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Submission #941276

# Submission time Handle Problem Language Result Execution time Memory
941276 2024-03-08T12:27:48 Z Zero_OP Split the sequence (APIO14_sequence) C++14
100 / 100
 653 ms 83152 KB 
#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

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
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 2396 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 2392 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 4440 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 4444 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 2396 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 2396 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 2396 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 4444 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 4440 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 2396 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 4444 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 2396 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 4444 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 2396 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 5 ms 20996 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 2396 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 6492 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 4444 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 12636 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 6492 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 4440 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 6492 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 2396 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 26 ms 78428 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 2396 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 7 ms 55896 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 9 ms 72284 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 9 ms 78428 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 18896 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 12636 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 22876 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2396 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 14 ms 78428 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 2604 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 14 ms 78428 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 12 ms 68176 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 13 ms 78428 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 13 ms 78428 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 16848 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 11 ms 33112 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2652 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 2904 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 58 ms 78736 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 2776 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 43 ms 50124 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 47 ms 56144 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 49 ms 60240 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 37 ms 50248 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 44 ms 56228 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 55 ms 72624 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 7516 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 13 ms 7716 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 498 ms 83152 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 13 ms 8020 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 653 ms 82808 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 438 ms 61036 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 438 ms 65460 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 339 ms 53072 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 377 ms 61376 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 474 ms 75708 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845