제출 #868489

#제출 시각아이디문제언어결과실행 시간메모리
868489atom수열 (APIO14_sequence)C++17
100 / 100
640 ms82940 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 ll INF = 1e18;
    const int MOD = 1e9 + 7;
    const int N = 1e5 + 5;
    const int K = 205;
    // Query for min;
    struct ConvexHull {
        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;
        void add(ll a, ll b, ll id) {
        Line nLine = Line(a, b, id);
        // need to change when a is increasing or decreasing
        while (q.size() >= 2 
            && (q.back().cross(nLine) <= q.back().cross(q[q.size() - 2]) 
                || (q.back().a == nLine.a && q.back().b <= nLine.b)))
            q.pop_back();
        q.push_back(nLine);
    }
     
        pair <ll, int> qry(ll x) {
            while (q.size() >= 2 && q[0].cal(x) <= q[1].cal(x))
                q.pop_front();
            return {q[0].cal(x), q[0].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 step = 1; step <= k + 1; ++step) {
            ConvexHull hull;
            hull.add(0, 0, -1);
     
            for (int i = 1; i <= n; ++i) {
                pair <ll, int> ret = hull.qry(prf[i]);
                dp[1][i] = ret.fi + prf[i] * (prf[n] - prf[i]);
                opt[step][i] = ret.se;
                
                if (step != 1)
                    hull.add(prf[i], dp[0][i] - prf[i] * prf[n], i);
            }
            for (int i = 1; i <= n; ++i)
                dp[0][i] = dp[1][i];
        }
        cout << dp[0][n] << "\n";
        vector <int> ids;
        for (int i = k + 1, id = n; i > 0; --i) {
            if (id != n)
                ids.push_back(id);
            id = opt[i][id];
        }
        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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