Submission #732604

#	Time	Username	Problem	Language	Result	Execution time	Memory
732604		ac2hu	Split the sequence (APIO14_sequence)	C++14	50 / 100	1232 ms	131072 KiB

sequence

#include<bits/stdc++.h>
using namespace std;
#define int long long 
using ll = long long;
const int N = 1e5 + 10;
const int K = 200 + 10;
int n, k, a[N], dp[N][K], b[N][K];
struct Line {
    int id;
    mutable ll k, m, p;
    bool operator<(const Line& o) const { return k < o.k; }
    bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
    // (for doubles, use inf = 1/.0, div(a,b) = a/b)
    static const ll inf = LLONG_MAX;
    ll div(ll a, ll b) { // floored division
        return a / b - ((a ^ b) < 0 && a % b); }
    bool isect(iterator x, iterator y) {
        if (y == end()) return x->p = inf, 0;
        if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
        else x->p = div(y->m - x->m, x->k - y->k);
        return x->p >= y->p;
    }
    void add(ll k, ll m, int id) {
        auto z = insert({id, k, m, 0}), y = z++, x = y;
        while (isect(y, z)) z = erase(z);
        if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
        while ((y = x) != begin() && (--x)->p >= y->p)
            isect(x, erase(y));
    }
    pair<ll, int> query(ll x) {
        if(size() == 0) return {0ll, 0};
        auto l = *lower_bound(x);
        return {l.k * x + l.m, l.id};
    }
};
signed main(){
    iostream::sync_with_stdio(false);cin.tie(nullptr);
    cin >> n >> k;
    for(int i = 1;i<=n;i++)cin >> a[i];
    for(int i = 1;i<=n;i++)a[i] += a[i - 1];
    vector<LineContainer> lc(k + 1);
    for(int i = 1;i<=n;i++){
        for(int l = 1;l<min(i, k + 1);l++){
            auto [val, id] = lc[l - 1].query(a[i]);
            dp[i][l] = val; b[i][l] = id;
        }
        for(int l = 0;l<min(i, k + 1);l++){
            lc[l].add(a[i], -a[i]*a[i] + dp[i][l], i);
        }
    }
    cout << dp[n][k] << "\n";
    vector<int> v = {n}; 
    for(int l = k;l>=1;l--){
        v.push_back(b[v.back()][l]);
    }
    reverse(v.begin(), v.end());v.pop_back();reverse(v.begin(), v.end());
    for(int e : v)cout << e << " ";
    cout << "\n";
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:46:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   46 |             auto [val, id] = lc[l - 1].query(a[i]);
      |                  ^

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