Submission #1111977

#	Time	Username	Problem	Language	Result	Execution time	Memory
1111977		tintingyn21	Split the sequence (APIO14_sequence)	C++17	100 / 100	1387 ms	91548 KiB

sequence

// author : daohuyenchi



#include <bits/stdc++.h>

using namespace std;

#define ull unsigned long long
#define db double
#define i32 int32_t  
#define i64 int64_t 
#define ll long long
// 
#define fi first
#define se second


//                                      #define int long long    // consider carefully


//
#define pii pair<int, int>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define pil pair<int, ll> 
#define PAIR make_pair 
//                                      TIME IS LIMITED ...  
#define  rep(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define repd(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define repv(v, H) for(auto &v: H)
//                                      REFLECT ON THE PAST ...
#define RESET(c, x) memset(c, x, sizeof(c))
#define MASK(i) (1LL << (i))
#define BIT(mask, i) (((mask) >> (i)) & 1LL)
#define ONBIT(mask, i) ((mask) | (1LL << (i)))
#define OFFBIT(mask, i) ((mask) &~ (1LL << (i)))
#define COUNTBIT __builtin_popcountll
//                                      30 / 1 / 2024 ? love is zero... start from zero 
#define PB push_back
#define EB emplace_back
#define vi vector<int>
#define vll vector<ll>
#define lwb lower_bound
#define upb upper_bound
#define all(v) (v).begin(), (v).end()
#define special(H) (H).resize(distance(H.begin(), unique(all(H))))
//                                      
#define sp ' ' 
#define nl '\n'
#define EL {cerr << '\n';}
#define yes "YES"
#define no "NO"
#define Log2(n) (63 - __builtin_clzll(n))
#define left __left__
#define right __right__ 

//____________________________________________________________________


template <class X, class Y> bool maximize(X &a, const Y &b) {
    if(a < b) return a = b, true;
    return false;
}

template <class X, class Y> bool minimize(X &a, const Y &b) {
    if(a > b) return a = b, true;
    return false;
}

template <class... T>
void print(T&&... n) {
    using exp = int[];
    exp{0, (cerr << n << sp, 0)...};
    cerr << nl;
}

template <class... T>
void print2(T&&... n) {
    using exp = int[];
    exp{0, (cerr << n << sp, 0)...};
    // cerr << sp;
}

template <class T, class... C>
void assign(int n, T v, C&&... a) {
    using e = int[];
    e{(a.assign(n, v), 0)...};
}

template <class... C>
void resize(int n, C&&... a) {
    using e = int[];
    e{(a.resize(n), 0)...};
}

template <class T>
using vector2d = vector<vector<T>>;
template <class T>
using vector3d = vector<vector2d<T>>;

template <class T> int ssize(T &a) { return (int) a.size(); }


//____________________________________________________________________


mt19937 rng(chrono::steady_clock().now().time_since_epoch().count());

const int MOD      = 1000000007;
// const int MOD[2] = {1000000009, 998244353};

template<class X> void modmize(X &x, int cur_Mod = MOD) {
    if(x >= cur_Mod) x -= cur_Mod;
    if(x < 0) x += cur_Mod;
}

const long long oo = 1e18 + 7;
const int INF      = 2e9;
const int nmax     = 2e5 + 10;
const int MAX      = 2e5;
const int base     = 311;
const db eps       = 1e-6;
const int block    = 500;
static const double PI = acos(-1.0);

//____________________________________________________________________


double division(ll a, ll b) {
    return 1.0 * a / b;
}

struct Line {
 
    ll m, c;
    int id;
 
    Line() {}
    Line(ll _m, ll _c, int _id) : m(_m), c(_c), id(_id) {}
    // y = m * x + c
 
    //. m is angle
        // if (m < 0) obtuse angle
        // else acute angle
        // imagine to ccw 
 
        // if (m < 0) to close to 0, to large 
        // if (m > 0) to far to 0, to large
 
    // y = m1 * x * c1
    // y = m2 * x + c2
 
    // c2 - c1 = x * (m1 - m2) 
 
    double isect_X(const Line &ot) const {
        return division(ot.c - c, m - ot.m);
    }
 
    friend double isect_X(Line l1, Line l2) {
        return l1.isect_X(l2);
    } ; 
 
    ll eval(ll x) {
        return m * x + c;
    }
 
    bool operator < (const Line &ot) {
        return m < ot.m;
    } 
 
} ;
 
struct convex_hull_trick {
 
    // default for hull min 
    // condition to use : all the line is sort by slope 
        
    // if order goto is not sort, we use set instead by vector 
 
    vector <Line> hull;
    vector <double> dot;
 
    void Reset() {
        hull.clear();
        dot.clear();
        dot.push_back(-oo);
    }
 
    void Init(Line L) {
        // hull.clear();
        // dot.clear();
        dot.push_back(-oo);
        hull.push_back(L);
    }
 
    bool check_bad(Line &x, Line y, Line z) {
        // hull min condition : isect(x, y) < isect(x, z)
        // hull max condition : isect(x, y) > isect(x, z)
        return isect_X(x, y) <= isect_X(x, z);
    }
 
    void add_line(ll m, ll c, int id) {
        Line L = Line(m, c, id);
        // print(L.m, L.c, id);
        while (ssize(hull) > 1 && dot.back() >= L.isect_X(hull[ssize(hull) - 2])) {
            hull.pop_back();
            if (ssize(dot) > 0) 
                dot.pop_back();
        }
        if (hull.empty() == 0) {
            // assert(fabs(isect_X(L, hull.back()) - L.isect_X(hull.back())) <= eps) ; 
            // cerr << fixed << setprecision(6) << L.isect_X(hull.back()) << nl;
            // cerr << fixed << setprecision(6) << isect_X(L, hull.back()) << nl;
            dot.push_back(L.isect_X(hull.back()));
        }
        hull.push_back(L);
    }
 
    pli cal(ll x) {
        
        // if (dot.empty() == 1) return ;
 
        int i = upper_bound(all(dot), x) - dot.begin() - 1;
        // cerr << i << ' ' << x << '\n';
        // print(i, x, hull[i].m, hull[i].c);
        return PAIR(hull[i].eval(x), hull[i].id); 
    }
 
} ; 

int n, k;
int a[nmax];
ll pf[nmax];
ll f[nmax], g[nmax];

int pre[nmax][205];

void tintingyn() {

    cin >> n >> k;
    rep (i, 1, n) {
        cin >> a[i];
        pf[i] = pf[i - 1] + a[i];
    }

    // {
    //     vector2d <ll> dp(n + 2, vll(k + 2, -oo));
    //     dp[0][0] = 0;
    //     rep (i, 1, n) {
    //         rep (t, 1, min(k + 1, i)) {
    //             rep (j, 1, i) {
    //                 maximize(dp[i][t], dp[j - 1][t - 1] + (pf[i] - pf[j - 1]) * pf[j - 1]);
    //             }
    //         }
    //     }
    //     cout << dp[n][k + 1] << nl;

    //     // rep (i, 1, n) {
    //     //     cerr << dp[i][1] << sp;
    //     // }
    //     // EL
    // }

    rep (i, 1, n) {
        f[i] = g[i] = 0;
    }

    rep (_i, 2, k + 1) {
        rep (i, 1, n) {
            g[i] = f[i];
            f[i] = -1e15;
        }
        convex_hull_trick cht;
        cht.Reset();
        // cht.add_line(0, 0, 0);
        rep (i, 1, n) {
            if (i >= _i) {
                auto mx = cht.cal(pf[i]);
                f[i] = mx.fi;
                // print(_i, i, mx.fi);
                pre[i][_i] = mx.se; 
            }
            cht.add_line(pf[i], - pf[i] * pf[i] + g[i], i);
            // print(_i, i);
        }
    }

    vector <int> List;
    {
        int x = n;
        int k2 = k + 1;
        while (x != 0) {
            List.push_back(x);
            x = pre[x][k2--];
        }
    }

    cout << f[n] << nl;

    reverse(all(List)); List.pop_back();
    repv (i, List) cout << i << sp;
}

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

    //________________________________________________________________

    #define TASK "3"
    if(fopen(TASK".inp", "r")) {
        freopen(TASK".inp", "r", stdin);
        freopen(TASK".out", "w", stdout);
    }

    //________________________________________________________________
    
    //  CODE FROM HERE ...! 





    int num_test = 1; 
    // cin >> num_test;

    while(num_test--) {

        tintingyn();

    }


    cerr << '\n' << "Time elapsed: " << (1.0 * clock() / CLOCKS_PER_SEC) << " s\n" << nl;

    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:316:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  316 |         freopen(TASK".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:317:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  317 |         freopen(TASK".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

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