Submission #312594

#	Time	Username	Problem	Language	Result	Execution time	Memory
312594		aZvezda	Split the sequence (APIO14_sequence)	C++14	71 / 100	142 ms	131076 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
//#pragma GCC optimize ("O3")
//#pragma GCC target ("sse4")
#define endl "\n"
typedef long long ll;
template<class T, class T2> inline ostream &operator <<(ostream &out, const pair<T, T2> &x) { out << x.first << " " << x.second; return out;}
template<class T, class T2> inline istream &operator >>(istream &in, pair<T, T2> &x) { in >> x.first >> x.second; return in;}
template<class T, class T2> inline bool chkmax(T &x, const T2 &y) { return x < y ? x = y, 1 : 0; }
template<class T, class T2> inline bool chkmin(T &x, const T2 &y) { return x > y ? x = y, 1 : 0; }
const ll mod = 1e9 + 7;
#define out(x) "{" << (#x) << ": " << x << "} "

const int MAX_N = 1e5 + 10, MAX_K = 210;
ll dp[MAX_N][MAX_K], hist[MAX_N][MAX_K];
ll pref[MAX_N], arr[MAX_N];

struct Line {
    ll a, b, ind;
    long double p;
    Line() {}
    Line(ll _a, ll _b, ll _ind) {a = _a; b = _b; ind = _ind;}
    ll y(ll x) {return a * x + b;}
    long double getWhere(const Line &other) {
        if(a == other.a) {
            return -mod;
        } else {
            return (long double)(b - other.b) / (long double)(other.a - a);
        }
    }
};

struct LineContainer {
    deque<Line> lines;
    void addLine(Line curr) {
        while(!lines.empty() && lines.back().getWhere(curr) <= lines.back().p) {
            lines.pop_back();
        }
        if(lines.empty()) {
            curr.p = -mod;
        } else {
            curr.p = lines.back().getWhere(curr);
        }
        lines.push_back(curr);
    }
    pair<ll, int> get(ll x) {
        while(lines.size() > 1 && lines[1].p <= x) {
            lines.pop_front();
        }
        return {lines.front().y(x), lines.front().ind};
    }
};

LineContainer lc[MAX_K];

void output(int n, int k) {
    if(k == 0) {
        return;
    }
    output(hist[n][k], k - 1);
    cout << hist[n][k] << " ";
}

signed main() {
    //ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
    int n, k;
    cin >> n >> k;
    for(int i = 1; i <= n; i ++) {
        cin >> arr[i];
        pref[i] = pref[i - 1] + arr[i];
    }
    for(int i = 0; i <= n; i ++) {
        for(int j = 1; j <= k; j ++) {
            dp[i][j] = -mod;
        }
    }
    for(int i = 1; i <= k; i ++) {
        lc[i].addLine(Line(0, -mod, -1));
    }
    lc[0].addLine(Line(0, 0, -1));
    for(int i = 1; i <= n; i ++) {
        for(int j = k; j >= 1; j --) {
            auto get = lc[j - 1].get(pref[i]);
            dp[i][j] = get.first;
            hist[i][j] = get.second;
            lc[j].addLine(Line(pref[i], dp[i][j] - pref[i] * pref[i], i));
        }
        lc[0].addLine(Line(pref[i], 0 - pref[i] * pref[i], i));
    }

    /*for(int i = 1; i <= n; i ++) {
        for(int j = 1; j <= k; j ++) {
            for(int q = 1; q < i; q ++) {
                if(chkmax(dp[i][j], dp[q][j - 1] + pref[q] * pref[i] - pref[q] * pref[q])) {
                    hist[i][j] = q;
                }
            }
        }
    }*/
    cout << dp[n][k] << endl;
    output(n, k);
    return 0;
}

/*
7 3
4 1 3 4 0 2 3
*/

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