Submission #1169334

#	Time	Username	Problem	Language	Result	Execution time	Memory
1169334		icebear	Split the sequence (APIO14_sequence)	C++20	100 / 100	642 ms	84552 KiB

sequence

//https://dmoj.ca/problem/apio14p2
// ~~ icebear love attttt ~~
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;

template<class T>
    bool minimize(T &a, const T &b) {
        if (a > b) return a = b, true;
        return false;
    }

template<class T>
    bool maximize(T &a, const T &b) {
        if (a < b) return a = b, true;
        return false;
    }

#define FOR(i,a,b) for(int i=(a); i<=(b); ++i)
#define FORR(i,a,b) for(int i=(a); i>=(b); --i)
#define REP(i, n) for(int i=0; i<(n); ++i)
#define RED(i, n) for(int i=(n)-1; i>=0; --i)
#define MASK(i) (1LL << (i))
#define BIT(S, i) (((S) >> (i)) & 1)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define all(x) x.begin(), x.end()
#define task "icebearat"

const int MOD = 1e9 + 7;
const int inf = 1e9 + 27092008;
const ll INF = 1e18 + 27092008;
const int N = 1e5 + 5;
int n, k, a[N], trace[N][205];
ll dp_before[N], dp_cur[N], pref[N];

class ConvexHullTrick {
private:
    struct Line {
        long long a, b;
        int id;
        Line (long long _a = 0, long long _b = 0, int _id = 0):
            a(_a), b(_b), id(_id) {}
        long long eval(long long x) {
            return a * x + b;
        }
    };

    deque<Line> hull;

    bool bad(Line l1, Line l2, Line l3) {
//        assert(l1.a != l2.a);
//        assert(l1.a != l3.a);
        /**
            if intersect of (l1, l3) < intersect of (l1, l2) then we dont need to use l2
            because f_i(x) will better with l1 or l3
        */
        return (l3.b - l1.b) * (l1.a - l2.a) <= (l1.a - l3.a) * (l2.b - l1.b);
    }

    void eraseLine(long long x) {
        while(hull.size() >= 2 && hull[0].eval(x) <= hull[1].eval(x)) hull.pop_front();
    }

public:
    void reset() { hull.clear(); }

    void addLine(long long a, long long b, int id) {
        Line l = Line(a, b, id);
        while(hull.size() >= 2 && bad(hull[hull.size() - 2], hull.back(), l))
            hull.pop_back();
        hull.push_back(l);
    }

    pair<long long, int> query(long long x) {
        /**
            find max f_i(x)
        */
        assert(hull.size());
        eraseLine(x);
        return make_pair(hull[0].eval(x), hull[0].id);
    }
} CHT;

void init(void) {
    cin >> n >> k;
    FOR(i, 1, n) {
        cin >> a[i];
        pref[i] = pref[i - 1] + a[i];
    }
}

void process(void) {
    memset(dp_before, -0x3f, sizeof dp_before);
    const ll NEG_INF = dp_before[0];
    dp_before[0] = 0;
    k++;
    FOR(j, 1, k) {
        memset(dp_cur, -0x3f, sizeof dp_cur);
        CHT.reset();
        FOR(i, j, n) {
            if (dp_before[i - 1] != NEG_INF)
                CHT.addLine(pref[i - 1], dp_before[i - 1] - pref[i - 1] * pref[n], i - 1);
            auto cht = CHT.query(pref[i]);
            if (maximize(dp_cur[i], cht.first + pref[i] * (pref[n] - pref[i])))
                trace[i][j] = cht.second;
        }
        FOR(i, 0, n) dp_before[i] = dp_cur[i];
    }
    cout << dp_cur[n] << endl;
    while(n && k > 1) {
        cout << (n = trace[n][k--]) << ' ';
    }
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    if (fopen(task".inp", "r")) {
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }
    int tc = 1;
//    cin >> tc;
    while(tc--) {
        init();
        process();
    }
    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:125:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  125 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:126:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  126 |         freopen(task".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

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