Submission #659429

# Submission time Handle Problem Language Result Execution time Memory
659429 2022-11-17T17:26:46 Z jhnah917 Split the sequence (APIO14_sequence) C++14
100 / 100
398 ms 14276 KB
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using T = __int128_t;

struct Line{
    T a, b; int i;
    Line() = default;
    Line(T a, T b, int i) : a(a), b(b), i(i) {}
    T f(T x){ return a * x + b; }
};

struct CHT{
    vector<Line> v; int p;
    CHT() : v(), p(0) {}
    bool check(Line a, Line b, Line c){
        return (a.b - c.b) * (b.a - a.a) <= (a.b - b.b) * (c.a - a.a);
    }
    void add(Line l){
        while(p + 1 < v.size() && (v.back().b <= l.b || check(v[v.size()-2], v.back(), l))) v.pop_back();
        v.push_back(l);
    }
    pair<T, int> get(T x){
        while(p + 1 < v.size() && v[p].f(x) < v[p+1].f(x)) p++;
        return {v[p].f(x), v[p].i};
    }
};

int N, K, C[101010], P[101010];
ll A[101010];
T D[101010];

pair<T, int> Check(ll c){
    CHT S;
    S.add({0, 0, 0});
    for(int i=1; i<=N; i++){
        tie(D[i],P[i]) = S.get(A[i]);
        D[i] += c; C[i] = C[P[i]] + 1;
        S.add({A[i]*2, D[i] - 2*A[i]*A[i], i});
        // S.add({A[i], D[i] - A[i]*A[i], i});
    }
    return {D[N], C[N]};
}

vector<int> Track(ll c){
    Check(c); vector<int> ret;
    for(int i=N; i; i=P[i]) ret.push_back(i);
    ret.push_back(0); reverse(ret.begin(), ret.end());
    return ret;
}

// given partition p, q (p.size() >= q.size()), return k partition
// 1-based, p[0] = q[0] = 0, range : ( v[i-1], v[i] ]
vector<int> AliensTrack(int k, vector<int> p, vector<int> q){
    if(p.size() == k + 1) return p; if(q.size() == k + 1) return q;
    vector<int> ret;
    for(int i=1, j=1; i<p.size(); i++){
        while(j < q.size() && p[i-1] > q[j]) j++;
        if(p[i] <= q[j] && i - j == k - (int)q.size() + 1){
            ret.insert(ret.end(), p.begin(), p.begin()+i);
            ret.insert(ret.end(), q.begin()+j, q.end());
            return ret;
        }
    }
    assert(false);
}

int main(){
    ios_base::sync_with_stdio(false); cin.tie(nullptr);
    cin >> N >> K; K++;
    for(int i=1; i<=N; i++) cin >> A[i], A[i] += A[i-1];

    T l = -1e18, r = 0;
    while(l < r){
        T m = (l + r + 1) / 2;
        auto [dp,cnt] = Check(m*2+1);
        if(cnt <= K) l = m; else r = m - 1;
    }
    auto P1 = Track(l*2+1), P2 = Track(l*2+3);
    auto V = AliensTrack(K, P2, P1); assert(V.size() == K + 1);
    ll R = 0;
    for(int i=1; i+1<V.size(); i++) R += (A[V[i]] - A[V[i-1]]) * (A[N] - A[V[i]]);
    cout << R << "\n";
    for(int i=1; i+1<V.size(); i++) cout << V[i] << " ";
}

Compilation message

sequence.cpp: In member function 'void CHT::add(Line)':
sequence.cpp:20:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   20 |         while(p + 1 < v.size() && (v.back().b <= l.b || check(v[v.size()-2], v.back(), l))) v.pop_back();
      |               ~~~~~~^~~~~~~~~~
sequence.cpp: In member function 'std::pair<__int128, int> CHT::get(T)':
sequence.cpp:24:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   24 |         while(p + 1 < v.size() && v[p].f(x) < v[p+1].f(x)) p++;
      |               ~~~~~~^~~~~~~~~~
sequence.cpp: In function 'std::vector<int> AliensTrack(int, std::vector<int>, std::vector<int>)':
sequence.cpp:55:17: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   55 |     if(p.size() == k + 1) return p; if(q.size() == k + 1) return q;
      |        ~~~~~~~~~^~~~~~~~
sequence.cpp:55:5: warning: this 'if' clause does not guard... [-Wmisleading-indentation]
   55 |     if(p.size() == k + 1) return p; if(q.size() == k + 1) return q;
      |     ^~
sequence.cpp:55:37: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'if'
   55 |     if(p.size() == k + 1) return p; if(q.size() == k + 1) return q;
      |                                     ^~
sequence.cpp:55:49: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   55 |     if(p.size() == k + 1) return p; if(q.size() == k + 1) return q;
      |                                        ~~~~~~~~~^~~~~~~~
sequence.cpp:57:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   57 |     for(int i=1, j=1; i<p.size(); i++){
      |                       ~^~~~~~~~~
sequence.cpp:58:17: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   58 |         while(j < q.size() && p[i-1] > q[j]) j++;
      |               ~~^~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:76:14: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
   76 |         auto [dp,cnt] = Check(m*2+1);
      |              ^
In file included from /usr/include/c++/10/cassert:44,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:33,
                 from sequence.cpp:1:
sequence.cpp:80:54: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   80 |     auto V = AliensTrack(K, P2, P1); assert(V.size() == K + 1);
      |                                             ~~~~~~~~~^~~~~~~~
sequence.cpp:82:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   82 |     for(int i=1; i+1<V.size(); i++) R += (A[V[i]] - A[V[i-1]]) * (A[N] - A[V[i]]);
      |                  ~~~^~~~~~~~~
sequence.cpp:84:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   84 |     for(int i=1; i+1<V.size(); i++) cout << V[i] << " ";
      |                  ~~~^~~~~~~~~
# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 212 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 212 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 340 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 340 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 340 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 340 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 340 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 340 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 212 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 212 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 340 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 212 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 212 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 212 KB contestant found the optimal answer: 999919994 == 999919994
# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 340 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 464 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 340 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 340 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 340 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 332 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 340 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 340 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 328 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 340 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 340 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 328 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 340 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 340 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 340 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 340 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 340 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 340 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 2 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 2 ms 468 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 404 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 2 ms 340 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 2 ms 340 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 3 ms 468 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 2 ms 468 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 468 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 2 ms 468 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 16 ms 1040 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 21 ms 1424 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 42 ms 1920 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 24 ms 1360 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 21 ms 1488 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 21 ms 1460 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 32 ms 2024 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 26 ms 1888 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 31 ms 1872 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 29 ms 1992 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 244 ms 8760 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 223 ms 9380 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 369 ms 14276 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 267 ms 9684 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 278 ms 13308 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 314 ms 12988 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 398 ms 14108 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 331 ms 14060 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 373 ms 14060 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 350 ms 13840 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845