Submission #928927

#	Time	Username	Problem	Language	Result	Execution time	Memory
928927		Foolestboy	Split the sequence (APIO14_sequence)	C++14	100 / 100	423 ms	84420 KiB

sequence

#include <bits/stdc++.h>

#define SQR(x)    (1LL * ((x) * (x)))
#define MASK(i)   (1LL << (i))
#define BIT(x, i) (((x) >> (i)) & 1)
#define fi        first
#define se        second
#define pb        push_back
#define all(x)    x.begin(), x.end()
#define rall(x)   x.rbegin(), x.rend()
#define sz(s)     (int)s.size()
#define prev      __prev
#define next      __next
#define left      __left
#define right     __right

#define mp make_pair
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
#define vll vector<ll>

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef unsigned int ui;

using namespace std;

const int mod = 1e9 + 7;
const int INF = 1e9 + 7;
const ll INFLL = (ll)2e18 + 7LL;
const ld PI = acos(-1);

const int dx[] = {1, -1, 0, 0, -1, 1, 1, -1};
const int dy[] = {0, 0, 1, -1, -1, -1, 1, 1};

template<class BUI, class TRONG>
    bool minimize(BUI &x, const TRONG y){
        if(x > y){
            x = y;
            return true;
        } else return false;
    }
template<class BUI, class TRONG>
    bool maximize(BUI &x, const TRONG y){
        if(x < y){
            x = y;
            return true;
        } else return false;
    }

/* Author : Bui Nguyen Duc Trong, Luong Van Chanh High School for the gifted*/
/* Template is copied by Trong */

                           /** Losing in Provincial Contests **/
                                    /** TRYING HARDER**/
                                   /**      ORZ     **/

/* -----------------[ MAIN CODE GOES HERE ]----------------- */

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int N = 1e5 + 10;

int n, k;
int a[N];

struct Line{
    ll a, b;
    int id;

    Line() : a(0), b(0) {}

    Line(ll a, ll b, int id) : a(a), b(b), id(id) {}

    ll f(ll x) { return a * x + b; }

};

struct ConvexHullTrick{
    vector<Line> vec;
    int iter = 0;

    void reset(){
        vec.clear();
        iter = 0;
    }

    ld inter(Line A, Line B){
        return (ld)(A.b - B.b) / (B.a - A.a);
    }

    void insertLine(Line l){
        if(!vec.empty() && l.a == vec.back().a){
            if(vec.back().b <= l.b) vec.back() = l;
//            if(maximize(vec.back().b, l.b)) vec.back() = l;
        }
        else{
            while(sz(vec) >= 2 && inter(l, vec.back()) <= inter(vec.back(), vec[sz(vec) - 2])) vec.pop_back();
            vec.push_back(l);
        }
    }

    pair<ll, int> query(ll x){
        if(vec.empty()) return {-INFLL, 0};
        minimize(iter, sz(vec) - 1);
        while(iter + 1 < sz(vec) && vec[iter + 1].f(x) >= vec[iter].f(x)) ++iter;
        return mp(vec[iter].f(x), vec[iter].id);
    }

} cht;

ll f[N][2];
int trace[N][202];

void solve(){
    cin >> n >> k;
    for(int i = 1; i <= n; i++){
        cin >> a[i]; a[i] += a[i - 1];
    }
    memset(f, -0x3f, sizeof f);
    for(int i = 0; i <= n; i++) f[i][0] = 0;
    for(int j = 1; j <= k; j++){
        cht.reset();
        for(int i = 1; i <= n; i++) f[i][j & 1] = -INFLL;
        for(int i = 1; i <= n; i++){
            if(f[i - 1][(j - 1) & 1] >= 0) cht.insertLine(Line(a[i - 1], f[i - 1][(j - 1) & 1] - 1LL * a[i - 1] * a[i - 1], i));
            auto [x, y] = cht.query(a[i]);
            f[i][j & 1] = x;
            trace[i][j] = y;
        }
    }
//    cout << "huhu " << trace[n][k] << '\n';
    int r = n;
    vector<int> ans;
    for(int i = k; i >= 1; i--){
        ans.push_back(trace[r][i] - 1);
        r = trace[r][i] - 1;
    }
    cout << f[n][k & 1] << '\n';
    reverse(all(ans));
    ll tot = 0, s = 0;
    vector<int> tmp = ans;
    tmp.insert(tmp.begin(), 0);
    tmp.push_back(n);
    for(int i = 1; i < sz(tmp); i++){
        int sum = a[tmp[i]] - a[tmp[i - 1]];
        tot += s * sum;
        s += sum;
    }
    assert(tot == f[n][k & 1]);
    for(int x : ans) cout << x << ' '; cout << '\n';
}

/*
2 1
0 0
*/

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);

    const bool multitest = 0;
    int tt = 1; if(multitest) cin >> tt;

    while( tt-- ){

        solve();

    }

    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'void solve()':
sequence.cpp:129:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
  129 |             auto [x, y] = cht.query(a[i]);
      |                  ^
sequence.cpp:153:5: warning: this 'for' clause does not guard... [-Wmisleading-indentation]
  153 |     for(int x : ans) cout << x << ' '; cout << '\n';
      |     ^~~
sequence.cpp:153:40: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'for'
  153 |     for(int x : ans) cout << x << ' '; cout << '\n';
      |                                        ^~~~

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