Submission #588730

#	Time	Username	Problem	Language	Result	Execution time	Memory
588730		Bench0310	Islands (IOI08_islands)	C++17	90 / 100	909 ms	131072 KiB

islands

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n;
    cin >> n;
    vector<array<int,3>> v;
    vector<array<int,3>> bad_edges;
    vector<int> u(n+1,0);
    for(int i=1;i<=n;i++) u[i]=i;
    function<int(int)> find_set=[&](int a)->int
    {
        if(a==u[a]) return a;
        else return u[a]=find_set(u[a]);
    };
    auto merge_sets=[&](int a,int b)->int
    {
        a=find_set(a);
        b=find_set(b);
        if(a==b) return 0;
        u[b]=a;
        return 1;
    };
    for(int a=1;a<=n;a++)
    {
        int b,c;
        cin >> b >> c;
        if(merge_sets(a,b))
        {
            v.push_back({a,b,c});
            v.push_back({b,a,c});
        }
        else bad_edges.push_back({a,b,c});
    }
    sort(v.begin(),v.end());
    vector<int> vidx(n+1,0);
    for(int i=(int)v.size()-1;i>=0;i--) vidx[v[i][0]]=i;
    ll res=0;
    auto chmax=[&](ll &a,ll b){a=max(a,b);};
    u.assign(n+1,0);
    vector<int> ucost(n+1,0);
    vector<bool> in_cycle(n+1,0);
    vector<ll> dp(n+1,0);
    vector<ll> down(n+1,0);
    for(auto [x,y,bad_cost]:bad_edges)
    {
        vector<int> cc;
        vector<int> cycle;
        function<void(int)> dfs=[&](int a)
        {
            cc.push_back(a);
            ll one=0,two=0;
            for(int i=vidx[a];i<(int)v.size()&&v[i][0]==a;i++)
            {
                auto [_,to,c]=v[i];
                if(to==u[a]) continue;
                u[to]=a;
                ucost[to]=c;
                dfs(to);
                ll len=c+down[to];
                if(len>one){two=one; one=len;}
                else if(len>two){two=len;}
                chmax(dp[a],dp[to]);
                chmax(down[a],len);
            }
            chmax(dp[a],one+two);
        };
        dfs(x);
        ll now=dp[x];
        int t=y;
        while(t!=0)
        {
            cycle.push_back(t);
            in_cycle[t]=1;
            t=u[t];
        }
        for(int a:cc) down[a]=dp[a]=0;
        function<void(int,int)> go=[&](int a,int p)
        {
            for(int i=vidx[a];i<(int)v.size()&&v[i][0]==a;i++)
            {
                auto [_,to,c]=v[i];
                if(to==p||in_cycle[to]) continue;
                go(to,a);
                chmax(down[a],c+down[to]);
            }
        };
        for(int a:cycle) go(a,0);
        int len=cycle.size();
        ll path=0;
        for(int i=0;i<len;i++)
        {
            if(i>0) dp[cycle[i]]=dp[cycle[i-1]];
            chmax(dp[cycle[i]],path+down[cycle[i]]);
            path+=ucost[cycle[i]];
        }
        path=0;
        ll opt=0;
        for(int i=len-1;i>=0;i--)
        {
            path+=ucost[cycle[i]];
            chmax(opt,path+down[cycle[i]]);
            if(i>0) chmax(now,dp[cycle[i-1]]+bad_cost+opt);
        }
        res+=now;
    }
    cout << res << "\n";
    return 0;
}

• Subtask 1: 33 / 33
• Subtask 2: 3 / 3
• Subtask 3: 4 / 4
• Subtask 4: 10 / 10
• Subtask 5: 10 / 10
• Subtask 6: 10 / 10
• Subtask 7: 10 / 10
• Subtask 8: 10 / 10
• Subtask 9: 0 / 10