oj.uz

Submission #788689

# Submission time Handle Problem Language Result Execution time Memory
788689 2023-07-20T13:27:25 Z hugo_pm Chorus (JOI23_chorus) C++17
61 / 100
 157 ms 10016 KB 
#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 {
	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);
		if (v1 == v2) {
			// on simule m += eps*cnt
			v1 = (c.p - a.p) * (a.cnt - b.cnt);
			v2 = (b.p - a.p) * (a.cnt - c.cnt);
			return v1 <= v2;
		}
		return v1 > v2;
	}
	void add (Line l) {
		int szFs = sz(fs);
		while (szFs >= 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;
		}
	}
	assert(lo == hi);
	int lambda = lo;
	auto [score, groupsMade] = calc(lambda);
	assert(groupsMade <= K);
	cout << score - lambda*K << '\n';
}

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 0 ms 256 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct

Subtask #2
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 0 ms 256 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 1 ms 340 KB Output is correct

Subtask #3
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 0 ms 256 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 4 ms 852 KB Output is correct
30 Correct 8 ms 720 KB Output is correct
31 Correct 8 ms 804 KB Output is correct
32 Correct 4 ms 744 KB Output is correct
33 Correct 4 ms 740 KB Output is correct
34 Correct 4 ms 852 KB Output is correct
35 Correct 4 ms 852 KB Output is correct
36 Correct 6 ms 620 KB Output is correct
37 Correct 6 ms 728 KB Output is correct
38 Correct 4 ms 892 KB Output is correct
39 Correct 6 ms 760 KB Output is correct
40 Correct 4 ms 596 KB Output is correct
41 Correct 4 ms 596 KB Output is correct
42 Correct 5 ms 596 KB Output is correct

Subtask #4
0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 0 ms 256 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 4 ms 852 KB Output is correct
30 Correct 8 ms 720 KB Output is correct
31 Correct 8 ms 804 KB Output is correct
32 Correct 4 ms 744 KB Output is correct
33 Correct 4 ms 740 KB Output is correct
34 Correct 4 ms 852 KB Output is correct
35 Correct 4 ms 852 KB Output is correct
36 Correct 6 ms 620 KB Output is correct
37 Correct 6 ms 728 KB Output is correct
38 Correct 4 ms 892 KB Output is correct
39 Correct 6 ms 760 KB Output is correct
40 Correct 4 ms 596 KB Output is correct
41 Correct 4 ms 596 KB Output is correct
42 Correct 5 ms 596 KB Output is correct
43 Correct 85 ms 4352 KB Output is correct
44 Correct 137 ms 7288 KB Output is correct
45 Correct 143 ms 7212 KB Output is correct
46 Correct 77 ms 7192 KB Output is correct
47 Correct 77 ms 7300 KB Output is correct
48 Correct 97 ms 10000 KB Output is correct
49 Correct 98 ms 10016 KB Output is correct
50 Correct 157 ms 7112 KB Output is correct
51 Correct 147 ms 7004 KB Output is correct
52 Correct 97 ms 9924 KB Output is correct
53 Correct 97 ms 9988 KB Output is correct
54 Incorrect 148 ms 7204 KB Output isn't correct
55 Halted 0 ms 0 KB -

Subtask #5
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 0 ms 256 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 4 ms 852 KB Output is correct
30 Correct 8 ms 720 KB Output is correct
31 Correct 8 ms 804 KB Output is correct
32 Correct 4 ms 744 KB Output is correct
33 Correct 4 ms 740 KB Output is correct
34 Correct 4 ms 852 KB Output is correct
35 Correct 4 ms 852 KB Output is correct
36 Correct 6 ms 620 KB Output is correct
37 Correct 6 ms 728 KB Output is correct
38 Correct 4 ms 892 KB Output is correct
39 Correct 6 ms 760 KB Output is correct
40 Correct 4 ms 596 KB Output is correct
41 Correct 4 ms 596 KB Output is correct
42 Correct 5 ms 596 KB Output is correct
43 Correct 85 ms 4352 KB Output is correct
44 Correct 137 ms 7288 KB Output is correct
45 Correct 143 ms 7212 KB Output is correct
46 Correct 77 ms 7192 KB Output is correct
47 Correct 77 ms 7300 KB Output is correct
48 Correct 97 ms 10000 KB Output is correct
49 Correct 98 ms 10016 KB Output is correct
50 Correct 157 ms 7112 KB Output is correct
51 Correct 147 ms 7004 KB Output is correct
52 Correct 97 ms 9924 KB Output is correct
53 Correct 97 ms 9988 KB Output is correct
54 Incorrect 148 ms 7204 KB Output isn't correct
55 Halted 0 ms 0 KB -