Submission #409219

#	Time	Username	Problem	Language	Result	Execution time	Memory
409219		Falcon	Split the sequence (APIO14_sequence)	C++17	100 / 100	988 ms	86508 KiB

sequence

#include <bits/stdc++.h>

#ifdef DEBUG
#include "debug.hpp"
#endif

using namespace std;

#define all(c)              (c).begin(), (c).end()
#define rall(c)             (c).rbegin(), (c).rend()
#define traverse(c, it)     for(auto it = (c).begin(); it != (c).end(); ++it)
#define rep(i, N)           for(int i = 0; i < (N); ++i)
#define rrep(i, N)          for(int i = (N) - 1; i >= 0; --i)
#define rep1(i, N)          for(int i = 1; i <= (N); ++i)
#define rep2(i, s, e)       for(int i = (s); i <= (e); ++i)

#ifdef DEBUG
#define debug(x...)         { \
                            ++dbg::depth; \
                            string dbg_vals = dbg::to_string(x); \
                            --dbg::depth; \
                            dbg::fprint(__func__, __LINE__, #x, dbg_vals); \
                            }

#define light_debug(x)      { \
                            dbg::light = true; \
                            dbg::dout << __func__ << ":" << __LINE__; \
                            dbg::dout << "  " << #x << " = " << x << endl; \
                            dbg::light = false; \
                            }

#else
#define debug(x...)         42
#define light_debug(x)      42
#endif


using ll = long long;

template<typename T>
inline T& ckmin(T& a, T b) { return a = a > b ? b : a; }

template<typename T>
inline T& ckmax(T& a, T b) { return a = a < b ? b : a; }

using point = complex<long long>;
namespace CHT {
    deque<point> v;
    deque<int> arg;

    long long dot(point p, point q) {
        return (conj(p) * q).real();
    }

    long long cross(point p, point q) {
        return (conj(p) * q).imag();
    }

    void clear() {
        v.clear(), arg.clear();
    }

    // assumes p.real is increasing.
    void add_line(point p, int i) {
        while(v.size() > 1) {
            point a{v[int(v.size()) - 1]}, b{v[int(v.size()) - 2]};
            if(cross(b - a, p - a) <= 0) v.pop_back(), arg.pop_back();
            else break;
        }
        v.push_back(p); arg.push_back(i);
    }

    // assumes x is increasing.
    pair<long long, int> get_best(long long x) {
        point p(x, 1);
        while(v.size() > 1 && dot(p, v[0]) <= dot(p, v[1]))
            v.pop_front(), arg.pop_front();
        return {dot(p, v[0]), arg[0]};
    }
};

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

    int n, K; cin >> n >> K;
    vector<long long> p(n); rep(i, n) cin >> p[i]; partial_sum(all(p), p.begin());

    vector<long long> dp(n), dp_old(n);
    rep(i, n) dp_old[i] = p[i] * p[i];

    vector<vector<int>> pre(n, vector<int>(K));
    rep1(k, K) {
        CHT::clear();
        rep2(i, k, n - 1) {
            CHT::add_line(point(2 * p[i-1], -p[i-1] * p[i-1] - dp_old[i-1]), i-1);
            auto [v, j] = CHT::get_best(p[i]);
            dp[i] = p[i] * p[i] - v;
            pre[i][k - 1] = j;
        }
        debug(dp_old);
        dp_old = dp;
    }
    debug(dp_old);

    cout << (p.back() * p.back() - dp.back()) / 2 << '\n';
    
    int i{n - 1};
    rrep(k, K) {
        i = pre[i][k];
        cout << i + 1 << ' ';
    } 

    cout << '\n';
    
    
    #ifdef DEBUG
    dbg::dout << "\nExecution time: "
              << clock() * 1000 / CLOCKS_PER_SEC 
              << "ms" << endl;
    #endif
    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:33:29: warning: statement has no effect [-Wunused-value]
   33 | #define debug(x...)         42
      |                             ^~
sequence.cpp:101:9: note: in expansion of macro 'debug'
  101 |         debug(dp_old);
      |         ^~~~~
sequence.cpp:33:29: warning: statement has no effect [-Wunused-value]
   33 | #define debug(x...)         42
      |                             ^~
sequence.cpp:104:5: note: in expansion of macro 'debug'
  104 |     debug(dp_old);
      |     ^~~~~

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