oj.uz

Submission #543124

# Submission time Handle Problem Language Result Execution time Memory
543124 2022-03-29T11:40:13 Z square1001 Road Construction (JOI21_road_construction) C++14
65 / 100
 221 ms 19468 KB 
#include <set>
#include <cmath>
#include <cstdio>
#include <cstdint>
#include <algorithm>
using namespace std;

uint64_t seed = 123456789;
uint64_t xorshift64() {
	seed ^= seed << 13;
	seed ^= seed >> 17;
	seed ^= seed << 7;
	return seed;
}
int rand_int(int l, int r) {
	return l + int(xorshift64() % (r - l));
}
int inv_binomial(int N, double p, double alpha) {
	// least N such that P(x <= N) >= alpha
	const double log_p1 = log(p);
	const double log_p2 = log(1.0 - p);
	double sum = 0.0;
	double logval = log_p2 * N;
	for (int i = 0; i < N; i++) {
		sum += exp(logval);
		if (sum >= alpha) {
			return i;
		}
		logval += log_p1 - log_p2 + log(double(N - i) / (i + 1));
	}
	return N;
}

int X[262144], Y[262144], A[262144], B[262144], perm[262144], permtmp[262144], cnt[66560];
unsigned dist[3014656], res[786432], restmp[786432];

int readint() {
	char ch = getchar_unlocked();
	bool minus = false;
	if (ch == '-') {
		minus = true;
		ch = getchar_unlocked();
	}
	int res = 0;
	while ('0' <= ch && ch <= '9') {
		res = res * 10 + int(ch - '0');
		ch = getchar_unlocked();
	}
	return (minus ? -res : res);
}

char buf[64];
void writeint(unsigned x) {
	int pos = 0;
	while (x > 0) {
		buf[pos++] = x % 10 + '0';
		x /= 10;
	}
	while (pos--) {
		putchar_unlocked(buf[pos]);
	}
	putchar_unlocked('\n');
}

int main() {
	// step #1. read input
	int N = readint();
	int K = readint();
	for (int i = 0; i < N; i++) {
		X[i] = readint();
		Y[i] = readint();
	}
	
	// step #2. random sampling setup
	const double p = double(K) / (1LL * N * (N - 1) / 2);
	const int samples = 2000000;
	const int rank = (p != 1.0 ? inv_binomial(samples, p, 0.97) : samples);
	
	// step #3. random sampling
	long long border;
	if (rank == samples) {
		border = (1LL << 32);
	}
	else {
		for (int i = 0; i < samples; i++) {
			int va = rand_int(0, N);
			int vb = (va + rand_int(1, N)) % N;
			dist[i] = abs(X[va] - X[vb]) + abs(Y[va] - Y[vb]);
		}
		nth_element(dist, dist + rank, dist + samples);
		border = dist[rank] - 1;
	}
	
	// step #4. rotate 45 degrees
	for (int i = 0; i < N; i++) {
		A[i] = X[i] + Y[i];
		B[i] = X[i] - Y[i];
	}
	
	// step #5. sort by A[i]
	for (int i = 0; i < N; i++) cnt[(A[i] & 65535) + 1]++;
	for (int i = 0; i < 65536; i++) cnt[i + 1] += cnt[i];
	for (int i = 0; i < N; i++) permtmp[cnt[A[i] & 65535]++] = i;
	for (int i = 0; i < 65537; i++) cnt[i] = 0;
	for (int i = 0; i < N; i++) cnt[(A[i] >> 16) + 32769]++;
	for (int i = 0; i < 65536; i++) cnt[i + 1] += cnt[i];
	for (int i = 0; i < N; i++) perm[cnt[(A[permtmp[i]] >> 16) + 32768]++] = permtmp[i];
	
	// step #6. sweepline algorithm
	int C = 0, pl = 0;
	set<pair<int, int> > s;
	for (int i = 0; i < N; i++) {
		int u = perm[i];
		int BL = max(B[u] - border, -2000000000LL);
		int BR = min(B[u] + border, +2000000000LL);
		while (A[u] - A[perm[pl]] > border) {
			s.erase(make_pair(B[perm[pl]], perm[pl]));
			pl++;
		}
		set<pair<int, int> >::iterator it = s.lower_bound(make_pair(BL, -1));
		while (it != s.end() && it->first <= BR) {
			res[C++] = abs(X[it->second] - X[u]) + abs(Y[it->second] - Y[u]);
			it++;
		}
		s.insert(make_pair(B[u], u));
	}
	
	// step #7. sort the distance
	for (int i = 0; i < 65537; i++) cnt[i] = 0;
	for (int i = 0; i < C; i++) cnt[(res[i] & 65535) + 1]++;
	for (int i = 0; i < 65536; i++) cnt[i + 1] += cnt[i];
	for (int i = 0; i < C; i++) restmp[cnt[res[i] & 65535]++] = res[i];
	for (int i = 0; i < 65537; i++) cnt[i] = 0;
	for (int i = 0; i < C; i++) cnt[(res[i] >> 16) + 1U]++;
	for (int i = 0; i < 65536; i++) cnt[i + 1] += cnt[i];
	for (int i = 0; i < C; i++) res[cnt[restmp[i] >> 16]++] = restmp[i];
	
	// step #8. final answer
	for (int i = 0; i < K; i++) {
		writeint(i < C ? res[i] : border + 1);
	}
	
	return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 164 ms 13004 KB Output is correct
2 Correct 161 ms 13008 KB Output is correct
3 Correct 26 ms 5256 KB Output is correct
4 Correct 23 ms 5196 KB Output is correct
5 Correct 145 ms 11808 KB Output is correct
6 Correct 89 ms 8396 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 139 ms 17872 KB Output is correct
2 Correct 147 ms 19468 KB Output is correct
3 Correct 23 ms 5076 KB Output is correct
4 Correct 134 ms 18864 KB Output is correct
5 Correct 122 ms 17400 KB Output is correct
6 Correct 124 ms 17484 KB Output is correct
7 Correct 123 ms 17256 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 155 ms 14268 KB Output is correct
2 Correct 197 ms 14504 KB Output is correct
3 Correct 1 ms 596 KB Output is correct
4 Correct 110 ms 14232 KB Output is correct
5 Correct 157 ms 14232 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 155 ms 14268 KB Output is correct
2 Correct 197 ms 14504 KB Output is correct
3 Correct 1 ms 596 KB Output is correct
4 Correct 110 ms 14232 KB Output is correct
5 Correct 157 ms 14232 KB Output is correct
6 Correct 162 ms 14348 KB Output is correct
7 Correct 171 ms 14236 KB Output is correct
8 Correct 1 ms 596 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 163 ms 14284 KB Output is correct
11 Correct 101 ms 14228 KB Output is correct
12 Correct 163 ms 14360 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 164 ms 13004 KB Output is correct
2 Correct 161 ms 13008 KB Output is correct
3 Correct 26 ms 5256 KB Output is correct
4 Correct 23 ms 5196 KB Output is correct
5 Correct 145 ms 11808 KB Output is correct
6 Correct 89 ms 8396 KB Output is correct
7 Correct 141 ms 14796 KB Output is correct
8 Correct 144 ms 14796 KB Output is correct
9 Correct 25 ms 5260 KB Output is correct
10 Correct 134 ms 14308 KB Output is correct
11 Correct 105 ms 14248 KB Output is correct
12 Correct 123 ms 12748 KB Output is correct
13 Correct 129 ms 13444 KB Output is correct

Subtask #6
0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 164 ms 13004 KB Output is correct
2 Correct 161 ms 13008 KB Output is correct
3 Correct 26 ms 5256 KB Output is correct
4 Correct 23 ms 5196 KB Output is correct
5 Correct 145 ms 11808 KB Output is correct
6 Correct 89 ms 8396 KB Output is correct
7 Correct 139 ms 17872 KB Output is correct
8 Correct 147 ms 19468 KB Output is correct
9 Correct 23 ms 5076 KB Output is correct
10 Correct 134 ms 18864 KB Output is correct
11 Correct 122 ms 17400 KB Output is correct
12 Correct 124 ms 17484 KB Output is correct
13 Correct 123 ms 17256 KB Output is correct
14 Correct 155 ms 14268 KB Output is correct
15 Correct 197 ms 14504 KB Output is correct
16 Correct 1 ms 596 KB Output is correct
17 Correct 110 ms 14232 KB Output is correct
18 Correct 157 ms 14232 KB Output is correct
19 Correct 162 ms 14348 KB Output is correct
20 Correct 171 ms 14236 KB Output is correct
21 Correct 1 ms 596 KB Output is correct
22 Correct 1 ms 596 KB Output is correct
23 Correct 163 ms 14284 KB Output is correct
24 Correct 101 ms 14228 KB Output is correct
25 Correct 163 ms 14360 KB Output is correct
26 Correct 141 ms 14796 KB Output is correct
27 Correct 144 ms 14796 KB Output is correct
28 Correct 25 ms 5260 KB Output is correct
29 Correct 134 ms 14308 KB Output is correct
30 Correct 105 ms 14248 KB Output is correct
31 Correct 123 ms 12748 KB Output is correct
32 Correct 129 ms 13444 KB Output is correct
33 Correct 221 ms 19168 KB Output is correct
34 Incorrect 193 ms 18076 KB Output isn't correct
35 Halted 0 ms 0 KB -