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Submission #462309

# Submission time Handle Problem Language Result Execution time Memory
462309 2021-08-10T10:51:40 Z grt Akvizna (COCI19_akvizna) C++17
130 / 130
 322 ms 3612 KB 
#include <bits/stdc++.h>
#define PB push_back
#define ST first
#define ND second
#define _ ios_base::sync_with_stdio(0); cin.tie(0);
//mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

using namespace std;

using ll = long long;
using pi = pair<int,int>;
using vi = vector<int>;


const int nax = 100 * 1000 + 10;
int n, k;
long double dp[nax];
int cnt[nax];

struct Line {
	long double a, b;
	int id;
	long double intersect(Line &he) {
		return (b - he.b) / (he.a - a);
	}
	long double eval(int x) {
		return a * x + b;
	}
};

deque<Line>lines;

int main() {_
	cin >> n >> k;
	long double low = 0.0, high = 1.0000, mid;
	for(int rep = 0; rep < 40; ++rep) {
		mid = (low + high) / 2.0;
		while((int)lines.size() > 0) lines.pop_back();
		for(int used = 0; used <= n; ++used) {
			dp[used] = 0;
			cnt[used] = 0;
			while((int)lines.size() > 1 && lines[0].eval(used - n) <= lines[1].eval(used - n)) {
				lines.pop_front();
			}
			long double res = 0.0;
			if((int)lines.size() > 0) {
				res = lines[0].eval(used - n) - mid;
				cnt[used] = cnt[lines[0].id] + 1;
			}
			dp[used] = max(dp[used], res);
			if(used < n) {
				Line l = {(long double)1/(n - used), dp[used] + 1.0, used};
				while((int)lines.size() > 1 && lines[(int)lines.size() - 2].intersect(l) <= lines[(int)lines.size() - 2].intersect(lines.back())) {
					lines.pop_back();
				}
				lines.push_back(l);
			}
		}
		if(cnt[n] <= k) {
			high = mid;
		} else {
			low = mid;
		}
	}
	mid = high;
	while((int)lines.size() > 0) lines.pop_back();
		for(int used = 0; used <= n; ++used) {
			dp[used] = 0;
			cnt[used] = 0;
			while((int)lines.size() > 1 && lines[0].eval(used - n) <= lines[1].eval(used - n)) {
				lines.pop_front();
			}
			long double res = 0.0;
			if((int)lines.size() > 0) {
				res = lines[0].eval(used - n) - mid;
				cnt[used] = cnt[lines[0].id] + 1;
			}
			dp[used] = max(dp[used], res);
			if(used < n) {
				Line l = {(long double)1/(n - used), dp[used] + 1.0, used};
				while((int)lines.size() > 1 && lines[(int)lines.size() - 2].intersect(l) <= lines[(int)lines.size() - 2].intersect(lines.back())) {
					lines.pop_back();
				}
				lines.push_back(l);
			}
		}
	cout << setprecision(10);
	cout << fixed;
	cout << dp[n] + mid * k;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct

Subtask #2
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct

Subtask #3
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct

Subtask #4
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct

Subtask #5
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 412 KB Output is correct
2 Correct 11 ms 332 KB Output is correct
3 Correct 9 ms 416 KB Output is correct

Subtask #6
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 332 KB Output is correct
2 Correct 12 ms 424 KB Output is correct
3 Correct 8 ms 464 KB Output is correct

Subtask #7
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 412 KB Output is correct
2 Correct 8 ms 332 KB Output is correct
3 Correct 7 ms 332 KB Output is correct

Subtask #8
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 332 KB Output is correct
2 Correct 9 ms 332 KB Output is correct
3 Correct 7 ms 332 KB Output is correct

Subtask #9
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 420 KB Output is correct
2 Correct 9 ms 332 KB Output is correct
3 Correct 8 ms 332 KB Output is correct

Subtask #10
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 404 KB Output is correct
2 Correct 9 ms 332 KB Output is correct
3 Correct 8 ms 332 KB Output is correct

Subtask #11
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 416 KB Output is correct
2 Correct 8 ms 332 KB Output is correct
3 Correct 8 ms 412 KB Output is correct

Subtask #12
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 412 KB Output is correct
2 Correct 8 ms 332 KB Output is correct
3 Correct 8 ms 412 KB Output is correct

Subtask #13
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 420 KB Output is correct
2 Correct 8 ms 416 KB Output is correct
3 Correct 8 ms 416 KB Output is correct

Subtask #14
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 281 ms 3404 KB Output is correct
2 Correct 269 ms 3376 KB Output is correct
3 Correct 242 ms 3164 KB Output is correct

Subtask #15
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 262 ms 3296 KB Output is correct
2 Correct 284 ms 3404 KB Output is correct
3 Correct 287 ms 3376 KB Output is correct

Subtask #16
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 270 ms 3276 KB Output is correct
2 Correct 282 ms 3512 KB Output is correct
3 Correct 267 ms 3404 KB Output is correct

Subtask #17
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 272 ms 3352 KB Output is correct
2 Correct 270 ms 3404 KB Output is correct
3 Correct 259 ms 3312 KB Output is correct

Subtask #18
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 322 ms 3304 KB Output is correct
2 Correct 272 ms 3612 KB Output is correct
3 Correct 253 ms 3340 KB Output is correct

Subtask #19
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 308 ms 3404 KB Output is correct
2 Correct 289 ms 3368 KB Output is correct
3 Correct 274 ms 3344 KB Output is correct

Subtask #20
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 279 ms 3428 KB Output is correct
2 Correct 250 ms 3160 KB Output is correct
3 Correct 262 ms 3276 KB Output is correct

Subtask #21
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 267 ms 3256 KB Output is correct
2 Correct 276 ms 3404 KB Output is correct
3 Correct 256 ms 3148 KB Output is correct

Subtask #22
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 304 ms 3404 KB Output is correct
2 Correct 273 ms 3404 KB Output is correct
3 Correct 298 ms 3512 KB Output is correct

Subtask #23
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 286 ms 3404 KB Output is correct
2 Correct 268 ms 3360 KB Output is correct
3 Correct 274 ms 3404 KB Output is correct

Subtask #24
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 285 ms 3404 KB Output is correct
2 Correct 285 ms 3404 KB Output is correct
3 Correct 275 ms 3404 KB Output is correct

Subtask #25
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 288 ms 3404 KB Output is correct
2 Correct 291 ms 3488 KB Output is correct
3 Correct 299 ms 3404 KB Output is correct

Subtask #26
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 283 ms 3432 KB Output is correct
2 Correct 285 ms 3504 KB Output is correct
3 Correct 278 ms 3436 KB Output is correct