Submission #345275

#	Time	Username	Problem	Language	Result	Execution time	Memory
345275		DrearyJoke	Split the sequence (APIO14_sequence)	C++17	71 / 100	138 ms	131076 KiB

sequence

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<bool> vb;
typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update> indexed_set;

template <typename T, typename U> std::istream&operator>>(std::istream&i, pair<T,U>&p) {i >> p.x >> p.y; return i;}
template<typename T>std::istream&operator>>(std::istream&i,vector<T>&t) {for(auto&v:t){i>>v;}return i;}
template <typename T, typename U> std::ostream&operator<<(std::ostream&o, const pair<T,U>&p) {o << p.x << ' ' << p.y; return o;}
template<typename T>std::ostream&operator<<(std::ostream&o,const vector<T>&t) {if(t.empty())o<<'\n';for(size_t i=0;i<t.size();++i){o<<t[i]<<" \n"[i == t.size()-1];}return o;}

#define deb(x) cout << '>' << #x << ':' << x << endl;
#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define END '\n'
#define inf 9e18
#define ff first
#define ss second
#define pb push_back

const ll maxVal = 1e18;

struct Line {
    ll m, c, idx;
    Line (ll _m, ll _c, ll _idx) {
        m = _m;
        c = _c;
        idx = _idx;
    }
    ll eval(ll x) {
        return m * x + c;
    }
    ll getX(Line L) {
        if (m == L.m) {
            if (c > L.c) return maxVal;
            else return -maxVal;
        }
        return (L.c - c) / (m - L.m);
    }
};

struct LowerHull {
    deque<Line> A;
    void addLine(ll m, ll c, ll idx) {
        Line now(m, c, idx);
        while((int)A.size() >= 2 && now.getX(A[0]) >= A[0].getX(A[1])) A.pop_front();
        A.push_front(now);
    }
    pair<ll, int> query(ll x) {
        if (A.empty()) return {0, 0};
        while((int)A.size() >= 2 && A.back().eval(x) <= A[(int)A.size() - 2].eval(x)) A.pop_back();
        return {A.back().eval(x), A.back().idx};
    }
};

void solve(){
    int n, k;
    cin >> n >> k;
    vll A(n + 1), pref(n + 1, 0), suf(n + 2, 0);
    for (int i = 1; i <= n; ++i) cin >> A[i], pref[i] = pref[i - 1] + A[i];
    for (int i = n; i; --i) suf[i] = suf[i + 1] + A[i];
    vvll dp(n + 1, vll(k + 1, 0));
    vvi par(n + 1, vi(k + 1, 0));
    ll ans = 0;
    int beg;
    vector<LowerHull> hulls(k + 1);
    for (int i = 1; i < n; ++i) {
        vector<array<ll, 3>> cur(k + 1);
        for (int j = 1; j <= k; ++j) {
            // cout << "CURRENT: " << i << " " << j << " " << l << END;
            // cout << dp[l - 1][j - 1] << " " << pref[i] << " " << pref[l - 1] << " " << suf[i + 1] << END;
            ll x = suf[i + 1];
            auto u = hulls[j - 1].query(x);
            ll val = pref[i] * suf[i + 1] + u.ff;
            // ll val = dp[l - 1][j - 1] + (pref[i] - pref[l - 1]) * (suf[i + 1]);
            // cout << i << " " << j << " " << u.ff << " " << u.ss << END;
            if (val >= dp[i][j]) dp[i][j] = val, par[i][j] = u.ss;
            ll m = -pref[i], c = dp[i][j], idx = i;
            cur[j] = {m, c, idx};
            // dp[i][j] = max(dp[i][j], dp[l - 1][j - 1] + (pref[i] - pref[l - 1]) * (suf[i + 1]));

            if (j == k) {
                if (dp[i][j] >= ans) ans = dp[i][j], beg = i;
                ans = max(ans, dp[i][j]);
            }
        }
        for (int j = 1; j <= k; ++j) {
            hulls[j].addLine(cur[j][0], cur[j][1], cur[j][2]);
        }
    }
    // for (int i = 1; i <= n; ++i) {
    //     for (int j = 1; j <= k; ++j) cout << dp[i][j] << " ";
    //     cout << END;
    // }
    // cout << "LO\n";
    // for (int i = 1; i <= n; ++i) {
    //     for (int j = 1; j <= k; ++j) cout << par[i][j] << " ";
    //     cout << END;
    // }
    // cout << "HULLS\n";
    // for (int i = 1; i <= k - 1; ++i) {
    //     cout << "For " << i << " moves: \n";
    //     for (auto u: hulls[i].A) {
    //         cout << u.m << " " << u.c << " " << u.idx << END;
    //     }
    // }
    int idx = k;
    vi fin;
    while(k) fin.pb(beg), beg = par[beg][k--]; 
    cout << ans << END << fin;
}
int main()
{
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
    int t = 1;
    // cin >> t;
    while(t--){
        solve();
    }
    return 0;
}
/*
7 3
4 1 3 4 0 2 3
*/

Compilation message (stderr)

sequence.cpp: In function 'void solve()':
sequence.cpp:116:9: warning: unused variable 'idx' [-Wunused-variable]
  116 |     int idx = k;
      |         ^~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29