QOJ.ac

QOJ

IDSubmission IDProblemHackerOwnerResultSubmit timeJudge time
#1119#711152#9545. Magical SetquailtyquailtySuccess!2024-11-05 01:07:202024-11-05 01:07:21

Details

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'

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#711152#9545. Magical SetquailtyWA 25ms5660kbC++237.6kb2024-11-05 01:06:592024-11-05 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);
}