Submission #659429

#	Time	Username	Problem	Language	Result	Execution time	Memory
659429		jhnah917	Split the sequence (APIO14_sequence)	C++14	100 / 100	398 ms	14276 KiB

sequence

#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 (stderr)

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] << " ";
      |                  ~~~^~~~~~~~~

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