oj.uz

Submission #833775

# Submission time Handle Problem Language Result Execution time Memory
833775 2023-08-22T08:35:23 Z CSQ31 Chorus (JOI23_chorus) C++17
100 / 100
 1469 ms 91604 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 = 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
16.0 / 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 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 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 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 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 364 KB Output is correct
19 Correct 1 ms 272 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 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 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 364 KB Output is correct
19 Correct 1 ms 272 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 6 ms 880 KB Output is correct
30 Correct 6 ms 736 KB Output is correct
31 Correct 6 ms 756 KB Output is correct
32 Correct 4 ms 748 KB Output is correct
33 Correct 4 ms 748 KB Output is correct
34 Correct 4 ms 880 KB Output is correct
35 Correct 4 ms 880 KB Output is correct
36 Correct 6 ms 596 KB Output is correct
37 Correct 6 ms 736 KB Output is correct
38 Correct 5 ms 880 KB Output is correct
39 Correct 5 ms 732 KB Output is correct
40 Correct 4 ms 752 KB Output is correct
41 Correct 4 ms 724 KB Output is correct
42 Correct 3 ms 596 KB Output is correct

Subtask #4
26.0 / 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 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 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 364 KB Output is correct
19 Correct 1 ms 272 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 6 ms 880 KB Output is correct
30 Correct 6 ms 736 KB Output is correct
31 Correct 6 ms 756 KB Output is correct
32 Correct 4 ms 748 KB Output is correct
33 Correct 4 ms 748 KB Output is correct
34 Correct 4 ms 880 KB Output is correct
35 Correct 4 ms 880 KB Output is correct
36 Correct 6 ms 596 KB Output is correct
37 Correct 6 ms 736 KB Output is correct
38 Correct 5 ms 880 KB Output is correct
39 Correct 5 ms 732 KB Output is correct
40 Correct 4 ms 752 KB Output is correct
41 Correct 4 ms 724 KB Output is correct
42 Correct 3 ms 596 KB Output is correct
43 Correct 98 ms 5456 KB Output is correct
44 Correct 144 ms 9580 KB Output is correct
45 Correct 137 ms 9540 KB Output is correct
46 Correct 80 ms 7452 KB Output is correct
47 Correct 80 ms 7496 KB Output is correct
48 Correct 100 ms 10212 KB Output is correct
49 Correct 99 ms 10200 KB Output is correct
50 Correct 143 ms 7132 KB Output is correct
51 Correct 144 ms 7180 KB Output is correct
52 Correct 103 ms 10148 KB Output is correct
53 Correct 113 ms 10244 KB Output is correct
54 Correct 142 ms 7380 KB Output is correct

Subtask #5
13.0 / 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 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 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 364 KB Output is correct
19 Correct 1 ms 272 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 6 ms 880 KB Output is correct
30 Correct 6 ms 736 KB Output is correct
31 Correct 6 ms 756 KB Output is correct
32 Correct 4 ms 748 KB Output is correct
33 Correct 4 ms 748 KB Output is correct
34 Correct 4 ms 880 KB Output is correct
35 Correct 4 ms 880 KB Output is correct
36 Correct 6 ms 596 KB Output is correct
37 Correct 6 ms 736 KB Output is correct
38 Correct 5 ms 880 KB Output is correct
39 Correct 5 ms 732 KB Output is correct
40 Correct 4 ms 752 KB Output is correct
41 Correct 4 ms 724 KB Output is correct
42 Correct 3 ms 596 KB Output is correct
43 Correct 98 ms 5456 KB Output is correct
44 Correct 144 ms 9580 KB Output is correct
45 Correct 137 ms 9540 KB Output is correct
46 Correct 80 ms 7452 KB Output is correct
47 Correct 80 ms 7496 KB Output is correct
48 Correct 100 ms 10212 KB Output is correct
49 Correct 99 ms 10200 KB Output is correct
50 Correct 143 ms 7132 KB Output is correct
51 Correct 144 ms 7180 KB Output is correct
52 Correct 103 ms 10148 KB Output is correct
53 Correct 113 ms 10244 KB Output is correct
54 Correct 142 ms 7380 KB Output is correct
55 Correct 1012 ms 51768 KB Output is correct
56 Correct 1412 ms 89024 KB Output is correct
57 Correct 1469 ms 85644 KB Output is correct
58 Correct 658 ms 67448 KB Output is correct
59 Correct 1156 ms 81328 KB Output is correct
60 Correct 1215 ms 91496 KB Output is correct
61 Correct 1208 ms 91540 KB Output is correct
62 Correct 1396 ms 64904 KB Output is correct
63 Correct 1409 ms 65416 KB Output is correct
64 Correct 1288 ms 91476 KB Output is correct
65 Correct 1296 ms 91528 KB Output is correct
66 Correct 1413 ms 67156 KB Output is correct
67 Correct 1226 ms 91604 KB Output is correct