Submission #879379

#	Time	Username	Problem	Language	Result	Execution time	Memory
879379		marvinthang	Split the sequence (APIO14_sequence)	C++17	100 / 100	485 ms	88656 KiB

sequence

/*************************************
*    author: marvinthang             *
*    created: 27.11.2023 15:25:09    *
*************************************/

#include <bits/stdc++.h>

using namespace std;

#define                  fi  first
#define                  se  second
#define                left  ___left
#define               right  ___right
#define                TIME  (1.0 * clock() / CLOCKS_PER_SEC)
#define             MASK(i)  (1LL << (i))
#define           BIT(x, i)  ((x) >> (i) & 1)
#define  __builtin_popcount  __builtin_popcountll
#define              ALL(v)  (v).begin(), (v).end()
#define           REP(i, n)  for (int i = 0, _n = (n); i < _n; ++i)
#define          REPD(i, n)  for (int i = (n); i-- > 0; )
#define        FOR(i, a, b)  for (int i = (a), _b = (b); i < _b; ++i) 
#define       FORD(i, b, a)  for (int i = (b), _a = (a); --i >= _a; ) 
#define       FORE(i, a, b)  for (int i = (a), _b = (b); i <= _b; ++i) 
#define      FORDE(i, b, a)  for (int i = (b), _a = (a); i >= _a; --i) 
#define        scan_op(...)  istream & operator >> (istream &in, __VA_ARGS__ &u)
#define       print_op(...)  ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
    #include "debug.h"
#else
    #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
    #define DB(...) 23
    #define db(...) 23
    #define debug(...) 23
#endif

template <class U, class V> scan_op(pair <U, V>)  { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>)  { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>)  { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")";  else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
template <class A, class B> bool minimize(A &a, B b)  { if (a > b) { a = b; return true; } return false; }
template <class A, class B> bool maximize(A &a, B b)  { if (a < b) { a = b; return true; } return false; }

const long long INF = 1e18;

struct Line {
    long long a, b;
    int pos;
    Line(long long a = 0, long long b = INF, int pos = -1): a(a), b(b), pos(pos) {}
    long long eval(long long x) { return a * x + b; }
};
struct ConvexHullTrick {
    vector <Line> lines; int ptr;
    ConvexHullTrick(): ptr(0) {}
    bool bad(Line a, Line b, Line c) { return (long double) (c.b - a.b) / (a.a - c.a) < (long double) (b.b - a.b) / (a.a - b.a); }
    void addLine(long long a, long long b, int c) {
        Line l(a, b, c);
        if (!lines.empty() && lines.back().a == a) {
        	if (lines.back().b <= b) return;
        	lines.pop_back();
        }
        while (lines.size() >= 2 && bad(lines.end()[-2], lines.back(), l)) lines.pop_back();
        lines.push_back(l);
    }
    Line getMin(long long x) {
        if (ptr >= (int) lines.size()) ptr = (int) lines.size() - 1;
        while (ptr < (int) lines.size() - 1 && lines[ptr].eval(x) > lines[ptr + 1].eval(x)) ++ptr;
        return lines[ptr];
    }
};
using CHT = ConvexHullTrick;

// end of template

void process(void) {

	int n, k; cin >> n >> k; ++k;
	vector <int> a(n), pref(n + 1); cin >> a;
	partial_sum(ALL(a), pref.begin() + 1);
	vector dp(2, vector(n + 1, INF));
	vector trace(n + 1, vector(k + 1, 0));
	dp[0][0] = 0;
	CHT cht;
	REP(c, k) {
		cht.lines.clear(); cht.ptr = 0;
		int cur = c & 1;
		FORE(i, c, n) {
			if (i > c) {
				Line l = cht.getMin(pref[i]);
				dp[!cur][i] = l.eval(pref[i]) + 1LL * pref[i] * pref[i];
				trace[i][c + 1] = l.pos;
			}
			if (dp[cur][i] < INF) cht.addLine(-2 * pref[i], dp[cur][i] + 1LL * pref[i] * pref[i], i);
		}
	}
	cout << (1LL * pref[n] * pref[n] - dp[k & 1][n]) / 2 << '\n';
	vector <int> res;
	int i = n;
	FORDE(c, k, 2) {
		i = trace[i][c];
		res.push_back(i);
	}
	reverse(ALL(res));
	for (int x: res) cout << x << ' ';
}

int main(void) {
	ios_base::sync_with_stdio(false); cin.tie(nullptr); // cout.tie(nullptr);
	file("sequence");
	// int t; cin >> t; while (t--)
	process();
	// cerr << "Time elapsed: " << TIME << " s.\n";
	return (0^0);
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:30:61: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   30 |     #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
      |                                                      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:110:2: note: in expansion of macro 'file'
  110 |  file("sequence");
      |  ^~~~
sequence.cpp:30:94: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   30 |     #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
      |                                                                                       ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:110:2: note: in expansion of macro 'file'
  110 |  file("sequence");
      |  ^~~~

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