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Submission #503343

# Submission time Handle Problem Language Result Execution time Memory
503343 2022-01-07T16:51:23 Z atoiz Present (RMI21_present) C++14
100 / 100
 3071 ms 2344 KB 
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>

using namespace std;

int max_val;
vector<int> chosen;
int arr[1 << 20], gcd_val[50][50];
int64_t cnt;

bool on(int mask, int i) { return (mask >> i) & 1; }
int& toggle(int &mask, int i) { return mask ^= 1 << i; }

void proc_odd(int val, int forced_mask, int odd_mask) {
	if (val < 0) {
		int mask = 0;
		for (int even = 2; even <= max_val; even += 2) {
			bool good = true;

			for (int odd = 1; odd <= max_val && good; odd += 2) {
				if (on(odd_mask, odd / 2) && !on(odd_mask, gcd_val[odd][even] / 2)) {
					good = false;
					break;
				}
			}

			if (good) for (int oth : chosen) {
				if ((gcd_val[oth][even] & 1) && !on(odd_mask, gcd_val[oth][even] / 2)) {
					good = false;
					break;
				}
			}

			if (good) toggle(mask, even / 2);
		}
		++arr[mask];
		return;
	}

	if (!on(forced_mask, val / 2)) proc_odd(val - 2, forced_mask, odd_mask);
	toggle(odd_mask, val / 2);
	for (int odd = val + 2; odd <= max_val; odd += 2) {
		if (on(odd_mask, odd / 2) && not on(forced_mask, gcd_val[odd][val] / 2)) {
			toggle(forced_mask, gcd_val[odd][val] / 2);
		}
	}
	for (int oth : chosen) {
		if (not on(forced_mask, gcd_val[oth][val] / 2)) {
			toggle(forced_mask, gcd_val[oth][val] / 2);
		}
	}
	proc_odd(val - 2, forced_mask, odd_mask);
}

void calc_sum() {
	int n = max_val / 2 + 1;
	for (int k = 0; k < n; ++k) {
		for (int i = 0; i < (1 << n); ++i) {
			if (!((i >> k) & 1)) {
				arr[i] += arr[i ^ (1 << k)];
			}
		}
	}
}

void proc_even(int val, int forced_mask, int even_mask) {
	if (val == 0) {
		cnt += arr[even_mask];
		return;
	}

	if (!on(forced_mask, val / 2)) proc_even(val - 2, forced_mask, even_mask);
	toggle(even_mask, val / 2);
	for (int even = val + 2; even <= max_val; even += 2) {
		if (on(even_mask, even / 2) && not on(forced_mask, gcd_val[even][val] / 2)) {
			toggle(forced_mask, gcd_val[even][val] / 2);
		}
	}
	for (int oth : chosen) if (oth % 2 == 0) {
		if (not on(forced_mask, gcd_val[oth][val] / 2)) {
			toggle(forced_mask, gcd_val[oth][val] / 2);
		}
	}
	proc_even(val - 2, forced_mask, even_mask);
}

int64_t calc(int val, vector<int> vec) {
	max_val = val;
	chosen = vec;
	cnt = 0;
	memset(arr, 0, sizeof(int) * (1 << (max_val / 2 + 1)));

	int forced_odd = 0, forced_even = 0;
	for (int i : vec) for (int j : vec) {
		int k = gcd_val[i][j];
		if (val < k && k < *min_element(vec.begin(), vec.end())) return 0;
		if (k & 1) forced_odd |= 1 << (k / 2);
		else forced_even |= 1 << (k / 2);
	}

	proc_odd(max_val - !(max_val & 1), forced_odd, 0);
	calc_sum();
	proc_even(max_val - (max_val & 1), forced_even, 0);
	return cnt;
}

int main() {
	for (int i = 1; i < 50; ++i) {
		for (int j = 1; j < 50; ++j) {
			gcd_val[i][j] = __gcd(i, j);
		}
	}

	int t; cin >> t;
	// t = 100;
	while (t--) {
		int64_t x; cin >> x;
		// x = 99 - t;

		vector<int> vec = {};
		int lo = 0, hi = 37;
		while (x) {
			// cout << "x = " << x << ", lo = " << lo << ", hi = " << hi << endl;
			while (lo < hi) {
				int mid = (lo + hi + 1) / 2;
				int64_t cur = calc(mid, vec);
				if (cur <= x) lo = mid;
				else hi = mid - 1;
			}
			x -= calc(hi, vec);
			vec.push_back(hi + 1);

			lo = 0;
		}

		if (!vec.empty()) for (int k = vec.back() - 1; k >= 1; --k) {
			bool cont = true;
			for (int i = (int) vec.size() - 1; i >= 0; --i) {
				for (int j = i - 1; j >= 0; --j) if (k == gcd_val[vec[i]][vec[j]]) {
					vec.push_back(k);
					cont = false;
					break;
				}
				if (!cont) break;
			}
		}

		reverse(vec.begin(), vec.end());
		cout << vec.size();
		for (auto i : vec) cout << ' ' << i;
		cout << endl;
	}
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 204 KB Output is correct
2 Correct 2 ms 204 KB Output is correct
3 Correct 2 ms 256 KB Output is correct
4 Correct 2 ms 204 KB Output is correct
5 Correct 2 ms 204 KB Output is correct
6 Correct 2 ms 296 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 204 KB Output is correct
2 Correct 2 ms 204 KB Output is correct
3 Correct 2 ms 256 KB Output is correct
4 Correct 2 ms 204 KB Output is correct
5 Correct 2 ms 204 KB Output is correct
6 Correct 2 ms 296 KB Output is correct
7 Correct 37 ms 328 KB Output is correct
8 Correct 45 ms 440 KB Output is correct
9 Correct 44 ms 436 KB Output is correct
10 Correct 47 ms 332 KB Output is correct
11 Correct 36 ms 332 KB Output is correct
12 Correct 51 ms 332 KB Output is correct

Subtask #3
41.0 / 41.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 204 KB Output is correct
2 Correct 2 ms 204 KB Output is correct
3 Correct 2 ms 256 KB Output is correct
4 Correct 2 ms 204 KB Output is correct
5 Correct 2 ms 204 KB Output is correct
6 Correct 2 ms 296 KB Output is correct
7 Correct 37 ms 328 KB Output is correct
8 Correct 45 ms 440 KB Output is correct
9 Correct 44 ms 436 KB Output is correct
10 Correct 47 ms 332 KB Output is correct
11 Correct 36 ms 332 KB Output is correct
12 Correct 51 ms 332 KB Output is correct
13 Correct 884 ms 1316 KB Output is correct
14 Correct 827 ms 1196 KB Output is correct
15 Correct 1108 ms 1196 KB Output is correct
16 Correct 924 ms 2340 KB Output is correct
17 Correct 1166 ms 1324 KB Output is correct
18 Correct 558 ms 1196 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 204 KB Output is correct
2 Correct 2 ms 204 KB Output is correct
3 Correct 2 ms 256 KB Output is correct
4 Correct 2 ms 204 KB Output is correct
5 Correct 2 ms 204 KB Output is correct
6 Correct 2 ms 296 KB Output is correct
7 Correct 37 ms 328 KB Output is correct
8 Correct 45 ms 440 KB Output is correct
9 Correct 44 ms 436 KB Output is correct
10 Correct 47 ms 332 KB Output is correct
11 Correct 36 ms 332 KB Output is correct
12 Correct 51 ms 332 KB Output is correct
13 Correct 884 ms 1316 KB Output is correct
14 Correct 827 ms 1196 KB Output is correct
15 Correct 1108 ms 1196 KB Output is correct
16 Correct 924 ms 2340 KB Output is correct
17 Correct 1166 ms 1324 KB Output is correct
18 Correct 558 ms 1196 KB Output is correct
19 Correct 1473 ms 2340 KB Output is correct
20 Correct 1627 ms 2244 KB Output is correct
21 Correct 1998 ms 2340 KB Output is correct
22 Correct 2079 ms 2344 KB Output is correct
23 Correct 1794 ms 2340 KB Output is correct
24 Correct 2104 ms 2340 KB Output is correct

Subtask #5
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 204 KB Output is correct
2 Correct 2 ms 204 KB Output is correct
3 Correct 2 ms 256 KB Output is correct
4 Correct 2 ms 204 KB Output is correct
5 Correct 2 ms 204 KB Output is correct
6 Correct 2 ms 296 KB Output is correct
7 Correct 37 ms 328 KB Output is correct
8 Correct 45 ms 440 KB Output is correct
9 Correct 44 ms 436 KB Output is correct
10 Correct 47 ms 332 KB Output is correct
11 Correct 36 ms 332 KB Output is correct
12 Correct 51 ms 332 KB Output is correct
13 Correct 884 ms 1316 KB Output is correct
14 Correct 827 ms 1196 KB Output is correct
15 Correct 1108 ms 1196 KB Output is correct
16 Correct 924 ms 2340 KB Output is correct
17 Correct 1166 ms 1324 KB Output is correct
18 Correct 558 ms 1196 KB Output is correct
19 Correct 1473 ms 2340 KB Output is correct
20 Correct 1627 ms 2244 KB Output is correct
21 Correct 1998 ms 2340 KB Output is correct
22 Correct 2079 ms 2344 KB Output is correct
23 Correct 1794 ms 2340 KB Output is correct
24 Correct 2104 ms 2340 KB Output is correct
25 Correct 2950 ms 2340 KB Output is correct
26 Correct 2934 ms 2340 KB Output is correct
27 Correct 3007 ms 2340 KB Output is correct
28 Correct 3071 ms 2340 KB Output is correct
29 Correct 2684 ms 2340 KB Output is correct
30 Correct 2840 ms 2344 KB Output is correct