Submission #960791

#	Time	Username	Problem	Language	Result	Execution time	Memory
960791		Whisper	Split the sequence (APIO14_sequence)	C++17	71 / 100	55 ms	131072 KiB

sequence

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

#define int long long
#define FOR(i, a, b) for (int i = a; i <= b; i++)
#define FORD(i, a, b) for (int i = b; i >= a; i --)
#define REP(i, n) for (int i = 0; i < n; ++i)
#define REPD(i, n) for (int i = n - 1; i >= 0; --i)

#define MASK(i) (1LL << (i))
#define BIT(x, i) (((x) >> (i)) & 1)

constexpr ll LINF = (1ll << 60);
constexpr int INF = (1ll << 30);
constexpr int Mod = 1e9 + 7;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

void setupIO(){
    #define name "Whisper"
    //Phu Trong from Nguyen Tat Thanh High School for gifted student
    srand(time(NULL));
    cin.tie(nullptr)->sync_with_stdio(false); cout.tie(nullptr);
    //freopen(name".inp", "r", stdin);
    //freopen(name".out", "w", stdout);
    cout << fixed << setprecision(10);
}

template <class X, class Y>
    bool minimize(X &x, const Y &y){
        X eps = 1e-9;
        if (x > y + eps) {x = y; return 1;}
        return 0;
    }

template <class X, class Y>
    bool maximize(X &x, const Y &y){
        X eps = 1e-9;
        if (x + eps < y) {x = y; return 1;}
        return 0;
    }
int nArr, nGroup;
const int MAX = 1e5 + 5;
int a[MAX];


int dp[MAX][202];
int opt[MAX][202];
int s[MAX];

struct Line{
    int a, b, id;
    Line(): a(0), b(0), id(-1){}
    Line(int _a, int _b, int _id): a(_a), b(_b), id(_id){}

    int f(int x){ return a * x + b; }
    double cross(Line o){
        return (double) (b - o.b) / (double)(o.a - a);
    }
};

//slope is increasing and query is also increasing

struct CHT{
    deque<Line> q;
    bool bad(Line a, Line b, Line c){
        return a.cross(c) <= a.cross(b);
    }
    void addLine(Line line){
        while (q.size() >= 2 && (bad(q.end()[-1], q.end()[-2], line) || (q.back().a == line.a && q.back().b <= line.b)))
            q.pop_back();
        q.push_back(line);
    }

    pair<int, int> query(int x){
        while (q.size() >= 2 && q[0].f(x) <= q[1].f(x))
            q.pop_front();
        return make_pair(q[0].f(x), q[0].id);
    }
};
void Whisper(){
    cin >> nArr >> nGroup; ++nGroup;

    for (int i = 1; i <= nArr; ++i) cin >> a[i], s[i] = s[i - 1] + a[i];
    for (int i = 1; i <= nArr; ++i) dp[i][1] = s[i] * (s[nArr] - s[i]);

    //s[nArr] * s[i] - s[nArr] * s[j] - s[i] * s[i] + s[i] * s[j]
    //using s(j) as x we have equation
    //s(j) * x + - s(nArr) * s(j) - s(i) * s(i) + s(nArr) * s(i) + dp(j, k - 1)
    for (int k = 2; k <= nGroup; ++k){
        CHT cht;
        cht.addLine(Line(0, 0, -1));
        for (int i = 1; i <= nArr; ++i){
            pair<int, int> ret = cht.query(s[i]);
            dp[i][k] = ret.first + s[nArr] * s[i] - s[i] * s[i];
            opt[i][k] = ret.second;
            cht.addLine(Line(s[i], - s[i] * s[nArr] + dp[i][k - 1], i));
        }
    }
    cout << dp[nArr][nGroup] << '\n';
    vector<int> ans;
    int current = nArr;
    while(nGroup > 0){
        if (current != nArr)
            ans.push_back(current);
        current = opt[current][nGroup];
        nGroup--;
    }
    reverse(ans.begin(), ans.end());
    for (int&v : ans) cout << v << " ";
}


signed main(){
    setupIO();
    int Test = 1;
//    cin >> Test;
    for ( int i = 1 ; i <= Test ; i++ ){
        Whisper();
        if (i < Test) cout << '\n';
    }
}

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