vis[t]);
for(int v=0;v<n;v++){
if(!vis[v]) continue;
dual[v] -= dist[t] - dist[v];
}
return true;
};
auto dual_ref_BF = [&]()->bool{
fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
fill(pv.begin(), pv.end(), -1);
fill(pe.begin(), pe.end(), -1);
fill(vis.begin(), vis.end(), false);
dist[s] = 0;
vis[s] = true;
for(int itr=0;itr<n-1;itr++){
for(int v=0;v<n;v++){
// if(dist[v] == INF_cost) continue;
if(!vis[v]) continue;
for(int i=0;i<(int)g[v].size();i++){
auto &e = g[v][i];
if(!e.available) continue;
if(dist[e.to] > dist[v] + e.cost){
dist[e.to] = dist[v] + e.cost;
pv[e.to] = v;
pe[e.to] = i;
vis[e.to] = true;
}
}
}
}
// check feasibility
if(!vis[t]){
return false;
}
// detect negative cycle
for(int v=0;v<n;v++){
// if(dist[v] == INF_cost) continue;
if(!vis[v]) continue;
for(auto &e: g[v]){
if(!e.available) continue;
assert(dist[v] + e.cost >= dist[e.to]);
}
}
for(int v=0;v<n;v++){
// assert(dist[v]<INF_cost);
if(!vis[v]) continue;
dual[v] -= dist[t] - dist[v];
}
return true;
};
auto update_edge = [&](edge &e){
auto &e_func = E[e.id];
if(e.is_rev){
if(e_func.flow == 0){
e.available = false;
e.cost = 0;
}else{
e.available = true;
e.cost = e_func.F(e_func.flow-1) - e_func.F(e_func.flow);
}
}else{
if(e_func.flow == e_func.cap){
e.available = false;
e.cost = 0;
}else{
e.available = true;
e.cost = e_func.F(e_func.flow+1) - e_func.F(e_func.flow);
}
}
return;
};
Flow flow_cur = 0;
while(flow_cur < flow_limit){
if(!flow_cur){
if(!dual_ref_BF()) break;
}else{
if(!dual_ref_Dijkstra()) break;
}
for(int v=t;v!=s;v=pv[v]){
auto& e = g[pv[v]][pe[v]];
auto& e_func = E[e.id];
auto& re = g[v][e.rev];
if(e.is_rev) e_func.flow--;
else e_func.flow++;
update_edge(e);
update_edge(re);
}
flow_cur++;
}
}
};
int main(){
int N, M;
std::cin >> N >> M;
std::vector<int> A(N), B(N);
for(int i=0;i<N;i++) std::cin >> A[i];
for(int i=0;i<N;i++) std::cin >> B[i];
std::vector<std::vector<int>> T(N, std::vector<int>(N, 0));
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
std::cin >> T[i][j];
}
}
// assert
int A_sum = 0, B_sum = 0;
for(int i=0;i<N;i++){
assert(A[i] >= 0);
A_sum += A[i];
}
for(int i=0;i<N;i++){
assert(B[i] >= 0);
B_sum += B[i];
}
assert(A_sum == M);
assert(B_sum == M);
// graph construction
mccf_graph<int64_t, int64_t> G(2*N+2);
int s = 2*N;
int t = s+1;
int INF_cap = 1e9;
for(int i=0;i<N;i++){
auto F = [](int64_t x){return 0;};
G.add_edge(s, i, F, A[i], 0);
}
for(int i=0;i<N;i++){
auto F = [](int64_t x){return 0;};
G.add_edge(N+i, t, F, B[i], 0);
}
for(int i=0;i<N;i++){
for(int j=0;j<N;j++){
auto F = [&T, i, j](int64_t x){return (x-T[i][j])*(x-T[i][j]);};
G.add_edge(i, N+j, F, INF_cap, 0);
}
}
G.solve_SSP(s, t, M);
std::vector<std::vector<int>> res(N, std::vector<int>(N, 0));
for(auto &e: G.E){
if(e.from != s and e.to!= t){
res[e.from][e.to-N] = e.flow;
}
}
// for(int i=0;i<N;i++){
// for(int j=0;j<N;j++){
// std::cout << res[i][j] << " ";
// }
// std::cout << "\n";
// }
std::cout << G.calc_objective() << "\n";
return 0;
}