Submission #636048

#	Time	Username	Problem	Language	Result	Execution time	Memory
636048		ghostwriter	Split the sequence (APIO14_sequence)	C++14	100 / 100	648 ms	83848 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.h>
#endif
#define st first
#define nd second
#define pb push_back
#define pf push_front
#define _pb pop_back
#define _pf pop_front
#define lb lower_bound
#define ub upper_bound
#define mtp make_tuple
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
typedef long long ll; typedef unsigned long long ull;
typedef double db; typedef long double ldb;
typedef pair<int, int> pi; typedef pair<ll, ll> pll;
typedef vector<int> vi; typedef vector<ll> vll; typedef vector<pi> vpi; typedef vector<pll> vpll;
typedef string str;
template<typename T> T gcd(T a, T b) { return (b == 0? a : gcd(b, a % b)); }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
#define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
#define FOS(i, r, l) for (int (i) = (r); (i) >= (l); --(i))
#define EACH(i, x) for (auto &(i) : (x))
#define WHILE while
#define file "TEST"
// mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
// ll rand(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rd); }
/*
    Tran The Bao
    CTL - Da Lat
    Cay ngay cay dem nhung deo duoc cong nhan
*/
struct Line {
    ll a, b;
    int id;
    Line() {}
    Line(ll a, ll b, int id) : a(a), b(b), id(id) {}
};
const ldb eps = 1e-7;
const ll oo = 2e18 + 5;
const int N = 1e5 + 1;
const int K = 202;
int n, k, s, f[N], pre[K][N];
ll d[N], d1[N];
ll cal(int f, ll a, ll b) { return 1LL * f * s - 1LL * f * f + 1LL * a * f + b; }
ldb it(Line a, Line b) {
    if (a.a == b.a) return -oo;
    return (ldb)(b.b - a.b) / (ldb)(a.a - b.a);
}
void trace(int i, int j) {
    int prev = pre[i][j];
    if (!prev) return;
    cout << prev << ' ';
    trace(i - 1, prev);
}
signed main() {
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    // freopen(file".inp", "r", stdin);
    // freopen(file".out", "w", stdout);
    cin >> n >> k;
    FOR(i, 1, n) cin >> f[i];
    FOR(i, 1, n) f[i] += f[i - 1];
    s = f[n];
    FOR(i, 1, n) d1[i] = -oo;
    vector<Line> cv;
    FOR(i, 1, k + 1) {
        cv.pb(Line(0, d1[0], 0));
        int l = 0;
        d[0] = -oo;
        FOR(j, 1, n) {
            l = min(l, sz(cv) - 1);
            WHILE(l < sz(cv) - 1 && (d1[cv[l].id] < 0 || cal(f[j], cv[l].a, cv[l].b) <= cal(f[j], cv[l + 1].a, cv[l + 1].b))) ++l;
            if (d1[cv[l].id] >= 0) {
                d[j] = cal(f[j], cv[l].a, cv[l].b);
                pre[i][j] = cv[l].id;
            }
            else d[j] = -oo;
            if (d1[j] < 0) continue;
            Line cur(2 * f[j], d1[j] - 1LL * f[j] * s - 1LL * f[j] * f[j], j);
            WHILE(sz(cv) > 1) {
                Line tmp = cv[sz(cv) - 1], tmp1 = cv[sz(cv) - 2];
                ldb x1 = it(tmp, tmp1), x2 = it(tmp, cur);
                if (x2 <= x1 || x2 - x1 <= eps) {
                    cv._pb();
                    continue;
                }
                if (x2 == -oo) cv._pb();
                break;
            }
            cv.pb(cur);
        }
        FOR(j, 0, n) d1[j] = d[j];
        cv.clear();
    }
    cout << d[n] / 2 << '\n';
    trace(k + 1, n);
    return 0;
}
/*
7 3
4 1 3 4 0 2 3

5 1
0 9 6 3 0
*/

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:24:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
   24 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
      |                               ^
sequence.cpp:64:5: note: in expansion of macro 'FOR'
   64 |     FOR(i, 1, n) cin >> f[i];
      |     ^~~
sequence.cpp:24:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
   24 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
      |                               ^
sequence.cpp:65:5: note: in expansion of macro 'FOR'
   65 |     FOR(i, 1, n) f[i] += f[i - 1];
      |     ^~~
sequence.cpp:24:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
   24 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
      |                               ^
sequence.cpp:67:5: note: in expansion of macro 'FOR'
   67 |     FOR(i, 1, n) d1[i] = -oo;
      |     ^~~
sequence.cpp:24:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
   24 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
      |                               ^
sequence.cpp:69:5: note: in expansion of macro 'FOR'
   69 |     FOR(i, 1, k + 1) {
      |     ^~~
sequence.cpp:24:31: warning: unnecessary parentheses in declaration of 'j' [-Wparentheses]
   24 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
      |                               ^
sequence.cpp:73:9: note: in expansion of macro 'FOR'
   73 |         FOR(j, 1, n) {
      |         ^~~
sequence.cpp:24:31: warning: unnecessary parentheses in declaration of 'j' [-Wparentheses]
   24 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
      |                               ^
sequence.cpp:95:9: note: in expansion of macro 'FOR'
   95 |         FOR(j, 0, n) d1[j] = d[j];
      |         ^~~

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