제출 #1190026

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1190026		vnedu	Split the sequence (APIO14_sequence)	C++17	100 / 100	1000 ms	81408 KiB

sequence

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

template<class T> bool maximize(T &a, const T &b){ return (a < b ? a = b, 1 : 0); }
template<class T> bool minimize(T &a, const T &b){ return (a > b ? a = b, 1 : 0); }

#define fi first
#define se second

#define pb push_back
#define ii pair<int, int>

#define all(x) x.begin(), x.end()

#define TASK "nonsense"

/// end of template ///

const int N = 1e5 + 5;
const int K = 200 + 5;
int n,k,a[N],p[N];
namespace sub12
{
    const int N = 50+1;
    const ll inf = LLONG_MAX/2;
    bool check()
    {
        return (n<N);
    }
    ll dp[N][N][N];
    ii trace[N][N][N];
    void work(int tri, int i, int j)
    {
        if(i==j || tri==0) return;
        int tri1=trace[tri][i][j].fi;
        int pos=trace[tri][i][j].se;
        cout<<pos<<' ';
        work(tri1,i,pos);
        work(tri-1-tri1,pos+1,j);
    }
    void solve()
    {
        for(int tri=1;tri<=k;++tri) for(int i=1;i<=n;++i) for(int j=i;j<=n;++j)
        {
            dp[tri][i][j]=-inf;
//            bool dbg=(tri==3 && i==1 && j==7);
            for(int tri1=0;tri1<=tri-1;++tri1)
            {
                int tri2=tri-1-tri1;
//                cout<<tri<<' '<<tri1<<' '<<tri2<<'\n';
                for(int pos=i;pos<j;++pos)
                {
//                    if(dbg) cout<<tri<<' '<<tri1<<' '<<tri2<<' '<<pos<<' '<<dp[tri1][i][pos]<<' '<<dp[tri2][pos+1][j]<<' '<<(p[j]-p[pos])*1LL*(p[pos]-p[i-1])<<'\n';
                    if(maximize(dp[tri][i][j],dp[tri1][i][pos]+dp[tri2][pos+1][j]+(p[j]-p[pos])*1LL*(p[pos]-p[i-1]))) trace[tri][i][j]=make_pair(tri1,pos);
                }
            }
//            cout<<tri<<' '<<i<<' '<<j<<' '<<dp[tri][i][j]<<'\n';
        }
        cout<<dp[k][1][n]<<'\n';
        work(k,1,n);
    }
}
namespace sub34
{
    bool check()
    {
        return (n<=1000);
    }
    const ll inf = 2e18;
    const int N = 1e3 + 10;
    const int K = 200 + 10;
    ll dp[K][N];
    int trace[K][N];
    void solve()
    {
        for(int i=1;i<=n;++i) dp[0][i]=inf;
        ++k;
        for(int tri=1;tri<=k;++tri) for(int i=0;i<=n;++i)
        {
            dp[tri][i]=inf;
            for(int pos=1;pos<=i;++pos) if(minimize(dp[tri][i],dp[tri-1][pos-1]+(p[i]-p[pos-1])*1LL*(p[i]-p[pos-1]))) trace[tri][i]=pos;
        }
        cout<<(p[n]*1LL*p[n]-dp[k][n])/2<<'\n';
        int tri=k,i=n;
//        return;
        while(tri>1)
        {
//            cout<<tri<<' '<<i<<'\n';
            cout<<trace[tri][i]-1<<' ';
            i=trace[tri][i]-1;
            --tri;
        }
    }
}
namespace subfull
{
    const ll inf = 2e18;
    ll dp[N],ndp[N];
    int opt[K][N];
    void dnc(int tri, int l, int r, int tl, int tr)
    {
        if(l>r) return;
        int mid=(l+r)>>1;
        ndp[mid]=inf;
        for(int cm=tl;cm<=min(mid,tr);++cm)
        {
            if(minimize(ndp[mid],dp[cm-1]+(p[mid]-p[cm-1])*1LL*(p[mid]-p[cm-1]))) opt[tri][mid]=cm;
        }
        dnc(tri,l,mid-1,tl,opt[tri][mid]);
        dnc(tri,mid+1,r,opt[tri][mid],tr);
    }
    void solve()
    {
        ++k;
        for(int i=1;i<=n;++i) dp[i]=inf;
        for(int tri=1;tri<=k;++tri)
        {
            ndp[0]=inf;
            dnc(tri,1,n,1,n);
            swap(dp,ndp);
        }
        cout<<(p[n]*1LL*p[n]-dp[n])/2<<'\n';
        int i=n,tri=k;
        while(tri>1)
        {
            cout<<opt[tri][i]-1<<' ';
            i=opt[tri][i]-1;
            --tri;
        }
    }
}
void solve()
{
    cin>>n>>k;
    for(int i=1;i<=n;++i) cin>>a[i],p[i]=p[i-1]+a[i];
    if(sub12::check()) return void(sub12::solve());
    if(sub34::check()) return void(sub34::solve());
    return void(subfull::solve());
}

int main()  {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

//    freopen(TASK".inp","r",stdin);
//    freopen(TASK".out","w",stdout);

    int testcase=1;
//    cin>>testcase;

    while (testcase--)
        solve();

    return 0;
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29