oj.uz

Submission #543121

# Submission time Handle Problem Language Result Execution time Memory
543121 2022-03-29T11:39:51 Z square1001 Road Construction (JOI21_road_construction) C++14
65 / 100
 241 ms 19452 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, 0.95) : 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 169 ms 12960 KB Output is correct
2 Correct 156 ms 13000 KB Output is correct
3 Correct 24 ms 5196 KB Output is correct
4 Correct 27 ms 5256 KB Output is correct
5 Correct 145 ms 11824 KB Output is correct
6 Correct 86 ms 8436 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 141 ms 17884 KB Output is correct
2 Correct 147 ms 19452 KB Output is correct
3 Correct 23 ms 5032 KB Output is correct
4 Correct 132 ms 18368 KB Output is correct
5 Correct 123 ms 17356 KB Output is correct
6 Correct 126 ms 17404 KB Output is correct
7 Correct 121 ms 17356 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 158 ms 14176 KB Output is correct
2 Correct 178 ms 14448 KB Output is correct
3 Correct 1 ms 492 KB Output is correct
4 Correct 109 ms 14156 KB Output is correct
5 Correct 156 ms 14184 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 158 ms 14176 KB Output is correct
2 Correct 178 ms 14448 KB Output is correct
3 Correct 1 ms 492 KB Output is correct
4 Correct 109 ms 14156 KB Output is correct
5 Correct 156 ms 14184 KB Output is correct
6 Correct 180 ms 14324 KB Output is correct
7 Correct 178 ms 14292 KB Output is correct
8 Correct 1 ms 596 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 176 ms 14340 KB Output is correct
11 Correct 106 ms 14216 KB Output is correct
12 Correct 177 ms 14288 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 169 ms 12960 KB Output is correct
2 Correct 156 ms 13000 KB Output is correct
3 Correct 24 ms 5196 KB Output is correct
4 Correct 27 ms 5256 KB Output is correct
5 Correct 145 ms 11824 KB Output is correct
6 Correct 86 ms 8436 KB Output is correct
7 Correct 152 ms 14984 KB Output is correct
8 Correct 146 ms 14740 KB Output is correct
9 Correct 28 ms 5196 KB Output is correct
10 Correct 136 ms 14284 KB Output is correct
11 Correct 110 ms 14260 KB Output is correct
12 Correct 134 ms 12752 KB Output is correct
13 Correct 140 ms 13420 KB Output is correct

Subtask #6
0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 169 ms 12960 KB Output is correct
2 Correct 156 ms 13000 KB Output is correct
3 Correct 24 ms 5196 KB Output is correct
4 Correct 27 ms 5256 KB Output is correct
5 Correct 145 ms 11824 KB Output is correct
6 Correct 86 ms 8436 KB Output is correct
7 Correct 141 ms 17884 KB Output is correct
8 Correct 147 ms 19452 KB Output is correct
9 Correct 23 ms 5032 KB Output is correct
10 Correct 132 ms 18368 KB Output is correct
11 Correct 123 ms 17356 KB Output is correct
12 Correct 126 ms 17404 KB Output is correct
13 Correct 121 ms 17356 KB Output is correct
14 Correct 158 ms 14176 KB Output is correct
15 Correct 178 ms 14448 KB Output is correct
16 Correct 1 ms 492 KB Output is correct
17 Correct 109 ms 14156 KB Output is correct
18 Correct 156 ms 14184 KB Output is correct
19 Correct 180 ms 14324 KB Output is correct
20 Correct 178 ms 14292 KB Output is correct
21 Correct 1 ms 596 KB Output is correct
22 Correct 1 ms 596 KB Output is correct
23 Correct 176 ms 14340 KB Output is correct
24 Correct 106 ms 14216 KB Output is correct
25 Correct 177 ms 14288 KB Output is correct
26 Correct 152 ms 14984 KB Output is correct
27 Correct 146 ms 14740 KB Output is correct
28 Correct 28 ms 5196 KB Output is correct
29 Correct 136 ms 14284 KB Output is correct
30 Correct 110 ms 14260 KB Output is correct
31 Correct 134 ms 12752 KB Output is correct
32 Correct 140 ms 13420 KB Output is correct
33 Correct 241 ms 19008 KB Output is correct
34 Incorrect 220 ms 18004 KB Output isn't correct
35 Halted 0 ms 0 KB -