제출 #868430

#제출 시각아이디문제언어결과실행 시간메모리
868430atom수열 (APIO14_sequence)C++17
0 / 100
66 ms20828 KiB
#include "bits/stdc++.h"
// @JASPER'S BOILERPLATE
using namespace std;
using ll = long long;
#define FOR(i, a, b) for(int i = a; i <= b; i++)
#define FORD(i, a, b) for(int i = a; i >= b; i--)
#define REP(i, b) for(int i = 0; i < b; i++)
#define PER(i, b) for(int i = b - 1; i >= 0; i--)
#define fi first
#define se second
#ifdef JASPER
#include "debug.h"
#else
#define debug(...) 166
#endif

using pii = pair < int, int >;
const int INF = 1e9;
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int K = 205;

struct CHT {
    // Querying for max
    struct Line {
        ll a, b, id;
        Line (ll _a = 0, ll _b = 0, ll _id = -1) { a = _a; b = _b; id = _id; };
        ll cal(ll x) { return a * x + b; }
        long double cross(Line o) { return (long double) (b - o.b) / (long double) (o.a - a); }
    };
    deque <Line> q;
    /*
        Decreasing slope;
        add: >= 
        Increasing slope;
        add: <=
    */
    void add(ll a, ll b, ll id) {
        Line nLine = Line(a, b, id);
        while (q.size() >= 2 && q[0].cross(nLine) >= q[0].cross(q[1]))
            q.pop_front();
        q.push_front(nLine);
    }
    pair <ll, int> qry(ll x) {
        int l = 0, r = (int) q.size() - 1;
        while (l < r) {
            int m = (l + r) / 2;
            if (q[m].cal(x) < q[m + 1].cal(x))
                l = m + 1;
            else
                r = m;
        }
        return {q[l].cal(x), q[l].id};
    }
};
int n, k;
ll dp[2][N];
ll prf[N];
int opt[K][N];
// dp[i][k] = max j / (dp[j][k−1] + (pi − pj)⋅(pn − pi))
void run_case() {
    cin >> n >> k;
    for (int i = 1; i <= n; ++i) {
        int x; cin >> x;
        prf[i] = prf[i - 1] + x;
    }

    // Base case, k = 0
    for (int i = 1; i <= n; ++i) {
        dp[0][i] = (prf[i] - prf[0]) * (prf[n] - prf[i]);
        opt[1][i] = i;
    }
    
    for (int step = 1; step <= k; ++step) {
        CHT hull;
        hull.add(0, 0, 0);
        for (int i = 1; i <= n; ++i) {
            ll x = prf[n] - prf[i];
            pair <ll, int> ret = hull.qry(x);
            dp[1][i] = ret.fi + prf[i] * x;
            opt[step][i] = ret.se;

            hull.add(-prf[i], dp[0][i], i);
        }
        for (int i = 1; i <= n; ++i)
            dp[0][i] = dp[1][i];
    }
    cout << dp[0][n] << "\n";

    int i = opt[k][n];
    vector <int> ids;
    while (k) {
        ids.push_back(i);
        i = opt[k - 1][i];
        --k;
    }
    reverse(ids.begin(), ids.end());
    for (int x : ids) cout << x << " ";
    cout << "\n";
}

signed main() {
    cin.tie(0) -> sync_with_stdio(0);
    #ifdef JASPER
        freopen("in1", "r", stdin);
    #endif

    int Test = 1;
    //cin >> Test;
    for (int test = 1; test <= Test; test++){

        run_case();
    }
}
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