Submission #154853

#	Time	Username	Problem	Language	Result	Execution time	Memory
154853		srvlt	Split the sequence (APIO14_sequence)	C++14	0 / 100	2040 ms	5368 KiB

sequence

//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse2,avx")
#include <bits/stdc++.h>
#define ll long long
#define db long double
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define fi first
#define se second
#define mp make_pair
#define endl "\n"
#define int long long
using namespace std;

void dout() {
    cerr << endl;
}

template <typename Head, typename... Tail>
void dout(Head H, Tail... T) {
    cerr << H << ' ';
    dout(T...);
}

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef pair <int, int> pii;
const int N = 1e5 + 3, K = 203;
int n, k, a[N], dp[K][N], p[N], last[K][N];

struct line {
    int k = 0, b = 0;
    int val(int x) {
        return k * x + b;
    }
    db intrsc(const line & l) {
        return (db)(l.b - b) / (k - l.k);
    }
    bool del(line & l1, line & l2) {
        if (k == l1.k) {
            return b > l1.b;
        }
        return intrsc(l2) < l1.intrsc(l2);
    }
};

vector <line> h;
vector <int> ind, ans;

void upd(int x, int y, int pos) {
    line tmp;
    tmp.k = x, tmp.b = y;
    while (h.size() > 1 && tmp.del(h[h.size() - 1], h[h.size() - 2])) {
        h.ppb();
        ind.ppb();
    }
    h.pb(tmp);
    ind.pb(pos);
}

pii getmax(int x) {
    if (h.empty()) {
        return {0, 0};
    }
//    int l = 0, r = h.size() - 1;
//    while (l < r) {
//        int mid = (l + r) / 2;
//        if (h[mid].val(x) < h[mid + 1].val(x)) {
//            l = mid + 1;
//        }   else {
//            r = mid;
//        }
//    }
//    return {h[l].val(x), ind[l]};
    int mx = -1;
    for (int i = 0; i < h.size(); i++) {
        if (mx == -1 || h[i].val(x) > h[mx].val(x)) {
            mx = i;
        }
    }
    return {h[mx].val(x), ind[mx]};
}

void getans(int x, int y) {
    if (!y) {
        return;
    }
    ans.pb(y);
    getans(x - 1, last[x][y]);
}

void solve(int tc) {
    cin >> n >> k;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        p[i] = p[i - 1] + a[i];
    }
    for (int i = 1; i <= k; i++) {
        h = {};
        ind = {};
        for (int j = 1; j < i; j++) {
            if (i > 1) {
                upd(-p[j], dp[i - 1][j], j);
            }
        }
        for (int j = i; j < n; j++) {
            int x = p[n] - p[j];
            pii z = getmax(x);
            dp[i][j] = p[j] * x + z.fi;
            last[i][j] = z.se;
            if (i > 1) {
                upd(-p[j], dp[i - 1][j], j);
            }
        }
    }
    int res = -1;
    for (int i = 1; i < n; i++) {
        if (res == -1 || dp[k][res] < dp[k][i]) {
            res = i;
        }
    }
    getans(k, res);
    cout << dp[k][res] << endl;
    reverse(ans.begin(), ans.end());
    for (auto i : ans) {
        cout << i << " ";
    }
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);
    int tc = 1;
//    cin >> tc;
    for (int i = 0; i < tc; i++) {
        solve(i);
//        cleanup();
    }
}

Compilation message (stderr)

sequence.cpp: In function 'pii getmax(long long int)':
sequence.cpp:77:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 0; i < h.size(); i++) {
                     ~~^~~~~~~~~~

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