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QOJ
ID | 提交记录ID | 题目 | Hacker | Owner | 结果 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|
#1119 | #711152 | #9545. Magical Set | quailty | quailty | Success! | 2024-11-05 01:07:20 | 2024-11-05 01:07:21 |
详细
Extra Test:
Wrong Answer
time: 0ms
memory: 3804kb
input:
4 1 2 3 42
output:
1
result:
wrong answer 1st lines differ - expected: '2', found: '1'
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#711152 | #9545. Magical Set | quailty | WA | 25ms | 5660kb | C++23 | 7.6kb | 2024-11-05 01:06:59 | 2024-11-05 01:12:58 |
answer
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
#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);
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 edge
std::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)C
for (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 = nC
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;
}
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[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 atcoder
using namespace std;
using namespace atcoder;
const int INF=0x3f3f3f3f;
map<int,int> mp,f;
int get_id(int x)
{
int t=mp.size();
if(!mp.count(x))
mp[x]=t;
return mp[x];
}
void dfs(int x,vector<pair<int,int>>& p)
{
if(f.count(x))return;
int& val=f[x];
for(auto& [v,w] : p)
{
if(w==0)continue;
val+=w;
--w;
dfs(x/v,p);
++w;
}
}
const int MAXN=305;
int ta[MAXN];
int main()
{
int n;
scanf("%d",&n);
for(int i=1;i<=n;i++)
{
int a;
scanf("%d",&a);
ta[i]=a;
vector<pair<int,int>> p;
for(int j=2;j*j<=a;j++)
{
if(a%j!=0)continue;
p.emplace_back(j,0);
while(a%j==0)a/=j,++p.back().second;
}
if(a>1)p.emplace_back(a,1);
dfs(ta[i],p);
}
int fn=f.size()+2;
vector<vector<tuple<int,int,int>>> flow_dag(fn);
vector<int> ind(fn);
int src=fn-2,dst=fn-1;
for(int i=1;i<=n;i++)
{
int u=get_id(ta[i]),fu=f[ta[i]],cnt=0;
for(auto& [c,fv] : f)
{
if(ta[i]<=c || ta[i]%c)continue;
int v=get_id(c);
flow_dag[u].emplace_back(v,INF,fv-fu);
++ind[v];
if(++cnt>=n)break;
}
}
for(int i=1;i<=n;i++)
{
flow_dag[src].emplace_back(get_id(ta[i]),1,0);
++ind[get_id(ta[i])];
}
for(int i=0;i<(int)f.size();i++)
{
flow_dag[i].emplace_back(dst,1,0);
++ind[dst];
}
vector<int> dis(fn,INF);
dis[src]=0;
queue<int,list<int>> que;
for(int i=0;i<fn;i++)
if(!ind[i])que.push(i);
while(!que.empty())
{
int u=que.front();
que.pop();
for(auto& [v,cap,cost] : flow_dag[u])
{
if(dis[u]<INF)dis[v]=min(dis[v],dis[u]+cost);
if(--ind[v]==0)que.push(v);
}
}
mcf_graph<int,int> flow_graph(fn);
for(int u=0;u<fn;u++)
{
if(dis[u]==INF)continue;
for(auto& [v,cap,cost] : flow_dag[u])
flow_graph.add_edge(u,v,cap,dis[u]+cost-dis[v]);
}
return 0*printf("%d\n",-n*dis[dst]-flow_graph.flow(src,dst,n).second);
}