Submission #1183071

#	Time	Username	Problem	Language	Result	Execution time	Memory
1183071		swishy123	Split the sequence (APIO14_sequence)	C++20	100 / 100	819 ms	82404 KiB

sequence

#include <iostream>
#include <algorithm>
#include <vector>
#include <random>
#include <chrono>
#include <set>
#include <map>
#include <stack>
#include <functional>
#include <iomanip>
#include <queue>
#include <cassert>
#include <complex>
#include <cstring>
#include <memory>
#include <bitset>
#include <sstream>
#include <cmath>
#include <numeric>
#include <numbers>
#include <fstream>

using namespace std;

#ifndef template
#ifndef define
 
#define ll long long
#define ld long double
#define pl pair<ll, ll>
#define pi pair<int, int>
#define nl cout << '\n';
#define x first
#define y second 
#define cbit(x) __builtin_popcountll(x)
#define uid(a, b) uniform_int_distribution<ll>(a, b)(rng) 
#define siz(x) (int)x.size()
 
#endif
 
#ifndef print
void print(size_t x) {cout << x << ' ';}
void print(int x) {cout << x << ' ';}
void print(long long x) {cout << x << ' ';}
void print(float x) {cout << x << ' ';}
void print(long double x) {cout << x << ' ';}
void print(char x) {cout << x << ' ';}
void print(const char* x) {cout << x << ' ';}
void print(bool x) {cout << x << ' ';}
void print(string &x) {cout << x << ' ';}
 
template<typename T, typename V>
void print(pair<T, V> &p) {print(p.x); print(p.y);}
template<typename T>
void print(vector<T> v) {for (int i = 0; i < v.size(); i++) print(v[i]);}
template<typename T>
void print(vector<vector<T>> v) {
    for (int i = 0; i < v.size(); i++){
        for (int j = 0; j < v[i].size(); j++)
            print(v[i][j]);
        nl;
    }
}
template <typename T, typename... V>
void print(T t, V&&... v) {print(t); print(v...);}
 
#endif
 
#ifndef read
void read(int &x) {cin >> x;}
void read(long long &x) {cin >> x;}
void read(unsigned &x) {cin >> x;}
void read(unsigned long long &x) {cin >> x;}
void read(float &x) {cin >> x;}
void read(long double &x) {cin >> x;}
void read(char &x) {cin >> x;}
void read(string &x) {cin >> x;}
void read(bool &x) {cin >> x;}
 
template<typename T> 
void read(vector<T> &v) {
    for (int i = 0; i < v.size(); i++)
        read(v[i]);
}
template <typename T, typename... V>
void read(T &t, V&... v) {read(t); read(v...);}
#endif
 
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<class T> bool maxi(T& a, const T& b) {
    return a < b ? a = b, 1 : 0;
}
template<class T> bool mini(T& a, const T& b) {
    return a > b ? a = b, 1 : 0;
}
template<class... Args>
auto vec(size_t n, Args&&... args) {
    if constexpr(sizeof...(args) == 1)
        return vector(n, args...);
    else
        return vector(n, vec(args...));
}

#endif

using namespace std;
const ll inf = 1e15;
const ll def = 1e5+1;
const ll mod = 998244353;

ll dp[def][2];
int trace[def][201];

bool check(__int128_t a1, __int128_t a2, __int128_t b1, __int128_t b2, __int128_t c1, __int128_t c2){;
    return (b2 - a2) * (a1 - c1) >= (a1 - b1) * (c2 - a2);
}

void solve(){  
    ll n, k;
    read(n, k);

    k++;
    auto a = vec(n, 0ll);
    read(a);

    auto pref = vec(n + 1, 0ll);
    for (int i = 1; i <= n; i++)
        pref[i] = pref[i - 1] + a[i - 1];

    for (int i = 1; i <= n; i++)
        dp[i][0] = pref[i] * (pref[n] - pref[i]);
    bool flag = 0;
    for (int j = 1; j < k; j++){
        deque<int> dq;
        for (int i = j + 1; i <= n; i++){
            ll suff = pref[n] - pref[i];
            while (dq.size() >= 2){
                int a = dq[dq.size() - 1], b = dq[dq.size() - 2];
                if (check(-pref[a], dp[a][flag], -pref[b], dp[b][flag], -pref[i - 1], dp[i - 1][flag]))
                    dq.pop_back();
                else
                    break;
            }
            dq.push_back(i - 1);
            while (dq.size() >= 2){
                int a = dq[0], b = dq[1];
                ll val1 = dp[a][flag] + (pref[i] - pref[a]) * suff;
                ll val2 = dp[b][flag] + (pref[i] - pref[b]) * suff;
                if (val1 <= val2)
                    dq.pop_front();
                else
                    break;
            }
            int x = dq[0];
            ll val = dp[x][flag] + (pref[i] - pref[x]) * suff;
            dp[i][!flag] = val;
            trace[i][j] = x; 
        }
        flag = !flag;
    }

    ll res = dp[n][flag];
    vector<int> pos;

    int u = n;
    for (int i = k - 1; i >= 1; i--){
        u = trace[u][i];
        pos.push_back(u);
    }
    reverse(pos.begin(), pos.end());
    print(res); nl;
    print(pos);
}       

/*
dp[i][j] = dp[l][j - 1] + (pref[i] - pref[l]) * suff[i + 1]
= dp[l][j - 1] - pref[l] * suff[i + 1] + pref[i] * suff[i + 1]

ax + b = cx + d
(a - c)x = d - b
x = (d - b) / (a - c)

(a - b) / (c - d) < (e - f) / (g - h) 
*/

int32_t main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    // if (ifstream("input.txt").good()){
    //     freopen("input.txt", "r", stdin);
    //     freopen("output.txt", "w", stdout);
    // }

    int t;  
    t = 1;

    while (t--){
        solve();
        nl;
    }
}

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