Submission #729143

#	Time	Username	Problem	Language	Result	Execution time	Memory
729143		Vanilla	Split the sequence (APIO14_sequence)	C++17	39 / 100	2076 ms	131072 KiB

sequence

#include <bits/stdc++.h>
#include <fstream>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
struct custom_hash {static uint64_t splitmix64(uint64_t x) {x += 0x9e3779b97f4a7c15;x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;x = (x ^ (x >> 27)) * 0x94d049bb133111eb;return x ^ (x >> 31);}size_t operator()(uint64_t x) const {static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();return splitmix64(x + FIXED_RANDOM);}};
// string __fname = ""; ifstream in (__fname + ".in"); ofstream out (__fname + ".out"); 
// #define cin in 
// #define cout out
#define int64 long long
#define uint64 unsigned long long
#define x first
#define y second
#define pb push_back
#define pii pair <int, int> 
#define pii64 pair <int64, int64>
#define db(x) cout << "> " << #x << ": " << (x) << "\n"
#define qr queries()
#define yn(x) if (x) {ctn("Yes");}else {ctn("No");}
void solve(int);
void queries(){int n;cin >> n;for (int i = 1; i <= n; i++) solve(i);}
template<class T>T ceildiv(T a, T b) {return a / b + !!(a % b);}
template<class T>T gcd (T a, T b){return (b ? gcd(b, a % b): a);}
template<class T>T lcm (T a, T b){return a * b / gcd(a, b);}
// // // // // // // // // // // // // // // // // // // // // // 
/*                  TEMPLATE - VANILLA                         */
// // // // // // // // // // // // // // // // // // // // // //
const int ddx[] = {-1, -1, 0, 1, 1, 1, 0, -1};
const int ddy[] = {0, 1, 1, 1, 0, -1, -1, -1};
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
const double pi = 3.14159265359;
const double eps = 1e-6;
const int64 hash_inv = 940594066;
const int64 hash_p = 101;
const int64 mod = 1e9 + 7;
const int maxn = 1e5 + 2;
const int maxk = 201;
int64 dp[maxn][maxk]; // dp[i][j] -> scor maxim folosind primele i elemente repartizate folosind j splits si ultimul split fiind la elementul i
int64 pref [maxn];
int64 dad[maxn][maxk];

void solve(int id){

    return;
}

struct line {
    int64 m;
    int64 b; // m * x + b;
    int64 idx;
 
    int64 calc (int64 x) {
        return m * x + b;
    }
};
 
struct lichao {
    int64 l,r;
    line v;
 
    lichao* left = NULL;
    lichao* right = NULL;
 
    lichao(int _l, int _r, line _v): l(_l), r(_r), v(_v) {};
 
};
lichao* lc[maxk];
 
inline void extend (lichao* t) {
    if (t->left != NULL) return;
    int64 mid = (t->l + t->r) / 2;
    t->left = new lichao(t->l, mid, {0, (int64) -1e18});
    t->right = new lichao(mid + 1, t->r, {0, (int64) -1e18});
}
 
inline void update (lichao* t, line ln) {
    if (t->l + 1 >= t->r) {
        if (ln.calc(t->l) > t->v.calc(t->l)) t->v = ln;
        return;
    }
    extend(t);
    int64 mid = (t->l + t->r) / 2;
    if (ln.m < t->v.m) swap(ln, t->v);
    if (ln.calc(mid) > t->v.calc(mid)) {
        swap(ln, t->v);
        update(t->left, ln);
    }
    else update(t->right, ln);
}
 
inline pii64 query (lichao*t, int64 x) {
    if (t->l + 1 >= t->r) return make_pair(t->v.calc(x), t->v.idx);
    if (t->l > x || t->r < x) return make_pair(-1e18, 0);
    extend(t);
    return max({query(t->left, x), query(t->right, x), make_pair(t->v.calc(x), t->v.idx)});
}

inline void clear (lichao* t) {
    if (t->left) clear(t->left);
    if (t->right) clear(t->right);
    delete t;
}

int64 calc (int64 i1, int64 i2, int64 i3) { // [i1;i3] -> [i1; i2 - 1] + [i2; i3]
    return (pref[i3] - pref[i2 - 1]) * (pref[i2 - 1] - pref[i1 - 1]);
}

int main(){
    ios_base::sync_with_stdio(0); cin.tie(0); cout << fixed; cout << setprecision(10); 
    int n,k;
    cin >> n >> k;
    for (int i = 1; i <= n; i++){
        int x;
        cin >> x;
        pref[i] = pref[i-1] + x;
    }
    if (n == 1) {
        cout << "0\n";
        return 0;
    }
    for (int i = 0; i <= n; i++) for (int j = 1; j <= k; j++) dp[i][j] = -1e15;
    lc[0] = new lichao (1, (int) 1e9, {0, 0});
    for (int t = 1; t <= k; t++){
        lc[t] = new lichao (1, (int) 1e9, {0, (int64) -1e15});
        for (int i = 1; i < n; i++){
            // (pref[n] - pref[i]) * (pref[i] - pref[j - 1]) + dp[j-1][t-1]
            // (p[i] * p[j-1] + (dp[j-1][t-1] - p[n] * p[j-1])) + p[i] * (p[n] - p[i])
            //   x        a                    b                          const
            auto [v, idx] = query(lc[t-1], pref[i]);
            dp[i][t] = v + pref[i] * (pref[n] - pref[i]);
            dad[i][t] = idx;
            update(lc[t-1], {pref[i], dp[i][t-1] - pref[n] * pref[i], i});

        }
        clear(lc[t-1]);
    }
    int64 mx = -1e18, mxi = 0;
    for (int i = 1; i <= n; i++){
        if (dp[i][k] > mx) {
            mx = dp[i][k];
            mxi = i;
        }
    }
    vector <int> v;
    v.push_back(mxi);
    while ((mxi = dad[mxi][k--]) > 0) {
        v.push_back(mxi);
    }
    cout << mx << "\n";
    reverse(v.begin(), v.end());
    for (int i: v) {
        cout << i << " ";
    }
    return 0;
}

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