Submission #941276

#	Time	Username	Problem	Language	Result	Execution time	Memory
941276		Zero_OP	Split the sequence (APIO14_sequence)	C++14	100 / 100	653 ms	83152 KiB

sequence

#include<bits/stdc++.h>

using namespace std;
using int64 = int64_t;

#define     REP(i, n) for(int i = 0, _n = n; i < _n; ++i)
#define    REPD(i, n) for(int i = n - 1; i >= 0; --i)
#define  FOR(i, l, r) for(int i = l, _r = r; i <= _r; ++i)
#define FORD(i, r, l) for(int i = r, _l = l; i >= _l; --i)
#define          left __left
#define         right __right
#define          prev __prev
#define          next __next
#define           div __div
#define            pb push_back
#define            pf push_front
#define         sz(v) (int)v.size()
#define      range(v) begin(v), end(v)
#define    compact(v) v.erase(unique(range(v)), end(v))
#define      debug(v) "[" #v " = " << (v) << "]"

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

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

template<int dimension, class T>
struct vec : public vector<vec<dimension - 1, T>> {
    static_assert(dimension > 0, "Dimension must be positive !\n");
    template<typename... Args>
    vec(int n = 0, Args... args) : vector<vec<dimension - 1, T>>(n, vec<dimension - 1, T>(args...)) {}
};

template<class T>
struct vec<1, T> : public vector<T> {
    vec(int n = 0, T val = T()) : vector<T>(n, val) {}
};

void init(void);
void process(void);

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

    #define task "antuvu"
    if(fopen(task".inp", "r")){
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }

    int T = 1; //cin >> T;
    while(T--) {
        init();
        process();
    }

    return 0;
}


struct line{
    int64 a, b; int id;
    line(int64 a = 0, int64 b = 0, int id = 0) : a(a), b(b), id(id) {}
    int64 eval(int64 x){ return a * x + b; }
};

bool bad(const line& d1, const line& d2, const line& d3){
    return (d2.a - d3.a) * (d3.b - d1.b) <= (d3.b - d2.b) * (d1.a - d3.a);
}

struct ConvexHullTrick{
    deque<line> dq;

    void add(line d){
        while(sz(dq) > 1 && bad(dq[sz(dq) - 2], dq[sz(dq) - 1], d)){
            dq.pop_back();
        }
        dq.push_back(d);
    }

    pair<int64, int> query(int64 x){
        if(dq.empty()) return make_pair(0, 0);
        while(sz(dq) > 1 and dq[0].eval(x) <= dq[1].eval(x)) dq.pop_front();
        return make_pair(dq[0].eval(x), dq[0].id);
    }

    void reset(){
        dq.clear();
        add(line(0, 0, 0));
    }
};

const int MAX = 1e5 + 5;
const int64 inf = 1e18;

int n, k, trace[202][MAX];
int64 pref[MAX], a[MAX], dp[2][MAX];

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

void process(){
    bool next = true, prev = false;
    ConvexHullTrick trick;
    REP(j, k){
        swap(next, prev);
        trick.reset();
        FOR(i, 1, n){
            pair<int64, int> cur = trick.query(pref[n] - pref[i]);
            dp[next][i] = cur.first + pref[i] * (pref[n] - pref[i]);
            trace[j][i] = cur.second;
            trick.add(line(-pref[i], dp[prev][i], i));
        }
    }

    int64 res = -1; int cut = -1;
    FOR(i, 1, n){
        if(res < dp[next][i]){
            res = dp[next][i];
            cut = i;
        }
    }

    vector<int> cuts;
    REPD(i, k){
        cuts.pb(cut);
        cut = trace[i][cut];
    }

    reverse(range(cuts));

    cout << res << '\n';
    REP(i, sz(cuts)) cout << cuts[i] << ' ';
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:60:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   60 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:61:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   61 |         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