oj.uz

Submission #543120

# Submission time Handle Problem Language Result Execution time Memory
543120 2022-03-29T11:38:55 Z square1001 Road Construction (JOI21_road_construction) C++14
65 / 100
 230 ms 19500 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[524288], restmp[524288];

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 166 ms 13100 KB Output is correct
2 Correct 161 ms 13128 KB Output is correct
3 Correct 25 ms 5196 KB Output is correct
4 Correct 27 ms 5144 KB Output is correct
5 Correct 155 ms 11880 KB Output is correct
6 Correct 91 ms 8404 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 139 ms 17960 KB Output is correct
2 Correct 145 ms 19500 KB Output is correct
3 Correct 23 ms 5068 KB Output is correct
4 Correct 137 ms 18484 KB Output is correct
5 Correct 123 ms 17580 KB Output is correct
6 Correct 124 ms 17484 KB Output is correct
7 Correct 128 ms 17472 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 161 ms 14384 KB Output is correct
2 Correct 176 ms 14580 KB Output is correct
3 Correct 1 ms 556 KB Output is correct
4 Correct 114 ms 14496 KB Output is correct
5 Correct 165 ms 14348 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 161 ms 14384 KB Output is correct
2 Correct 176 ms 14580 KB Output is correct
3 Correct 1 ms 556 KB Output is correct
4 Correct 114 ms 14496 KB Output is correct
5 Correct 165 ms 14348 KB Output is correct
6 Correct 167 ms 14484 KB Output is correct
7 Correct 171 ms 14408 KB Output is correct
8 Correct 1 ms 596 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 164 ms 14584 KB Output is correct
11 Correct 109 ms 14280 KB Output is correct
12 Correct 160 ms 14384 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 166 ms 13100 KB Output is correct
2 Correct 161 ms 13128 KB Output is correct
3 Correct 25 ms 5196 KB Output is correct
4 Correct 27 ms 5144 KB Output is correct
5 Correct 155 ms 11880 KB Output is correct
6 Correct 91 ms 8404 KB Output is correct
7 Correct 141 ms 15076 KB Output is correct
8 Correct 145 ms 14924 KB Output is correct
9 Correct 27 ms 5232 KB Output is correct
10 Correct 130 ms 14484 KB Output is correct
11 Correct 103 ms 14304 KB Output is correct
12 Correct 126 ms 12816 KB Output is correct
13 Correct 133 ms 13524 KB Output is correct

Subtask #6
0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 166 ms 13100 KB Output is correct
2 Correct 161 ms 13128 KB Output is correct
3 Correct 25 ms 5196 KB Output is correct
4 Correct 27 ms 5144 KB Output is correct
5 Correct 155 ms 11880 KB Output is correct
6 Correct 91 ms 8404 KB Output is correct
7 Correct 139 ms 17960 KB Output is correct
8 Correct 145 ms 19500 KB Output is correct
9 Correct 23 ms 5068 KB Output is correct
10 Correct 137 ms 18484 KB Output is correct
11 Correct 123 ms 17580 KB Output is correct
12 Correct 124 ms 17484 KB Output is correct
13 Correct 128 ms 17472 KB Output is correct
14 Correct 161 ms 14384 KB Output is correct
15 Correct 176 ms 14580 KB Output is correct
16 Correct 1 ms 556 KB Output is correct
17 Correct 114 ms 14496 KB Output is correct
18 Correct 165 ms 14348 KB Output is correct
19 Correct 167 ms 14484 KB Output is correct
20 Correct 171 ms 14408 KB Output is correct
21 Correct 1 ms 596 KB Output is correct
22 Correct 1 ms 596 KB Output is correct
23 Correct 164 ms 14584 KB Output is correct
24 Correct 109 ms 14280 KB Output is correct
25 Correct 160 ms 14384 KB Output is correct
26 Correct 141 ms 15076 KB Output is correct
27 Correct 145 ms 14924 KB Output is correct
28 Correct 27 ms 5232 KB Output is correct
29 Correct 130 ms 14484 KB Output is correct
30 Correct 103 ms 14304 KB Output is correct
31 Correct 126 ms 12816 KB Output is correct
32 Correct 133 ms 13524 KB Output is correct
33 Correct 230 ms 19192 KB Output is correct
34 Incorrect 198 ms 18116 KB Output isn't correct
35 Halted 0 ms 0 KB -