Submission #938822

#	Time	Username	Problem	Language	Result	Execution time	Memory
938822		sysia	Split the sequence (APIO14_sequence)	C++17	100 / 100	740 ms	87364 KiB

sequence

//Sylwia Sapkowska
#include <bits/stdc++.h>
#pragma GCC optimize("O3", "unroll-loops")
using namespace std;
 
void __print(int x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << "'" << x << "'";}
void __print(const char *x) {cerr << '"' << x << '"';}
void __print(const string &x) {cerr << '"' << x << '"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
 
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef LOCAL
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
 
#define int long long
typedef pair<int, int> T;
const int oo = 1e18, oo2 = 1e9+7, K = 30;
const int mod = 998244353;
 
void solve(){
    int n, k; cin >> n >> k;
    k++;
    vector<int>a(n+1), pref(n+1);
    for (int i = 1; i<=n; i++) {
        cin >> a[i];
        pref[i] = pref[i-1] + a[i];
    }
    vector dp(n+1, vector<int32_t>(k+1, -oo2));
    vector<int>DP(n+1, -oo);
    DP[0] = 0;
    deque<pair<T, int>>q;
    for (int j = 1; j<=k; j++){
        while ((int)q.size()) q.pop_back();
        q.push_back({{0, 0}, 0});
        auto inter = [&](T x, T y){
            return (long double)(y.second-x.second)/(long double)(x.first-y.first);
        };
        auto add = [&](T x, int i){
            while ((int)q.size() >= 2 && inter(q[0].first, q[1].first) <= inter(q[1].first, x)) q.pop_front();
            q.push_front({x, i});
        };
        auto query = [&](int x){
            auto get = [&](T curr){
                return curr.first * x + curr.second;
            };
            while ((int)q.size() >= 2 && get(q[(int)q.size()-2].first) >= get(q.back().first)) q.pop_back();
            return T{get(q.back().first), q.back().second};
        };
        debug(j);
        vector<int>new_dp(n+1, -oo);
        for (int i = 1; i<=n; i++){
            debug(i, q);
            auto [v, id] = query(pref[n]-pref[i]);
            v += (pref[n]-pref[i]) * pref[i];
            if (v >= DP[i]) {
                new_dp[i] = v;
                dp[i][j] = id;
            }
            add({-pref[i], DP[i]}, i);
        }
        DP.swap(new_dp);
    }
    cout << DP[n] << "\n";
    vector<int>ret;
    for (int pos = n, ile = k; ile; pos = dp[pos][ile], ile--){
        ret.emplace_back(pos);
    }
    reverse(ret.begin(), ret.end());
    ret.pop_back();
    for (auto x: ret) cout << x << " ";
    cout << "\n";
}
 
int32_t main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
 
    int t = 1;
    //cin >> t;
    while (t--) solve();
 
    return 0;
}

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