Submission #775819

#	Time	Username	Problem	Language	Result	Execution time	Memory
775819		marvinthang	Chorus (JOI23_chorus)	C++17	100 / 100	1771 ms	91708 KiB

chorus

/*************************************
*    author: marvinthang             *
*    created: 07.07.2023 10:11:54    *
*************************************/

#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--; )
#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 cnt;
    Line(long long a = 0, long long b = INF, int cnt = 0): a(a), b(b), cnt(cnt) {}
    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);
        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];
    }
};

// end of template

const int MAX = 1e6 + 6;

int N, K;
string S;
vector <int> pos[2];

void init(void) {
	cin >> N >> K >> S;
}

long long dp[MAX], pref[MAX], add[MAX];
int cnt[MAX], pf[MAX];

void calc(long long c) {
	ConvexHullTrick cht;
	FORE(i, 1, N) {
		int j = i - 1;
		cht.addLine(-j, dp[j] + 1LL * j * j - pref[j] + add[j], cnt[j]);
		Line l = cht.getMin(i);
		dp[i] = l.eval(i) + pref[i] + c;
		cnt[i] = l.cnt + 1;
		j = pf[j];
		if (j < i) {
			if (minimize(dp[i], dp[j] + c)) cnt[i] = cnt[j] + 1;
			else if (dp[i] == dp[j] + c) minimize(cnt[i], cnt[j] + 1);
		}
	}
}

void process(void) {
	REP(i, 2 * N) pos[S[i] - 'A'].push_back(i);
	int j = 0;
	REP(i, N) {
		while (j < N && pos[1][j] < pos[0][i]) ++j;
		pf[i] = j;
		pref[i + 1] = pref[i] + j;
	}
	j = 0;
	REP(i, N) {
		j = max(j, i);
		while (j < N && pf[j] <= i) ++j;
		add[i] = 1LL * (j - i) * i + pref[i] - pref[j];
	}

	long long l = 0, r = INF;
	while (l <= r) {
		long long m = l + r >> 1;
		calc(m);
		if (cnt[N] <= K) r = m - 1;
		else l = m + 1;
	}
	calc(l);
	cout << dp[N] - l * K << '\n';

}

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

Compilation message (stderr)

chorus.cpp: In function 'void process()':
chorus.cpp:121:19: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  121 |   long long m = l + r >> 1;
      |                 ~~^~~
chorus.cpp: In function 'int main()':
chorus.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); }
      |                                                      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
chorus.cpp:133:2: note: in expansion of macro 'file'
  133 |  file("chorus");
      |  ^~~~
chorus.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); }
      |                                                                                       ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
chorus.cpp:133:2: note: in expansion of macro 'file'
  133 |  file("chorus");
      |  ^~~~

• Subtask 1: 16 / 16
• Subtask 2: 24 / 24
• Subtask 3: 21 / 21
• Subtask 4: 26 / 26
• Subtask 5: 13 / 13