Submission #788491

#	Time	Username	Problem	Language	Result	Execution time	Memory
788491		hugo_pm	Chorus (JOI23_chorus)	C++17	0 / 100	1 ms	468 KiB

chorus

#include <bits/stdc++.h>
#define int long long
using namespace std;
	
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define rep(i, a, b) for(int i = (a); i < (b); i++)
#define sz(v) ((int)((v).size()))
	
template<typename T>
void chmax(T &x, const T &v) { if (x < v) x = v; }
template<typename T>
void chmin(T &x, const T &v) { if (x > v) x = v; }
	
using pii = pair<int, int>;
using vi = vector<int>;
	
string to_string(string s) { return s; }
template <typename T> string to_string(T v) {
	bool first = true;
	string res = "[";
	for (const auto &x : v) {
		if (!first)
			res += ", ";
		first = false;
		res += to_string(x);
	}
	res += "]";
	return res;
}
	
void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
	cout << ' ' << to_string(H);
	dbg_out(T...);
}
	
#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
	
const int INF = 1e12;
struct _Line {
	mutable int k, m, p;
	bool operator<(const _Line& o) const { return k < o.k; }
	bool operator<(int x) const { return p < x; }
};

struct _LineContainer : multiset<_Line, less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const int inf = LLONG_MAX;
	int div(int a, int b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) return x->p = inf, 0;
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	void add(int k, int m) {
		auto z = insert({k, m, 0}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p)
			isect(x, erase(y));
	}
	int queryMax(int x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};

struct LineContainer {
	_LineContainer fs;
	void add (int k, int m) { // kx+m
		// -f(x) = -(kx+m) = (-k)x + (-m)
		fs.add(-k, -m);
	}
	int min(int x) {
		return -fs.queryMax(x);
	}
};

int N, K;
string S;
// ferme[i] = nombre d'ouvrants avant Fi
vector<int> ouvre, ferme;
vector<int> cumuFerme;
int coutExclus(int left, int right) {
	if (left >= right) {
		return 0;
	}
	int projExclus = min(right, ouvre[right-1]);
	if (projExclus <= left) return 0;
	return (projExclus - left)*(right) - (cumuFerme[projExclus] - cumuFerme[left]);
}
signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	
	cin >> N >> K >> S;
	{
		int curOuvre = 0, curFerme = 0;
		cumuFerme.push_back(0);
		for (char c : S) {
			if (c == 'A') {
				++curOuvre;
				ouvre.push_back(curFerme);
			} else {
				++curFerme;
				ferme.push_back(curOuvre);
				cumuFerme.push_back(cumuFerme.back() + curOuvre);
			}
		}
	}
	
	vector<int> old(N+1, INF), now;
	old[N] = 0;
	rep(nbCoup, 1, K+1) {
		now.assign(N+1, INF);
		LineContainer cont;
		// [J EXCLUS]
		// gright(left) = (projExclus - left)*(right) - (cumuFerme[projExclus] - cumuFerme[left])
		// gj(x) = (pj - x)*j - (cf[pj] - cf[left])
		// gj(x) = -jx + (j*pj - cf[pj]) + cf[x]
		//         mx  + p               + terme fixe
		auto getWithFix = [&] (int x) {
			return cont.min(x) + cumuFerme[x];
		};
		auto proj = [&] (int j) {
			return min(j, ouvre[j-1]);
		};
		auto add = [&] (int j) {
			int pj = proj(j);
			cont.add(-j, old[j] + j*pj - cumuFerme[pj]);
		};
		int jToAdd = N;
		for (int left = N-1; left >= 0; --left) {
			while (jToAdd > 0 && left <= proj(jToAdd)) {
				add(jToAdd--);
			}
			chmin(now[left], getWithFix(left));
			if (jToAdd > 0) {
				chmin(now[left], old[jToAdd] + coutExclus(left, jToAdd));
			}
		}
		old = now;
	}
	cout << old[0] << '\n';
}

• Subtask 1: 0 / 16
• Subtask 2: 0 / 24
• Subtask 3: 0 / 21
• Subtask 4: 0 / 26
• Subtask 5: 0 / 13