oj.uz

Submission #543127

# Submission time Handle Problem Language Result Execution time Memory
543127 2022-03-29T11:41:27 Z square1001 Road Construction (JOI21_road_construction) C++14
100 / 100
 231 ms 20648 KB 
#include <set>
#include <cmath>
#include <cstdio>
#include <cstdint>
#include <algorithm>
using namespace std;

uint64_t seed = 987654321;
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[2097152], 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, 0.95) : 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 155 ms 13004 KB Output is correct
2 Correct 158 ms 12912 KB Output is correct
3 Correct 24 ms 5204 KB Output is correct
4 Correct 25 ms 5168 KB Output is correct
5 Correct 153 ms 11828 KB Output is correct
6 Correct 72 ms 8316 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 136 ms 19376 KB Output is correct
2 Correct 133 ms 18160 KB Output is correct
3 Correct 22 ms 5076 KB Output is correct
4 Correct 133 ms 17968 KB Output is correct
5 Correct 113 ms 17468 KB Output is correct
6 Correct 118 ms 17356 KB Output is correct
7 Correct 121 ms 17328 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 169 ms 14204 KB Output is correct
2 Correct 173 ms 14504 KB Output is correct
3 Correct 1 ms 596 KB Output is correct
4 Correct 114 ms 14252 KB Output is correct
5 Correct 170 ms 14280 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 169 ms 14204 KB Output is correct
2 Correct 173 ms 14504 KB Output is correct
3 Correct 1 ms 596 KB Output is correct
4 Correct 114 ms 14252 KB Output is correct
5 Correct 170 ms 14280 KB Output is correct
6 Correct 160 ms 14316 KB Output is correct
7 Correct 169 ms 14268 KB Output is correct
8 Correct 1 ms 596 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 166 ms 14276 KB Output is correct
11 Correct 108 ms 14132 KB Output is correct
12 Correct 166 ms 14284 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 155 ms 13004 KB Output is correct
2 Correct 158 ms 12912 KB Output is correct
3 Correct 24 ms 5204 KB Output is correct
4 Correct 25 ms 5168 KB Output is correct
5 Correct 153 ms 11828 KB Output is correct
6 Correct 72 ms 8316 KB Output is correct
7 Correct 135 ms 14680 KB Output is correct
8 Correct 133 ms 15564 KB Output is correct
9 Correct 25 ms 5208 KB Output is correct
10 Correct 133 ms 14524 KB Output is correct
11 Correct 111 ms 14024 KB Output is correct
12 Correct 126 ms 12732 KB Output is correct
13 Correct 133 ms 13412 KB Output is correct

Subtask #6
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 155 ms 13004 KB Output is correct
2 Correct 158 ms 12912 KB Output is correct
3 Correct 24 ms 5204 KB Output is correct
4 Correct 25 ms 5168 KB Output is correct
5 Correct 153 ms 11828 KB Output is correct
6 Correct 72 ms 8316 KB Output is correct
7 Correct 136 ms 19376 KB Output is correct
8 Correct 133 ms 18160 KB Output is correct
9 Correct 22 ms 5076 KB Output is correct
10 Correct 133 ms 17968 KB Output is correct
11 Correct 113 ms 17468 KB Output is correct
12 Correct 118 ms 17356 KB Output is correct
13 Correct 121 ms 17328 KB Output is correct
14 Correct 169 ms 14204 KB Output is correct
15 Correct 173 ms 14504 KB Output is correct
16 Correct 1 ms 596 KB Output is correct
17 Correct 114 ms 14252 KB Output is correct
18 Correct 170 ms 14280 KB Output is correct
19 Correct 160 ms 14316 KB Output is correct
20 Correct 169 ms 14268 KB Output is correct
21 Correct 1 ms 596 KB Output is correct
22 Correct 1 ms 596 KB Output is correct
23 Correct 166 ms 14276 KB Output is correct
24 Correct 108 ms 14132 KB Output is correct
25 Correct 166 ms 14284 KB Output is correct
26 Correct 135 ms 14680 KB Output is correct
27 Correct 133 ms 15564 KB Output is correct
28 Correct 25 ms 5208 KB Output is correct
29 Correct 133 ms 14524 KB Output is correct
30 Correct 111 ms 14024 KB Output is correct
31 Correct 126 ms 12732 KB Output is correct
32 Correct 133 ms 13412 KB Output is correct
33 Correct 209 ms 18296 KB Output is correct
34 Correct 231 ms 20648 KB Output is correct
35 Correct 184 ms 17776 KB Output is correct
36 Correct 168 ms 15944 KB Output is correct
37 Correct 173 ms 16172 KB Output is correct
38 Correct 181 ms 16640 KB Output is correct