제출 #833775

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
833775		CSQ31	Chorus (JOI23_chorus)	C++17	100 / 100	1469 ms	91604 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 = 3e12;
struct Line {
	int m, p, cnt;
	pii eval(int x) const {
		return {m*x+p, cnt};
	}
};
	
struct LineContainer {
	vector<Line> fs;
	int front = 0;
	bool bad(Line a, Line b, Line c) {
		// (cp-ap)/(am-cm) < (bp-ap)/(am-bm)
		int v1 = (c.p - a.p) * (a.m - b.m);
		int v2 = (b.p - a.p) * (a.m - c.m);
		return v1 >= v2;
	}
	void add (Line l) {
		int szFs = sz(fs);
		while (szFs >= front+2 && bad(fs[szFs-2], fs[szFs-1], l)) {
			fs.pop_back(), --szFs;
		}
		fs.push_back(l);
	}
	pii min(int x) {
		if (fs.empty()) return {INF, INF};
		chmin(front, sz(fs)-1);
		while (front+1 < sz(fs) && fs[front].eval(x) >= fs[front+1].eval(x)) {
			++front;
		}
		return fs[front].eval(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);
			}
		}
	}
	
	auto calc = [&] (int lambda) -> pii {
		vector<pii> dp(N+1, {INF, INF});
		dp[N] = {0, 0};
		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 proj = [&] (int j) {
			return min(j, ouvre[j-1]);
		};
		auto add = [&] (int j) {
			int pj = proj(j);
			// add -10 -9 -8.. pente croissante
			cont.add({-j, dp[j].first + j*pj - cumuFerme[pj], dp[j].second});
		};
		int jToAdd = N;
		for (int left = N-1; left >= 0; --left) {
			while (jToAdd > 0 && left <= min(proj(jToAdd), jToAdd-1)) {
				add(jToAdd--);
			}
			if (true) {
				// min(10) min(9) .. x décroissant
				pii prop = cont.min(left);
				chmin(dp[left], make_pair(
					prop.first + cumuFerme[left] + lambda,
					prop.second + 1
				));
			}
			if (jToAdd > 0) {
				chmin(dp[left], make_pair(
					dp[jToAdd].first + coutExclus(left, jToAdd) + lambda,
					dp[jToAdd].second + 1
				));
			}
		}
		return dp[0];
	};
	int lo = 0, hi = INF;
	while (lo <= hi) {
		int mid = (lo+hi) / 2;
		if(calc(mid).second > K) {
			lo = mid+1;
		} else {
			hi = mid-1;
		}
	}
	//assert(lo == hi);
	int lambda = lo;
	auto [score, groupsMade] = calc(lambda);
	assert(groupsMade <= K);
	cout << score - lambda*K << '\n';
}

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